id	sid	tid	token	lemma	pos
ejpam-4706	1	1	european	european	PROPN
ejpam-4706	1	2	journal	journal	PROPN
ejpam-4706	1	3	of	of	ADP
ejpam-4706	1	4	pure	pure	ADJ
ejpam-4706	1	5	and	and	CCONJ
ejpam-4706	1	6	applied	apply	VERB
ejpam-4706	1	7	mathematics	mathematic	NOUN
ejpam-4706	1	8	vol	vol	NOUN
ejpam-4706	1	9	.	.	PUNCT
ejpam-4706	2	1	16	16	NUM
ejpam-4706	2	2	,	,	PUNCT
ejpam-4706	2	3	no	no	INTJ
ejpam-4706	2	4	.	.	NOUN
ejpam-4706	2	5	2	2	NUM
ejpam-4706	2	6	,	,	PUNCT
ejpam-4706	2	7	2023	2023	NUM
ejpam-4706	2	8	,	,	PUNCT
ejpam-4706	2	9	806	806	NUM
ejpam-4706	2	10	-	-	SYM
ejpam-4706	2	11	818	818	NUM
ejpam-4706	2	12	issn	issn	PROPN
ejpam-4706	2	13	1307	1307	NUM
ejpam-4706	2	14	-	-	SYM
ejpam-4706	2	15	5543	5543	NUM
ejpam-4706	2	16	–	–	PUNCT
ejpam-4706	2	17	ejpam.com	ejpam.com	X
ejpam-4706	2	18	published	publish	VERB
ejpam-4706	2	19	by	by	ADP
ejpam-4706	2	20	new	new	PROPN
ejpam-4706	2	21	york	york	PROPN
ejpam-4706	2	22	business	business	PROPN
ejpam-4706	2	23	global	global	ADJ
ejpam-4706	2	24	new	new	ADJ
ejpam-4706	2	25	bounds	bound	NOUN
ejpam-4706	2	26	for	for	ADP
ejpam-4706	2	27	the	the	DET
ejpam-4706	2	28	eigenvalues	eigenvalue	NOUN
ejpam-4706	2	29	of	of	ADP
ejpam-4706	2	30	matrix	matrix	NOUN
ejpam-4706	2	31	polynomials	polynomial	NOUN
ejpam-4706	2	32	aliaa	aliaa	VERB
ejpam-4706	2	33	burqan1,∗	burqan1,∗	PROPN
ejpam-4706	2	34	,	,	PUNCT
ejpam-4706	2	35	hamdan	hamdan	PROPN
ejpam-4706	2	36	hbabesh1	hbabesh1	PROPN
ejpam-4706	2	37	,	,	PUNCT
ejpam-4706	2	38	ahmad	ahmad	PROPN
ejpam-4706	2	39	qazza1	qazza1	PROPN
ejpam-4706	2	40	,	,	PUNCT
ejpam-4706	2	41	mona	mona	PROPN
ejpam-4706	2	42	khandaqji2	khandaqji2	PROPN
ejpam-4706	2	43	1	1	NUM
ejpam-4706	2	44	department	department	NOUN
ejpam-4706	2	45	of	of	ADP
ejpam-4706	2	46	mathematics	mathematic	NOUN
ejpam-4706	2	47	,	,	PUNCT
ejpam-4706	2	48	faculty	faculty	NOUN
ejpam-4706	2	49	of	of	ADP
ejpam-4706	2	50	science	science	NOUN
ejpam-4706	2	51	,	,	PUNCT
ejpam-4706	2	52	zarqa	zarqa	PROPN
ejpam-4706	2	53	university	university	PROPN
ejpam-4706	2	54	,	,	PUNCT
ejpam-4706	2	55	zarqa	zarqa	PROPN
ejpam-4706	2	56	13110	13110	NUM
ejpam-4706	2	57	,	,	PUNCT
ejpam-4706	2	58	jordan	jordan	PROPN
ejpam-4706	2	59	2	2	NUM
ejpam-4706	2	60	department	department	NOUN
ejpam-4706	2	61	of	of	ADP
ejpam-4706	2	62	basic	basic	ADJ
ejpam-4706	2	63	science	science	NOUN
ejpam-4706	2	64	,	,	PUNCT
ejpam-4706	2	65	faculty	faculty	NOUN
ejpam-4706	2	66	of	of	ADP
ejpam-4706	2	67	arts	art	NOUN
ejpam-4706	2	68	and	and	CCONJ
ejpam-4706	2	69	science	science	NOUN
ejpam-4706	2	70	,	,	PUNCT
ejpam-4706	2	71	applied	apply	VERB
ejpam-4706	2	72	science	science	NOUN
ejpam-4706	2	73	private	private	ADJ
ejpam-4706	2	74	university	university	NOUN
ejpam-4706	2	75	,	,	PUNCT
ejpam-4706	2	76	amman	amman	PROPN
ejpam-4706	2	77	11931	11931	NUM
ejpam-4706	2	78	,	,	PUNCT
ejpam-4706	2	79	jordan	jordan	PROPN
ejpam-4706	2	80	abstract	abstract	PROPN
ejpam-4706	2	81	.	.	PUNCT
ejpam-4706	3	1	we	we	PRON
ejpam-4706	3	2	employ	employ	VERB
ejpam-4706	3	3	several	several	ADJ
ejpam-4706	3	4	numerical	numerical	ADJ
ejpam-4706	3	5	radius	radius	NOUN
ejpam-4706	3	6	inequalities	inequality	NOUN
ejpam-4706	3	7	to	to	ADP
ejpam-4706	3	8	the	the	DET
ejpam-4706	3	9	square	square	NOUN
ejpam-4706	3	10	of	of	ADP
ejpam-4706	3	11	the	the	DET
ejpam-4706	3	12	frobenius	frobenius	ADJ
ejpam-4706	3	13	companion	companion	NOUN
ejpam-4706	3	14	matrices	matrix	NOUN
ejpam-4706	3	15	of	of	ADP
ejpam-4706	3	16	monic	monic	ADJ
ejpam-4706	3	17	matrix	matrix	NOUN
ejpam-4706	3	18	polynomials	polynomial	NOUN
ejpam-4706	3	19	to	to	PART
ejpam-4706	3	20	provide	provide	VERB
ejpam-4706	3	21	new	new	ADJ
ejpam-4706	3	22	bounds	bound	NOUN
ejpam-4706	3	23	for	for	ADP
ejpam-4706	3	24	the	the	DET
ejpam-4706	3	25	eigenvalues	eigenvalue	NOUN
ejpam-4706	3	26	of	of	ADP
ejpam-4706	3	27	these	these	DET
ejpam-4706	3	28	polynomials	polynomial	NOUN
ejpam-4706	3	29	.	.	PUNCT
ejpam-4706	4	1	2020	2020	NUM
ejpam-4706	4	2	mathematics	mathematic	NOUN
ejpam-4706	4	3	subject	subject	NOUN
ejpam-4706	4	4	classifications	classification	NOUN
ejpam-4706	4	5	:	:	PUNCT
ejpam-4706	4	6	26a33	26a33	NUM
ejpam-4706	4	7	,	,	PUNCT
ejpam-4706	4	8	41a58	41a58	NOUN
ejpam-4706	4	9	key	key	ADJ
ejpam-4706	4	10	words	word	NOUN
ejpam-4706	4	11	and	and	CCONJ
ejpam-4706	4	12	phrases	phrase	NOUN
ejpam-4706	4	13	:	:	PUNCT
ejpam-4706	4	14	bounds	bound	VERB
ejpam-4706	4	15	for	for	ADP
ejpam-4706	4	16	the	the	DET
ejpam-4706	4	17	zeroes	zero	NOUN
ejpam-4706	4	18	of	of	ADP
ejpam-4706	4	19	polynomials	polynomial	NOUN
ejpam-4706	4	20	,	,	PUNCT
ejpam-4706	4	21	companion	companion	NOUN
ejpam-4706	4	22	matrix	matrix	NOUN
ejpam-4706	4	23	,	,	PUNCT
ejpam-4706	4	24	spectral	spectral	ADJ
ejpam-4706	4	25	radius	radius	NOUN
ejpam-4706	4	26	,	,	PUNCT
ejpam-4706	4	27	numerical	numerical	ADJ
ejpam-4706	4	28	radius	radius	PROPN
ejpam-4706	4	29	1	1	NUM
ejpam-4706	4	30	.	.	PUNCT
ejpam-4706	5	1	introduction	introduction	NOUN
ejpam-4706	5	2	let	let	VERB
ejpam-4706	5	3	mn×m(c	mn×m(c	NOUN
ejpam-4706	5	4	)	)	PUNCT
ejpam-4706	5	5	stands	stand	VERB
ejpam-4706	5	6	for	for	ADP
ejpam-4706	5	7	the	the	DET
ejpam-4706	5	8	algebra	algebra	NOUN
ejpam-4706	5	9	of	of	ADP
ejpam-4706	5	10	all	all	DET
ejpam-4706	5	11	n	n	PRON
ejpam-4706	6	1	×m	×m	NOUN
ejpam-4706	6	2	complex	complex	ADJ
ejpam-4706	6	3	matrices	matrix	NOUN
ejpam-4706	6	4	where	where	SCONJ
ejpam-4706	6	5	,	,	PUNCT
ejpam-4706	6	6	n	n	CCONJ
ejpam-4706	6	7	,	,	PUNCT
ejpam-4706	6	8	m	m	PROPN
ejpam-4706	6	9	∈	∈	NOUN
ejpam-4706	6	10	n.	n.	NOUN
ejpam-4706	6	11	for	for	ADP
ejpam-4706	6	12	n	n	PROPN
ejpam-4706	6	13	=	=	SYM
ejpam-4706	6	14	m	m	PROPN
ejpam-4706	6	15	,	,	PUNCT
ejpam-4706	6	16	we	we	PRON
ejpam-4706	6	17	may	may	AUX
ejpam-4706	6	18	use	use	VERB
ejpam-4706	6	19	the	the	DET
ejpam-4706	6	20	symbol	symbol	NOUN
ejpam-4706	6	21	mn(c	mn(c	X
ejpam-4706	6	22	)	)	PUNCT
ejpam-4706	6	23	.	.	PUNCT
ejpam-4706	7	1	for	for	ADP
ejpam-4706	7	2	a	a	DET
ejpam-4706	7	3	∈	∈	NOUN
ejpam-4706	7	4	mn(c	mn(c	X
ejpam-4706	7	5	)	)	PUNCT
ejpam-4706	7	6	,	,	PUNCT
ejpam-4706	7	7	let	let	VERB
ejpam-4706	7	8	σ(a	σ(a	PROPN
ejpam-4706	7	9	)	)	PUNCT
ejpam-4706	7	10	,	,	PUNCT
ejpam-4706	7	11	r(a	r(a	PROPN
ejpam-4706	7	12	)	)	PUNCT
ejpam-4706	7	13	,	,	PUNCT
ejpam-4706	7	14	w(a	w(a	X
ejpam-4706	7	15	)	)	PUNCT
ejpam-4706	7	16	and	and	CCONJ
ejpam-4706	7	17	∥a∥	∥a∥	NOUN
ejpam-4706	7	18	denote	denote	VERB
ejpam-4706	7	19	the	the	DET
ejpam-4706	7	20	spectrum	spectrum	NOUN
ejpam-4706	7	21	,	,	PUNCT
ejpam-4706	7	22	the	the	DET
ejpam-4706	7	23	spectral	spectral	ADJ
ejpam-4706	7	24	radius	radius	NOUN
ejpam-4706	7	25	,	,	PUNCT
ejpam-4706	7	26	the	the	DET
ejpam-4706	7	27	numerical	numerical	ADJ
ejpam-4706	7	28	radius	radius	PROPN
ejpam-4706	7	29	and	and	CCONJ
ejpam-4706	7	30	the	the	DET
ejpam-4706	7	31	spectral	spectral	ADJ
ejpam-4706	7	32	norm	norm	NOUN
ejpam-4706	7	33	of	of	ADP
ejpam-4706	7	34	a	a	PRON
ejpam-4706	7	35	,	,	PUNCT
ejpam-4706	7	36	respectively	respectively	ADV
ejpam-4706	7	37	.	.	PUNCT
ejpam-4706	8	1	recall	recall	VERB
ejpam-4706	8	2	that	that	PRON
ejpam-4706	8	3	σ(a	σ(a	PROPN
ejpam-4706	8	4	)	)	PUNCT
ejpam-4706	8	5	=	=	PRON
ejpam-4706	9	1	{	{	PUNCT
ejpam-4706	9	2	λ	λ	X
ejpam-4706	9	3	∈	∈	PROPN
ejpam-4706	9	4	c	c	NOUN
ejpam-4706	9	5	:	:	PUNCT
ejpam-4706	9	6	det(λi	det(λi	ADV
ejpam-4706	9	7	−	−	PROPN
ejpam-4706	9	8	a	a	X
ejpam-4706	9	9	)	)	PUNCT
ejpam-4706	9	10	=	=	SYM
ejpam-4706	9	11	0	0	NUM
ejpam-4706	9	12	}	}	PUNCT
ejpam-4706	9	13	,	,	PUNCT
ejpam-4706	9	14	r(a	r(a	PROPN
ejpam-4706	9	15	)	)	PUNCT
ejpam-4706	10	1	=	=	SYM
ejpam-4706	10	2	max{|λ|	max{|λ|	NOUN
ejpam-4706	10	3	:	:	PUNCT
ejpam-4706	10	4	λ	λ	X
ejpam-4706	10	5	∈	∈	PROPN
ejpam-4706	10	6	σ(a	σ(a	PROPN
ejpam-4706	10	7	)	)	PUNCT
ejpam-4706	10	8	}	}	PUNCT
ejpam-4706	10	9	,	,	PUNCT
ejpam-4706	10	10	w(a	w(a	NOUN
ejpam-4706	10	11	)	)	PUNCT
ejpam-4706	11	1	=	=	SYM
ejpam-4706	11	2	max	max	PROPN
ejpam-4706	11	3	∥x∥=1	∥x∥=1	PROPN
ejpam-4706	11	4	|⟨ax	|⟨ax	VERB
ejpam-4706	11	5	,	,	PUNCT
ejpam-4706	11	6	x⟩|	x⟩|	PROPN
ejpam-4706	11	7	and	and	CCONJ
ejpam-4706	11	8	∥a∥	∥a∥	PROPN
ejpam-4706	11	9	=	=	SYM
ejpam-4706	11	10	max	max	PROPN
ejpam-4706	11	11	{	{	PUNCT
ejpam-4706	11	12	√	√	PROPN
ejpam-4706	11	13	λ	λ	INTJ
ejpam-4706	11	14	:	:	PUNCT
ejpam-4706	11	15	λ	λ	PROPN
ejpam-4706	11	16	∈	∈	PROPN
ejpam-4706	11	17	σ(a∗a	σ(a∗a	NOUN
ejpam-4706	11	18	)	)	PUNCT
ejpam-4706	11	19	}	}	PUNCT
ejpam-4706	11	20	,	,	PUNCT
ejpam-4706	11	21	where	where	SCONJ
ejpam-4706	11	22	a∗	a∗	NOUN
ejpam-4706	11	23	=	=	PUNCT
ejpam-4706	12	1	[	[	X
ejpam-4706	12	2	āji	āji	NOUN
ejpam-4706	12	3	]	]	PUNCT
ejpam-4706	12	4	for	for	ADP
ejpam-4706	12	5	a	a	PRON
ejpam-4706	12	6	=	=	X
ejpam-4706	13	1	[	[	X
ejpam-4706	13	2	aij	aij	X
ejpam-4706	13	3	]	]	X
ejpam-4706	13	4	,	,	PUNCT
ejpam-4706	13	5	aij	aij	PROPN
ejpam-4706	13	6	∈	∈	PROPN
ejpam-4706	13	7	c.	c.	NOUN
ejpam-4706	13	8	the	the	DET
ejpam-4706	13	9	interesting	interesting	ADJ
ejpam-4706	13	10	inequality	inequality	NOUN
ejpam-4706	13	11	that	that	PRON
ejpam-4706	13	12	combines	combine	VERB
ejpam-4706	13	13	these	these	DET
ejpam-4706	13	14	concepts	concept	NOUN
ejpam-4706	13	15	is	be	AUX
ejpam-4706	13	16	|λ|	|λ|	ADP
ejpam-4706	13	17	≤	≤	PROPN
ejpam-4706	13	18	r(a	r(a	PROPN
ejpam-4706	13	19	)	)	PUNCT
ejpam-4706	13	20	≤	≤	NOUN
ejpam-4706	13	21	w(a	w(a	VERB
ejpam-4706	13	22	)	)	PUNCT
ejpam-4706	13	23	≤	≤	NUM
ejpam-4706	13	24	∥a∥	∥a∥	NOUN
ejpam-4706	13	25	,	,	PUNCT
ejpam-4706	13	26	for	for	ADP
ejpam-4706	13	27	any	any	DET
ejpam-4706	13	28	λ	λ	PROPN
ejpam-4706	13	29	∈	∈	PROPN
ejpam-4706	13	30	σ(a	σ(a	PROPN
ejpam-4706	13	31	)	)	PUNCT
ejpam-4706	13	32	.	.	PUNCT
ejpam-4706	14	1	the	the	DET
ejpam-4706	14	2	polynomial	polynomial	PROPN
ejpam-4706	14	3	eigenvalue	eigenvalue	PROPN
ejpam-4706	14	4	problem	problem	NOUN
ejpam-4706	14	5	(	(	PUNCT
ejpam-4706	14	6	pep	pep	NOUN
ejpam-4706	14	7	)	)	PUNCT
ejpam-4706	14	8	,	,	PUNCT
ejpam-4706	14	9	finding	find	VERB
ejpam-4706	14	10	and	and	CCONJ
ejpam-4706	14	11	locating	locate	VERB
ejpam-4706	14	12	the	the	DET
ejpam-4706	14	13	eigenvalues	eigenvalue	NOUN
ejpam-4706	14	14	of	of	ADP
ejpam-4706	14	15	matrix	matrix	NOUN
ejpam-4706	14	16	polynomials	polynomial	NOUN
ejpam-4706	14	17	,	,	PUNCT
ejpam-4706	14	18	are	be	AUX
ejpam-4706	14	19	very	very	ADV
ejpam-4706	14	20	important	important	ADJ
ejpam-4706	14	21	topics	topic	NOUN
ejpam-4706	14	22	in	in	ADP
ejpam-4706	14	23	scientific	scientific	ADJ
ejpam-4706	14	24	computation	computation	NOUN
ejpam-4706	14	25	that	that	PRON
ejpam-4706	14	26	has	have	AUX
ejpam-4706	14	27	attracted	attract	VERB
ejpam-4706	14	28	the	the	DET
ejpam-4706	14	29	attention	attention	NOUN
ejpam-4706	14	30	of	of	ADP
ejpam-4706	14	31	many	many	ADJ
ejpam-4706	14	32	researchers	researcher	NOUN
ejpam-4706	14	33	[	[	X
ejpam-4706	14	34	2	2	NUM
ejpam-4706	14	35	,	,	PUNCT
ejpam-4706	14	36	3	3	NUM
ejpam-4706	14	37	,	,	PUNCT
ejpam-4706	14	38	5	5	NUM
ejpam-4706	14	39	,	,	PUNCT
ejpam-4706	14	40	8	8	NUM
ejpam-4706	14	41	,	,	PUNCT
ejpam-4706	14	42	9	9	NUM
ejpam-4706	14	43	]	]	PUNCT
ejpam-4706	14	44	.	.	PUNCT
ejpam-4706	15	1	the	the	DET
ejpam-4706	15	2	pep	pep	NOUN
ejpam-4706	15	3	appears	appear	VERB
ejpam-4706	15	4	in	in	ADP
ejpam-4706	15	5	a	a	DET
ejpam-4706	15	6	variety	variety	NOUN
ejpam-4706	15	7	of	of	ADP
ejpam-4706	15	8	problems	problem	NOUN
ejpam-4706	15	9	in	in	ADP
ejpam-4706	15	10	a	a	DET
ejpam-4706	15	11	wide	wide	ADJ
ejpam-4706	15	12	range	range	NOUN
ejpam-4706	15	13	of	of	ADP
ejpam-4706	15	14	applications	application	NOUN
ejpam-4706	15	15	.	.	PUNCT
ejpam-4706	16	1	there	there	PRON
ejpam-4706	16	2	are	be	VERB
ejpam-4706	16	3	numerous	numerous	ADJ
ejpam-4706	16	4	examples	example	NOUN
ejpam-4706	16	5	of	of	ADP
ejpam-4706	16	6	physical	physical	ADJ
ejpam-4706	16	7	phenomena	phenomenon	NOUN
ejpam-4706	16	8	where	where	SCONJ
ejpam-4706	16	9	peps	pep	NOUN
ejpam-4706	16	10	arise	arise	VERB
ejpam-4706	16	11	naturally	naturally	ADV
ejpam-4706	16	12	such	such	ADJ
ejpam-4706	16	13	as	as	ADP
ejpam-4706	16	14	structural	structural	ADJ
ejpam-4706	16	15	mechanics	mechanic	NOUN
ejpam-4706	16	16	,	,	PUNCT
ejpam-4706	16	17	control	control	NOUN
ejpam-4706	16	18	theory	theory	NOUN
ejpam-4706	16	19	,	,	PUNCT
ejpam-4706	16	20	fluid	fluid	ADJ
ejpam-4706	16	21	mechanics	mechanic	NOUN
ejpam-4706	16	22	.	.	PUNCT
ejpam-4706	17	1	∗corresponding	∗corresponde	VERB
ejpam-4706	17	2	author	author	NOUN
ejpam-4706	17	3	.	.	PUNCT
ejpam-4706	18	1	doi	doi	NOUN
ejpam-4706	18	2	:	:	PUNCT
ejpam-4706	18	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4706	https://doi.org/10.29020/nybg.ejpam.v16i2.4706	PROPN
ejpam-4706	18	4	email	email	NOUN
ejpam-4706	18	5	addresses	address	VERB
ejpam-4706	18	6	:	:	PUNCT
ejpam-4706	18	7	aliaaburqan@zu.edu.jo	aliaaburqan@zu.edu.jo	ADJ
ejpam-4706	18	8	(	(	PUNCT
ejpam-4706	18	9	a.	a.	NOUN
ejpam-4706	18	10	burqan	burqan	PROPN
ejpam-4706	18	11	)	)	PUNCT
ejpam-4706	18	12	,	,	PUNCT
ejpam-4706	18	13	aqazza@zu.edu.jo	aqazza@zu.edu.jo	PROPN
ejpam-4706	18	14	(	(	PUNCT
ejpam-4706	18	15	a.qazza	a.qazza	PROPN
ejpam-4706	18	16	)	)	PUNCT
ejpam-4706	18	17	,	,	PUNCT
ejpam-4706	18	18	m	m	VERB
ejpam-4706	18	19	khandakji@asu.edu.jo	khandakji@asu.edu.jo	NOUN
ejpam-4706	18	20	(	(	PUNCT
ejpam-4706	18	21	m.	m.	NOUN
ejpam-4706	18	22	khandaqji	khandaqji	PROPN
ejpam-4706	18	23	)	)	PUNCT
ejpam-4706	18	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4706	18	25	806	806	NUM
ejpam-4706	18	26	©	©	PROPN
ejpam-4706	18	27	2023	2023	NUM
ejpam-4706	18	28	ejpam	ejpam	NOUN
ejpam-4706	18	29	all	all	DET
ejpam-4706	18	30	rights	right	NOUN
ejpam-4706	18	31	reserved	reserve	VERB
ejpam-4706	18	32	.	.	PUNCT
ejpam-4706	19	1	a.	a.	PROPN
ejpam-4706	19	2	burqan	burqan	PROPN
ejpam-4706	19	3	et	et	PROPN
ejpam-4706	19	4	al	al	PROPN
ejpam-4706	19	5	.	.	PUNCT
ejpam-4706	19	6	/	/	SYM
ejpam-4706	19	7	eur	eur	PROPN
ejpam-4706	19	8	.	.	PUNCT
ejpam-4706	20	1	j.	j.	PROPN
ejpam-4706	20	2	pure	pure	PROPN
ejpam-4706	20	3	appl	appl	PROPN
ejpam-4706	20	4	.	.	PROPN
ejpam-4706	20	5	math	math	PROPN
ejpam-4706	20	6	,	,	PUNCT
ejpam-4706	20	7	16	16	NUM
ejpam-4706	20	8	(	(	PUNCT
ejpam-4706	20	9	2	2	NUM
ejpam-4706	20	10	)	)	PUNCT
ejpam-4706	20	11	(	(	PUNCT
ejpam-4706	20	12	2023	2023	NUM
ejpam-4706	20	13	)	)	PUNCT
ejpam-4706	20	14	,	,	PUNCT
ejpam-4706	20	15	806	806	NUM
ejpam-4706	20	16	-	-	SYM
ejpam-4706	20	17	818	818	NUM
ejpam-4706	20	18	807	807	NUM
ejpam-4706	20	19	consider	consider	VERB
ejpam-4706	20	20	the	the	DET
ejpam-4706	20	21	monic	monic	ADJ
ejpam-4706	20	22	polynomial	polynomial	ADJ
ejpam-4706	20	23	p	p	PROPN
ejpam-4706	20	24	(	(	PUNCT
ejpam-4706	20	25	z	z	NOUN
ejpam-4706	20	26	)	)	PUNCT
ejpam-4706	20	27	=	=	SYM
ejpam-4706	20	28	izm	izm	PROPN
ejpam-4706	21	1	+	+	PUNCT
ejpam-4706	21	2	amzm−1	amzm−1	PROPN
ejpam-4706	21	3	+	+	CCONJ
ejpam-4706	21	4	·	·	PUNCT
ejpam-4706	21	5	·	·	PUNCT
ejpam-4706	21	6	·	·	PUNCT
ejpam-4706	22	1	+	+	CCONJ
ejpam-4706	22	2	a2z	a2z	PROPN
ejpam-4706	22	3	+	+	CCONJ
ejpam-4706	22	4	a1	a1	NOUN
ejpam-4706	22	5	,	,	PUNCT
ejpam-4706	22	6	with	with	ADP
ejpam-4706	22	7	degree	degree	NOUN
ejpam-4706	22	8	m	m	PROPN
ejpam-4706	22	9	≥	≥	NOUN
ejpam-4706	22	10	2	2	NUM
ejpam-4706	22	11	and	and	CCONJ
ejpam-4706	22	12	matrix	matrix	NOUN
ejpam-4706	22	13	coefficients	coefficient	NOUN
ejpam-4706	22	14	ai	ai	VERB
ejpam-4706	22	15	∈	∈	PROPN
ejpam-4706	22	16	mn	mn	PROPN
ejpam-4706	22	17	(	(	PUNCT
ejpam-4706	22	18	c	c	NOUN
ejpam-4706	22	19	)	)	PUNCT
ejpam-4706	22	20	for	for	ADP
ejpam-4706	22	21	i	i	PROPN
ejpam-4706	22	22	=	=	NOUN
ejpam-4706	22	23	1	1	NUM
ejpam-4706	22	24	,	,	PUNCT
ejpam-4706	22	25	.	.	PUNCT
ejpam-4706	22	26	.	.	PUNCT
ejpam-4706	22	27	.	.	PUNCT
ejpam-4706	23	1	,	,	PUNCT
ejpam-4706	23	2	m	m	PROPN
ejpam-4706	23	3	,	,	PUNCT
ejpam-4706	23	4	where	where	SCONJ
ejpam-4706	23	5	i	i	PRON
ejpam-4706	23	6	is	be	AUX
ejpam-4706	23	7	the	the	DET
ejpam-4706	23	8	identity	identity	NOUN
ejpam-4706	23	9	matrix	matrix	NOUN
ejpam-4706	23	10	in	in	ADP
ejpam-4706	23	11	mn	mn	PROPN
ejpam-4706	23	12	(	(	PUNCT
ejpam-4706	23	13	c	c	NOUN
ejpam-4706	23	14	)	)	PUNCT
ejpam-4706	23	15	.	.	PUNCT
ejpam-4706	24	1	the	the	DET
ejpam-4706	24	2	frobenius	frobenius	ADJ
ejpam-4706	24	3	companion	companion	NOUN
ejpam-4706	24	4	block	block	NOUN
ejpam-4706	24	5	matrix	matrix	NOUN
ejpam-4706	24	6	of	of	ADP
ejpam-4706	24	7	p	p	PROPN
ejpam-4706	24	8	(	(	PUNCT
ejpam-4706	24	9	z	z	NOUN
ejpam-4706	24	10	)	)	PUNCT
ejpam-4706	24	11	is	be	AUX
ejpam-4706	24	12	the	the	DET
ejpam-4706	24	13	mn×mn	mn×mn	ADJ
ejpam-4706	24	14	matrix	matrix	NOUN
ejpam-4706	24	15	given	give	VERB
ejpam-4706	24	16	by	by	ADP
ejpam-4706	24	17	f	f	PROPN
ejpam-4706	24	18	(	(	PUNCT
ejpam-4706	24	19	p	p	NOUN
ejpam-4706	24	20	)	)	PUNCT
ejpam-4706	24	21	=	=	SYM
ejpam-4706	24	22			NOUN
ejpam-4706	24	23	−am	−am	X
ejpam-4706	24	24	−am−1	−am−1	PROPN
ejpam-4706	24	25	·	·	PUNCT
ejpam-4706	24	26	·	·	PUNCT
ejpam-4706	24	27	·	·	PUNCT
ejpam-4706	25	1	−a2	−a2	NOUN
ejpam-4706	25	2	−a1	−a1	VERB
ejpam-4706	25	3	i	i	NOUN
ejpam-4706	25	4	0	0	PUNCT
ejpam-4706	25	5	·	·	PUNCT
ejpam-4706	25	6	·	·	PUNCT
ejpam-4706	25	7	·	·	PUNCT
ejpam-4706	25	8	0	0	NUM
ejpam-4706	26	1	0	0	NUM
ejpam-4706	26	2	0	0	NUM
ejpam-4706	27	1	i	i	PRON
ejpam-4706	27	2	.	.	PUNCT
ejpam-4706	27	3	.	.	PUNCT
ejpam-4706	27	4	.	.	PUNCT
ejpam-4706	28	1	0	0	NUM
ejpam-4706	28	2	0	0	NUM
ejpam-4706	28	3	...	...	PUNCT
ejpam-4706	28	4	...	...	PUNCT
ejpam-4706	28	5	.	.	PUNCT
ejpam-4706	28	6	.	.	PUNCT
ejpam-4706	28	7	.	.	PUNCT
ejpam-4706	29	1	...	...	PUNCT
ejpam-4706	30	1	...	...	PUNCT
ejpam-4706	31	1	0	0	NUM
ejpam-4706	31	2	0	0	NUM
ejpam-4706	31	3	·	·	PUNCT
ejpam-4706	31	4	·	·	PUNCT
ejpam-4706	31	5	·	·	PUNCT
ejpam-4706	32	1	i	i	PRON
ejpam-4706	32	2	0	0	NUM
ejpam-4706	32	3			NUM
ejpam-4706	32	4	.	.	PUNCT
ejpam-4706	33	1	this	this	DET
ejpam-4706	33	2	matrix	matrix	NOUN
ejpam-4706	33	3	builds	build	VERB
ejpam-4706	33	4	an	an	DET
ejpam-4706	33	5	important	important	ADJ
ejpam-4706	33	6	bridge	bridge	NOUN
ejpam-4706	33	7	between	between	ADP
ejpam-4706	33	8	matrix	matrix	NOUN
ejpam-4706	33	9	analysis	analysis	NOUN
ejpam-4706	33	10	and	and	CCONJ
ejpam-4706	33	11	the	the	DET
ejpam-4706	33	12	geometry	geometry	NOUN
ejpam-4706	33	13	of	of	ADP
ejpam-4706	33	14	polynomials	polynomial	NOUN
ejpam-4706	33	15	.	.	PUNCT
ejpam-4706	34	1	it	it	PRON
ejpam-4706	34	2	is	be	AUX
ejpam-4706	34	3	known	know	VERB
ejpam-4706	34	4	that	that	SCONJ
ejpam-4706	34	5	λ	λ	PROPN
ejpam-4706	34	6	is	be	AUX
ejpam-4706	34	7	an	an	DET
ejpam-4706	34	8	eigenvalue	eigenvalue	NOUN
ejpam-4706	34	9	of	of	ADP
ejpam-4706	34	10	p	p	PROPN
ejpam-4706	34	11	(	(	PUNCT
ejpam-4706	34	12	z	z	NOUN
ejpam-4706	34	13	)	)	PUNCT
ejpam-4706	34	14	iff	iff	PROPN
ejpam-4706	34	15	λ	λ	PROPN
ejpam-4706	34	16	∈	∈	PROPN
ejpam-4706	34	17	σ(f	σ(f	PROPN
ejpam-4706	34	18	(	(	PUNCT
ejpam-4706	34	19	p	p	NOUN
ejpam-4706	34	20	)	)	PUNCT
ejpam-4706	34	21	)	)	PUNCT
ejpam-4706	35	1	and	and	CCONJ
ejpam-4706	35	2	so	so	ADV
ejpam-4706	35	3	if	if	SCONJ
ejpam-4706	35	4	λ	λ	NOUN
ejpam-4706	35	5	is	be	AUX
ejpam-4706	35	6	an	an	DET
ejpam-4706	35	7	eigenvalue	eigenvalue	NOUN
ejpam-4706	35	8	of	of	ADP
ejpam-4706	35	9	p	p	PROPN
ejpam-4706	35	10	(	(	PUNCT
ejpam-4706	35	11	z	z	NOUN
ejpam-4706	35	12	)	)	PUNCT
ejpam-4706	35	13	,	,	PUNCT
ejpam-4706	35	14	then	then	ADV
ejpam-4706	35	15	|λ|	|λ|	VERB
ejpam-4706	35	16	≤	≤	NOUN
ejpam-4706	35	17	r(f	r(f	PROPN
ejpam-4706	35	18	(	(	PUNCT
ejpam-4706	35	19	p	p	NOUN
ejpam-4706	35	20	)	)	PUNCT
ejpam-4706	35	21	)	)	PUNCT
ejpam-4706	36	1	≤	≤	PROPN
ejpam-4706	36	2	w(f	w(f	ADJ
ejpam-4706	36	3	(	(	PUNCT
ejpam-4706	36	4	p	p	NOUN
ejpam-4706	36	5	)	)	PUNCT
ejpam-4706	36	6	)	)	PUNCT
ejpam-4706	36	7	≤	≤	PUNCT
ejpam-4706	37	1	∥f	∥f	PROPN
ejpam-4706	37	2	(	(	PUNCT
ejpam-4706	37	3	p	p	NOUN
ejpam-4706	37	4	)	)	PUNCT
ejpam-4706	37	5	∥.	∥.	NOUN
ejpam-4706	37	6	in	in	ADP
ejpam-4706	37	7	order	order	NOUN
ejpam-4706	37	8	to	to	PART
ejpam-4706	37	9	obtain	obtain	VERB
ejpam-4706	37	10	new	new	ADJ
ejpam-4706	37	11	upper	upper	ADJ
ejpam-4706	37	12	bounds	bound	NOUN
ejpam-4706	37	13	for	for	ADP
ejpam-4706	37	14	the	the	DET
ejpam-4706	37	15	eigenvalues	eigenvalue	NOUN
ejpam-4706	37	16	of	of	ADP
ejpam-4706	37	17	p	p	NOUN
ejpam-4706	37	18	(	(	PUNCT
ejpam-4706	37	19	z	z	NOUN
ejpam-4706	37	20	)	)	PUNCT
ejpam-4706	37	21	,	,	PUNCT
ejpam-4706	37	22	we	we	PRON
ejpam-4706	37	23	provide	provide	VERB
ejpam-4706	37	24	new	new	ADJ
ejpam-4706	37	25	estimates	estimate	NOUN
ejpam-4706	37	26	for	for	ADP
ejpam-4706	37	27	the	the	DET
ejpam-4706	37	28	numerical	numerical	ADJ
ejpam-4706	37	29	radius	radius	NOUN
ejpam-4706	37	30	of	of	ADP
ejpam-4706	37	31	f	f	PROPN
ejpam-4706	37	32	2(p	2(p	NUM
ejpam-4706	37	33	)	)	PUNCT
ejpam-4706	37	34	.	.	PUNCT
ejpam-4706	38	1	the	the	DET
ejpam-4706	38	2	references	reference	NOUN
ejpam-4706	38	3	[	[	X
ejpam-4706	38	4	3	3	NUM
ejpam-4706	38	5	,	,	PUNCT
ejpam-4706	38	6	5	5	NUM
ejpam-4706	38	7	,	,	PUNCT
ejpam-4706	38	8	7	7	NUM
ejpam-4706	38	9	,	,	PUNCT
ejpam-4706	38	10	8	8	NUM
ejpam-4706	38	11	]	]	PUNCT
ejpam-4706	38	12	contain	contain	VERB
ejpam-4706	38	13	bounds	bound	NOUN
ejpam-4706	38	14	for	for	ADP
ejpam-4706	38	15	the	the	DET
ejpam-4706	38	16	eigenvalues	eigenvalue	NOUN
ejpam-4706	38	17	of	of	ADP
ejpam-4706	38	18	matrix	matrix	NOUN
ejpam-4706	38	19	polynomials	polynomial	NOUN
ejpam-4706	38	20	based	base	VERB
ejpam-4706	38	21	on	on	ADP
ejpam-4706	38	22	various	various	ADJ
ejpam-4706	38	23	matrix	matrix	NOUN
ejpam-4706	38	24	inequalities	inequality	NOUN
ejpam-4706	38	25	.	.	PUNCT
ejpam-4706	39	1	in	in	ADP
ejpam-4706	39	2	fact	fact	NOUN
ejpam-4706	39	3	,	,	PUNCT
ejpam-4706	39	4	higham	higham	PROPN
ejpam-4706	39	5	and	and	CCONJ
ejpam-4706	39	6	tisseur	tisseur	NOUN
ejpam-4706	39	7	[	[	X
ejpam-4706	39	8	5	5	NUM
ejpam-4706	39	9	]	]	PUNCT
ejpam-4706	39	10	obtained	obtain	VERB
ejpam-4706	39	11	new	new	ADJ
ejpam-4706	39	12	bounds	bound	NOUN
ejpam-4706	39	13	for	for	ADP
ejpam-4706	39	14	the	the	DET
ejpam-4706	39	15	eigenvalues	eigenvalue	NOUN
ejpam-4706	39	16	of	of	ADP
ejpam-4706	39	17	matrix	matrix	NOUN
ejpam-4706	39	18	polynomials	polynomial	NOUN
ejpam-4706	39	19	using	use	VERB
ejpam-4706	39	20	norm	norm	NOUN
ejpam-4706	39	21	and	and	CCONJ
ejpam-4706	39	22	numerical	numerical	ADJ
ejpam-4706	39	23	radius	radius	PROPN
ejpam-4706	39	24	inequalities	inequality	NOUN
ejpam-4706	39	25	.	.	PUNCT
ejpam-4706	40	1	le	le	PROPN
ejpam-4706	40	2	,	,	PUNCT
ejpam-4706	40	3	du	du	X
ejpam-4706	40	4	,	,	PUNCT
ejpam-4706	40	5	and	and	CCONJ
ejpam-4706	40	6	nguyen	nguyen	NOUN
ejpam-4706	41	1	[	[	X
ejpam-4706	41	2	3	3	X
ejpam-4706	41	3	]	]	PUNCT
ejpam-4706	41	4	established	establish	VERB
ejpam-4706	41	5	specific	specific	ADJ
ejpam-4706	41	6	(	(	PUNCT
ejpam-4706	41	7	upper	upper	ADJ
ejpam-4706	41	8	and	and	CCONJ
ejpam-4706	41	9	lower	low	ADJ
ejpam-4706	41	10	)	)	PUNCT
ejpam-4706	41	11	bounds	bound	NOUN
ejpam-4706	41	12	for	for	ADP
ejpam-4706	41	13	the	the	DET
ejpam-4706	41	14	eigenvalues	eigenvalue	NOUN
ejpam-4706	41	15	of	of	ADP
ejpam-4706	41	16	matrix	matrix	NOUN
ejpam-4706	41	17	polynomials	polynomial	NOUN
ejpam-4706	41	18	using	use	VERB
ejpam-4706	41	19	the	the	DET
ejpam-4706	41	20	norms	norm	NOUN
ejpam-4706	41	21	of	of	ADP
ejpam-4706	41	22	the	the	DET
ejpam-4706	41	23	coefficients	coefficient	NOUN
ejpam-4706	41	24	matrices	matrix	NOUN
ejpam-4706	41	25	of	of	ADP
ejpam-4706	41	26	a	a	DET
ejpam-4706	41	27	matrix	matrix	NOUN
ejpam-4706	41	28	polynomial	polynomial	NOUN
ejpam-4706	41	29	.	.	PUNCT
ejpam-4706	42	1	eigenvalue	eigenvalue	NOUN
ejpam-4706	42	2	bounds	bound	NOUN
ejpam-4706	42	3	can	can	AUX
ejpam-4706	42	4	be	be	AUX
ejpam-4706	42	5	created	create	VERB
ejpam-4706	42	6	using	use	VERB
ejpam-4706	42	7	l	l	NOUN
ejpam-4706	42	8	-	-	PUNCT
ejpam-4706	42	9	ifications	ification	NOUN
ejpam-4706	42	10	,	,	PUNCT
ejpam-4706	42	11	or	or	CCONJ
ejpam-4706	42	12	lower	low	ADJ
ejpam-4706	42	13	order	order	NOUN
ejpam-4706	42	14	matrix	matrix	NOUN
ejpam-4706	42	15	polynomials	polynomial	NOUN
ejpam-4706	42	16	with	with	ADP
ejpam-4706	42	17	the	the	DET
ejpam-4706	42	18	same	same	ADJ
ejpam-4706	42	19	eigenvalues	eigenvalue	NOUN
ejpam-4706	42	20	as	as	ADP
ejpam-4706	42	21	a	a	DET
ejpam-4706	42	22	given	give	VERB
ejpam-4706	42	23	matrix	matrix	NOUN
ejpam-4706	42	24	polynomial	polynomial	NOUN
ejpam-4706	42	25	,	,	PUNCT
ejpam-4706	42	26	as	as	SCONJ
ejpam-4706	42	27	demonstrated	demonstrate	VERB
ejpam-4706	42	28	by	by	ADP
ejpam-4706	42	29	melman	melman	PROPN
ejpam-4706	42	30	[	[	X
ejpam-4706	42	31	8	8	NUM
ejpam-4706	42	32	]	]	PUNCT
ejpam-4706	42	33	.	.	PUNCT
ejpam-4706	43	1	jaradat	jaradat	PROPN
ejpam-4706	43	2	and	and	CCONJ
ejpam-4706	43	3	kittaneh	kittaneh	PROPN
ejpam-4706	44	1	[	[	X
ejpam-4706	44	2	7	7	X
ejpam-4706	44	3	]	]	PUNCT
ejpam-4706	44	4	,	,	PUNCT
ejpam-4706	44	5	derived	derive	VERB
ejpam-4706	44	6	new	new	ADJ
ejpam-4706	44	7	numerical	numerical	ADJ
ejpam-4706	44	8	radius	radius	PROPN
ejpam-4706	44	9	inequalities	inequality	NOUN
ejpam-4706	44	10	to	to	ADP
ejpam-4706	44	11	the	the	DET
ejpam-4706	44	12	frobenius	frobenius	ADJ
ejpam-4706	44	13	companion	companion	NOUN
ejpam-4706	44	14	block	block	NOUN
ejpam-4706	44	15	matrix	matrix	NOUN
ejpam-4706	44	16	of	of	ADP
ejpam-4706	44	17	p	p	PROPN
ejpam-4706	44	18	(	(	PUNCT
ejpam-4706	44	19	z	z	NOUN
ejpam-4706	44	20	)	)	PUNCT
ejpam-4706	44	21	and	and	CCONJ
ejpam-4706	44	22	implemented	implement	VERB
ejpam-4706	44	23	it	it	PRON
ejpam-4706	44	24	in	in	ADP
ejpam-4706	44	25	obtaining	obtain	VERB
ejpam-4706	44	26	a	a	DET
ejpam-4706	44	27	new	new	ADJ
ejpam-4706	44	28	upper	upper	ADJ
ejpam-4706	44	29	bound	bind	VERB
ejpam-4706	44	30	for	for	ADP
ejpam-4706	44	31	eigenvalues	eigenvalue	NOUN
ejpam-4706	44	32	of	of	ADP
ejpam-4706	44	33	p	p	NOUN
ejpam-4706	44	34	(	(	PUNCT
ejpam-4706	44	35	z	z	NOUN
ejpam-4706	44	36	)	)	PUNCT
ejpam-4706	44	37	.	.	PUNCT
ejpam-4706	45	1	2	2	X
ejpam-4706	45	2	.	.	X
ejpam-4706	45	3	main	main	ADJ
ejpam-4706	45	4	results	result	NOUN
ejpam-4706	45	5	the	the	DET
ejpam-4706	45	6	square	square	NOUN
ejpam-4706	45	7	of	of	ADP
ejpam-4706	45	8	the	the	DET
ejpam-4706	45	9	frobenius	frobenius	ADJ
ejpam-4706	45	10	companion	companion	NOUN
ejpam-4706	45	11	block	block	NOUN
ejpam-4706	45	12	matrix	matrix	NOUN
ejpam-4706	45	13	of	of	ADP
ejpam-4706	45	14	p	p	PROPN
ejpam-4706	45	15	(	(	PUNCT
ejpam-4706	45	16	z	z	NOUN
ejpam-4706	45	17	)	)	PUNCT
ejpam-4706	45	18	can	can	AUX
ejpam-4706	45	19	be	be	AUX
ejpam-4706	45	20	written	write	VERB
ejpam-4706	45	21	as	as	ADP
ejpam-4706	45	22	f	f	PROPN
ejpam-4706	45	23	2(p	2(p	NUM
ejpam-4706	45	24	)	)	PUNCT
ejpam-4706	46	1	=	=	SYM
ejpam-4706	46	2			NOUN
ejpam-4706	46	3	bm	bm	PROPN
ejpam-4706	46	4	bm−1	bm−1	PROPN
ejpam-4706	46	5	·	·	PUNCT
ejpam-4706	46	6	·	·	PUNCT
ejpam-4706	46	7	·	·	PUNCT
ejpam-4706	46	8	b3	b3	PROPN
ejpam-4706	46	9	b2	b2	NOUN
ejpam-4706	46	10	b1	b1	NOUN
ejpam-4706	46	11	−am	−am	X
ejpam-4706	46	12	−am−1	−am−1	PROPN
ejpam-4706	46	13	·	·	PUNCT
ejpam-4706	46	14	·	·	PUNCT
ejpam-4706	46	15	·	·	PUNCT
ejpam-4706	46	16	−a3	−a3	NOUN
ejpam-4706	46	17	−a2	−a2	NOUN
ejpam-4706	46	18	−a1	−a1	VERB
ejpam-4706	46	19	i	i	PRON
ejpam-4706	46	20	0	0	NUM
ejpam-4706	46	21	.	.	PUNCT
ejpam-4706	46	22	.	.	PUNCT
ejpam-4706	47	1	.	.	PUNCT
ejpam-4706	48	1	0	0	NUM
ejpam-4706	49	1	0	0	NUM
ejpam-4706	49	2	0	0	NUM
ejpam-4706	49	3	0	0	NUM
ejpam-4706	50	1	i	i	NOUN
ejpam-4706	50	2	0	0	NUM
ejpam-4706	50	3	...	...	PUNCT
ejpam-4706	50	4	...	...	PUNCT
ejpam-4706	50	5	...	...	PUNCT
ejpam-4706	50	6	...	...	PUNCT
ejpam-4706	50	7	...	...	PUNCT
ejpam-4706	50	8	.	.	PUNCT
ejpam-4706	50	9	.	.	PUNCT
ejpam-4706	50	10	.	.	PUNCT
ejpam-4706	51	1	0	0	NUM
ejpam-4706	52	1	0	0	NUM
ejpam-4706	52	2	0	0	NUM
ejpam-4706	52	3	0	0	NUM
ejpam-4706	52	4	0	0	NUM
ejpam-4706	52	5	0	0	NUM
ejpam-4706	53	1	i	i	NOUN
ejpam-4706	53	2	0	0	NUM
ejpam-4706	53	3	0	0	NUM
ejpam-4706	53	4			NUM
ejpam-4706	53	5	,	,	PUNCT
ejpam-4706	53	6	where	where	SCONJ
ejpam-4706	53	7	bj	bj	NOUN
ejpam-4706	53	8	=	=	SYM
ejpam-4706	53	9	amaj	amaj	NOUN
ejpam-4706	53	10	−aj−1	−aj−1	NOUN
ejpam-4706	53	11	,	,	PUNCT
ejpam-4706	53	12	j	j	PROPN
ejpam-4706	53	13	=	=	SYM
ejpam-4706	53	14	1	1	NUM
ejpam-4706	53	15	,	,	PUNCT
ejpam-4706	53	16	·	·	PUNCT
ejpam-4706	53	17	·	·	PUNCT
ejpam-4706	53	18	·	·	PUNCT
ejpam-4706	53	19	,	,	PUNCT
ejpam-4706	53	20	m	m	PROPN
ejpam-4706	53	21	,	,	PUNCT
ejpam-4706	53	22	with	with	ADP
ejpam-4706	53	23	a0	a0	PROPN
ejpam-4706	53	24	=	=	SYM
ejpam-4706	53	25	0	0	PROPN
ejpam-4706	53	26	.	.	PUNCT
ejpam-4706	53	27	to	to	PART
ejpam-4706	53	28	obtain	obtain	VERB
ejpam-4706	53	29	our	our	PRON
ejpam-4706	53	30	first	first	ADJ
ejpam-4706	53	31	new	new	ADJ
ejpam-4706	53	32	estimate	estimate	NOUN
ejpam-4706	53	33	for	for	ADP
ejpam-4706	53	34	the	the	DET
ejpam-4706	53	35	numerical	numerical	ADJ
ejpam-4706	53	36	radius	radius	NOUN
ejpam-4706	53	37	of	of	ADP
ejpam-4706	53	38	f	f	PROPN
ejpam-4706	53	39	2(p	2(p	NUM
ejpam-4706	53	40	)	)	PUNCT
ejpam-4706	53	41	,	,	PUNCT
ejpam-4706	53	42	we	we	PRON
ejpam-4706	53	43	need	need	VERB
ejpam-4706	53	44	the	the	DET
ejpam-4706	53	45	following	follow	VERB
ejpam-4706	53	46	lemmas	lemmas	NOUN
ejpam-4706	53	47	.	.	PUNCT
ejpam-4706	54	1	the	the	DET
ejpam-4706	54	2	first	first	ADJ
ejpam-4706	54	3	two	two	NUM
ejpam-4706	54	4	lemmas	lemma	NOUN
ejpam-4706	54	5	can	can	AUX
ejpam-4706	54	6	be	be	AUX
ejpam-4706	54	7	found	find	VERB
ejpam-4706	54	8	in	in	ADP
ejpam-4706	54	9	[	[	X
ejpam-4706	54	10	7	7	NUM
ejpam-4706	54	11	]	]	PUNCT
ejpam-4706	54	12	.	.	PUNCT
ejpam-4706	55	1	a.	a.	PROPN
ejpam-4706	55	2	burqan	burqan	PROPN
ejpam-4706	55	3	et	et	PROPN
ejpam-4706	55	4	al	al	PROPN
ejpam-4706	55	5	.	.	PUNCT
ejpam-4706	55	6	/	/	SYM
ejpam-4706	55	7	eur	eur	PROPN
ejpam-4706	55	8	.	.	PUNCT
ejpam-4706	56	1	j.	j.	PROPN
ejpam-4706	56	2	pure	pure	PROPN
ejpam-4706	56	3	appl	appl	PROPN
ejpam-4706	56	4	.	.	PROPN
ejpam-4706	56	5	math	math	PROPN
ejpam-4706	56	6	,	,	PUNCT
ejpam-4706	56	7	16	16	NUM
ejpam-4706	56	8	(	(	PUNCT
ejpam-4706	56	9	2	2	NUM
ejpam-4706	56	10	)	)	PUNCT
ejpam-4706	56	11	(	(	PUNCT
ejpam-4706	56	12	2023	2023	NUM
ejpam-4706	56	13	)	)	PUNCT
ejpam-4706	56	14	,	,	PUNCT
ejpam-4706	56	15	806	806	NUM
ejpam-4706	56	16	-	-	SYM
ejpam-4706	56	17	818	818	NUM
ejpam-4706	56	18	808	808	NUM
ejpam-4706	56	19	lemma	lemma	PROPN
ejpam-4706	56	20	1	1	NUM
ejpam-4706	56	21	.	.	PUNCT
ejpam-4706	57	1	let	let	VERB
ejpam-4706	57	2	a	a	DET
ejpam-4706	57	3	=	=	PUNCT
ejpam-4706	57	4	[	[	X
ejpam-4706	57	5	aij	aij	X
ejpam-4706	57	6	]	]	PUNCT
ejpam-4706	57	7	∈	∈	PROPN
ejpam-4706	57	8	mm(c	mm(c	X
ejpam-4706	57	9	)	)	PUNCT
ejpam-4706	57	10	be	be	AUX
ejpam-4706	57	11	the	the	DET
ejpam-4706	57	12	block	block	NOUN
ejpam-4706	57	13	matrix	matrix	NOUN
ejpam-4706	57	14	with	with	ADP
ejpam-4706	57	15	aij	aij	PROPN
ejpam-4706	57	16	∈	∈	PROPN
ejpam-4706	57	17	mni×nj(c	mni×nj(c	NOUN
ejpam-4706	57	18	)	)	PUNCT
ejpam-4706	57	19	and∑m	and∑m	VERB
ejpam-4706	57	20	i=1	i=1	PROPN
ejpam-4706	57	21	ni	ni	PROPN
ejpam-4706	57	22	=	=	PROPN
ejpam-4706	57	23	m	m	PROPN
ejpam-4706	57	24	,	,	PUNCT
ejpam-4706	57	25	where	where	SCONJ
ejpam-4706	57	26	1	1	NUM
ejpam-4706	57	27	≤	≤	PUNCT
ejpam-4706	57	28	i	i	PRON
ejpam-4706	57	29	,	,	PUNCT
ejpam-4706	57	30	j	j	PROPN
ejpam-4706	57	31	≤	≤	PROPN
ejpam-4706	57	32	m.	m.	NOUN
ejpam-4706	57	33	then	then	ADV
ejpam-4706	57	34	w(a	w(a	PROPN
ejpam-4706	57	35	)	)	PUNCT
ejpam-4706	57	36	≤	≤	NOUN
ejpam-4706	57	37	w([αij	w([αij	NOUN
ejpam-4706	57	38	]	]	X
ejpam-4706	57	39	)	)	PUNCT
ejpam-4706	57	40	,	,	PUNCT
ejpam-4706	57	41	where	where	SCONJ
ejpam-4706	57	42	αij	αij	NOUN
ejpam-4706	57	43	=	=	SYM
ejpam-4706	57	44	w	w	PROPN
ejpam-4706	57	45	(	(	PUNCT
ejpam-4706	57	46	[	[	PUNCT
ejpam-4706	57	47	0	0	NUM
ejpam-4706	57	48	aij	aij	PROPN
ejpam-4706	57	49	aji	aji	NOUN
ejpam-4706	57	50	0	0	NUM
ejpam-4706	57	51	]	]	PUNCT
ejpam-4706	57	52	)	)	PUNCT
ejpam-4706	57	53	.	.	PUNCT
ejpam-4706	58	1	in	in	ADP
ejpam-4706	58	2	particular	particular	ADJ
ejpam-4706	58	3	,	,	PUNCT
ejpam-4706	58	4	αii	αii	NOUN
ejpam-4706	58	5	=	=	SYM
ejpam-4706	58	6	w(aii	w(aii	PROPN
ejpam-4706	58	7	)	)	PUNCT
ejpam-4706	58	8	for	for	ADP
ejpam-4706	58	9	each	each	DET
ejpam-4706	58	10	i	i	NOUN
ejpam-4706	58	11	=	=	NOUN
ejpam-4706	58	12	1	1	NUM
ejpam-4706	58	13	,	,	PUNCT
ejpam-4706	58	14	2	2	NUM
ejpam-4706	58	15	,	,	PUNCT
ejpam-4706	58	16	.	.	PUNCT
ejpam-4706	58	17	.	.	PUNCT
ejpam-4706	58	18	.	.	PUNCT
ejpam-4706	59	1	,	,	PUNCT
ejpam-4706	59	2	m.	m.	NOUN
ejpam-4706	59	3	lemma	lemma	PROPN
ejpam-4706	59	4	2	2	X
ejpam-4706	59	5	.	.	PUNCT
ejpam-4706	60	1	let	let	VERB
ejpam-4706	60	2	tn	tn	NOUN
ejpam-4706	60	3	∈	∈	PROPN
ejpam-4706	60	4	mn(c	mn(c	X
ejpam-4706	60	5	)	)	PUNCT
ejpam-4706	60	6	be	be	AUX
ejpam-4706	60	7	the	the	DET
ejpam-4706	60	8	tridiagonal	tridiagonal	ADJ
ejpam-4706	60	9	matrix	matrix	NOUN
ejpam-4706	60	10	given	give	VERB
ejpam-4706	60	11	by	by	ADP
ejpam-4706	60	12	tn	tn	NOUN
ejpam-4706	60	13	=	=	SYM
ejpam-4706	60	14			NOUN
ejpam-4706	61	1	0	0	NUM
ejpam-4706	61	2	1	1	NUM
ejpam-4706	61	3	2	2	NUM
ejpam-4706	61	4	0	0	NUM
ejpam-4706	61	5	.	.	PUNCT
ejpam-4706	61	6	.	.	PUNCT
ejpam-4706	61	7	.	.	PUNCT
ejpam-4706	62	1	0	0	NUM
ejpam-4706	62	2	1	1	NUM
ejpam-4706	62	3	2	2	NUM
ejpam-4706	62	4	0	0	NUM
ejpam-4706	62	5	1	1	NUM
ejpam-4706	62	6	2	2	NUM
ejpam-4706	62	7	.	.	PUNCT
ejpam-4706	62	8	.	.	PUNCT
ejpam-4706	62	9	.	.	PUNCT
ejpam-4706	63	1	0	0	NUM
ejpam-4706	63	2	0	0	NUM
ejpam-4706	64	1	1	1	NUM
ejpam-4706	64	2	2	2	NUM
ejpam-4706	64	3	0	0	NUM
ejpam-4706	64	4	.	.	PUNCT
ejpam-4706	64	5	.	.	PUNCT
ejpam-4706	64	6	.	.	PUNCT
ejpam-4706	65	1	0	0	NUM
ejpam-4706	65	2	...	...	PUNCT
ejpam-4706	65	3	...	...	PUNCT
ejpam-4706	65	4	.	.	PUNCT
ejpam-4706	65	5	.	.	PUNCT
ejpam-4706	65	6	.	.	PUNCT
ejpam-4706	65	7	.	.	PUNCT
ejpam-4706	66	1	.	.	PUNCT
ejpam-4706	67	1	.	.	PUNCT
ejpam-4706	68	1	1	1	NUM
ejpam-4706	68	2	2	2	NUM
ejpam-4706	68	3	0	0	NUM
ejpam-4706	68	4	0	0	NUM
ejpam-4706	68	5	.	.	PUNCT
ejpam-4706	68	6	.	.	PUNCT
ejpam-4706	68	7	.	.	PUNCT
ejpam-4706	69	1	1	1	NUM
ejpam-4706	69	2	2	2	NUM
ejpam-4706	69	3	0	0	NUM
ejpam-4706	69	4			NOUN
ejpam-4706	69	5	.	.	PUNCT
ejpam-4706	70	1	then	then	ADV
ejpam-4706	70	2	w(tn	w(tn	NUM
ejpam-4706	70	3	)	)	PUNCT
ejpam-4706	70	4	=	=	SYM
ejpam-4706	70	5	cos	cos	PROPN
ejpam-4706	70	6	(	(	PUNCT
ejpam-4706	70	7	π	π	PROPN
ejpam-4706	70	8	n+	n+	ADP
ejpam-4706	70	9	1	1	NUM
ejpam-4706	70	10	)	)	PUNCT
ejpam-4706	70	11	.	.	PUNCT
ejpam-4706	71	1	the	the	DET
ejpam-4706	71	2	following	follow	VERB
ejpam-4706	71	3	lemmas	lemmas	PROPN
ejpam-4706	71	4	can	can	AUX
ejpam-4706	71	5	be	be	AUX
ejpam-4706	71	6	found	find	VERB
ejpam-4706	71	7	in	in	ADP
ejpam-4706	71	8	[	[	X
ejpam-4706	71	9	4	4	NUM
ejpam-4706	71	10	,	,	PUNCT
ejpam-4706	71	11	6	6	NUM
ejpam-4706	71	12	]	]	PUNCT
ejpam-4706	71	13	and	and	CCONJ
ejpam-4706	71	14	[	[	X
ejpam-4706	71	15	1	1	NUM
ejpam-4706	71	16	]	]	PUNCT
ejpam-4706	71	17	,	,	PUNCT
ejpam-4706	71	18	respectively	respectively	ADV
ejpam-4706	71	19	.	.	PUNCT
ejpam-4706	72	1	lemma	lemma	PROPN
ejpam-4706	72	2	3	3	X
ejpam-4706	72	3	.	.	PUNCT
ejpam-4706	73	1	let	let	VERB
ejpam-4706	73	2	a	a	PRON
ejpam-4706	73	3	=	=	PUNCT
ejpam-4706	73	4	[	[	PUNCT
ejpam-4706	73	5	a	a	PRON
ejpam-4706	73	6	b	b	NOUN
ejpam-4706	73	7	c	c	NOUN
ejpam-4706	73	8	d	d	NOUN
ejpam-4706	73	9	]	]	PUNCT
ejpam-4706	73	10	.	.	PUNCT
ejpam-4706	74	1	then	then	ADV
ejpam-4706	74	2	the	the	DET
ejpam-4706	74	3	spectral	spectral	ADJ
ejpam-4706	74	4	radius	radius	NOUN
ejpam-4706	74	5	of	of	ADP
ejpam-4706	74	6	a	a	PRON
ejpam-4706	74	7	is	be	AUX
ejpam-4706	74	8	r(a	r(a	X
ejpam-4706	74	9	)	)	PUNCT
ejpam-4706	74	10	=	=	SYM
ejpam-4706	74	11	1	1	NUM
ejpam-4706	74	12	2	2	NUM
ejpam-4706	74	13	(	(	PUNCT
ejpam-4706	74	14	a+	a+	X
ejpam-4706	74	15	d+	d+	NOUN
ejpam-4706	74	16	√	√	NUM
ejpam-4706	74	17	(	(	PUNCT
ejpam-4706	74	18	a−	a−	NOUN
ejpam-4706	74	19	d)2	d)2	NOUN
ejpam-4706	74	20	+	+	CCONJ
ejpam-4706	74	21	4bc	4bc	ADJ
ejpam-4706	74	22	)	)	PUNCT
ejpam-4706	74	23	.	.	PUNCT
ejpam-4706	75	1	lemma	lemma	PROPN
ejpam-4706	75	2	4	4	X
ejpam-4706	75	3	.	.	PUNCT
ejpam-4706	76	1	let	let	VERB
ejpam-4706	76	2	t	t	NOUN
ejpam-4706	76	3	=	=	PUNCT
ejpam-4706	77	1	[	[	X
ejpam-4706	77	2	tij	tij	X
ejpam-4706	77	3	]	]	PUNCT
ejpam-4706	77	4	∈	∈	PROPN
ejpam-4706	77	5	mn(c	mn(c	X
ejpam-4706	77	6	)	)	PUNCT
ejpam-4706	77	7	with	with	ADP
ejpam-4706	77	8	tkm	tkm	PROPN
ejpam-4706	77	9	∈	∈	PROPN
ejpam-4706	77	10	mkm(c	mkm(c	PROPN
ejpam-4706	77	11	)	)	PUNCT
ejpam-4706	77	12	.	.	PUNCT
ejpam-4706	78	1	then	then	ADV
ejpam-4706	78	2	w(t	w(t	PROPN
ejpam-4706	78	3	)	)	PUNCT
ejpam-4706	78	4	≤	≤	NOUN
ejpam-4706	78	5	1	1	NUM
ejpam-4706	78	6	2	2	NUM
ejpam-4706	78	7	n∑	n∑	NOUN
ejpam-4706	78	8	k=1	k=1	NOUN
ejpam-4706	78	9	w(tkk	w(tkk	NOUN
ejpam-4706	78	10	)	)	PUNCT
ejpam-4706	78	11	+	+	NUM
ejpam-4706	78	12	√√√√√w2(tkk	√√√√√w2(tkk	NOUN
ejpam-4706	78	13	)	)	PUNCT
ejpam-4706	79	1	+	+	CCONJ
ejpam-4706	79	2	n∑	n∑	NOUN
ejpam-4706	79	3	m=1	m=1	X
ejpam-4706	79	4	k	k	PROPN
ejpam-4706	79	5	̸=m	̸=m	PROPN
ejpam-4706	79	6	∥tkm∥2	∥tkm∥2	PROPN
ejpam-4706	79	7			PROPN
ejpam-4706	79	8	.	.	PUNCT
ejpam-4706	80	1	lemma	lemma	PROPN
ejpam-4706	80	2	5	5	X
ejpam-4706	80	3	.	.	PUNCT
ejpam-4706	80	4	let	let	VERB
ejpam-4706	80	5	a	a	PRON
ejpam-4706	80	6	=	=	PUNCT
ejpam-4706	80	7	[	[	PUNCT
ejpam-4706	80	8	a	a	PRON
ejpam-4706	80	9	b	b	NOUN
ejpam-4706	80	10	c	c	NOUN
ejpam-4706	80	11	d	d	NOUN
ejpam-4706	80	12	]	]	PUNCT
ejpam-4706	80	13	.	.	PUNCT
ejpam-4706	81	1	then	then	ADV
ejpam-4706	81	2	the	the	DET
ejpam-4706	81	3	spectral	spectral	ADJ
ejpam-4706	81	4	norm	norm	NOUN
ejpam-4706	81	5	of	of	ADP
ejpam-4706	81	6	a	a	PRON
ejpam-4706	81	7	is	be	AUX
ejpam-4706	81	8	∥a∥	∥a∥	NOUN
ejpam-4706	81	9	=	=	PUNCT
ejpam-4706	81	10	[	[	PUNCT
ejpam-4706	81	11	1	1	NUM
ejpam-4706	81	12	2	2	NUM
ejpam-4706	81	13	(	(	PUNCT
ejpam-4706	81	14	|a|2	|a|2	PROPN
ejpam-4706	81	15	+	+	CCONJ
ejpam-4706	81	16	|b|2	|b|2	PROPN
ejpam-4706	81	17	+	+	CCONJ
ejpam-4706	81	18	|c|2	|c|2	PROPN
ejpam-4706	81	19	+	+	NUM
ejpam-4706	81	20	|d|2	|d|2	NOUN
ejpam-4706	81	21	+	+	CCONJ
ejpam-4706	81	22	√	√	PROPN
ejpam-4706	81	23	(	(	PUNCT
ejpam-4706	81	24	|a|2	|a|2	PROPN
ejpam-4706	81	25	+	+	PROPN
ejpam-4706	81	26	|c|2	|c|2	PROPN
ejpam-4706	81	27	−	−	NOUN
ejpam-4706	81	28	|b|2	|b|2	ADJ
ejpam-4706	81	29	−	−	NOUN
ejpam-4706	81	30	|d|2)2	|d|2)2	NOUN
ejpam-4706	81	31	+	+	NUM
ejpam-4706	81	32	4|ab̄+	4|ab̄+	NOUN
ejpam-4706	81	33	cd̄|2	cd̄|2	NOUN
ejpam-4706	81	34	)	)	PUNCT
ejpam-4706	81	35	1	1	NUM
ejpam-4706	81	36	2	2	NUM
ejpam-4706	81	37	]	]	PUNCT
ejpam-4706	81	38	.	.	PUNCT
ejpam-4706	82	1	now	now	ADV
ejpam-4706	82	2	,	,	PUNCT
ejpam-4706	82	3	we	we	PRON
ejpam-4706	82	4	introduce	introduce	VERB
ejpam-4706	82	5	our	our	PRON
ejpam-4706	82	6	first	first	ADJ
ejpam-4706	82	7	estimate	estimate	NOUN
ejpam-4706	82	8	for	for	ADP
ejpam-4706	82	9	the	the	DET
ejpam-4706	82	10	numerical	numerical	ADJ
ejpam-4706	82	11	radius	radius	NOUN
ejpam-4706	82	12	of	of	ADP
ejpam-4706	82	13	f	f	PROPN
ejpam-4706	82	14	2(p	2(p	NUM
ejpam-4706	82	15	)	)	PUNCT
ejpam-4706	82	16	.	.	PUNCT
ejpam-4706	83	1	a.	a.	PROPN
ejpam-4706	83	2	burqan	burqan	PROPN
ejpam-4706	83	3	et	et	PROPN
ejpam-4706	83	4	al	al	PROPN
ejpam-4706	83	5	.	.	PUNCT
ejpam-4706	83	6	/	/	SYM
ejpam-4706	83	7	eur	eur	PROPN
ejpam-4706	83	8	.	.	PUNCT
ejpam-4706	84	1	j.	j.	PROPN
ejpam-4706	84	2	pure	pure	PROPN
ejpam-4706	84	3	appl	appl	PROPN
ejpam-4706	84	4	.	.	PROPN
ejpam-4706	84	5	math	math	PROPN
ejpam-4706	84	6	,	,	PUNCT
ejpam-4706	84	7	16	16	NUM
ejpam-4706	84	8	(	(	PUNCT
ejpam-4706	84	9	2	2	NUM
ejpam-4706	84	10	)	)	PUNCT
ejpam-4706	84	11	(	(	PUNCT
ejpam-4706	84	12	2023	2023	NUM
ejpam-4706	84	13	)	)	PUNCT
ejpam-4706	84	14	,	,	PUNCT
ejpam-4706	84	15	806	806	NUM
ejpam-4706	84	16	-	-	SYM
ejpam-4706	84	17	818	818	NUM
ejpam-4706	84	18	809	809	NUM
ejpam-4706	84	19	theorem	theorem	NOUN
ejpam-4706	84	20	1	1	NUM
ejpam-4706	84	21	.	.	PUNCT
ejpam-4706	85	1	an	an	DET
ejpam-4706	85	2	upper	upper	ADJ
ejpam-4706	85	3	bound	bound	NOUN
ejpam-4706	85	4	of	of	ADP
ejpam-4706	85	5	the	the	DET
ejpam-4706	85	6	numerical	numerical	ADJ
ejpam-4706	85	7	radius	radius	NOUN
ejpam-4706	85	8	of	of	ADP
ejpam-4706	85	9	f	f	PROPN
ejpam-4706	85	10	2(p	2(p	NUM
ejpam-4706	85	11	)	)	PUNCT
ejpam-4706	85	12	can	can	AUX
ejpam-4706	85	13	be	be	AUX
ejpam-4706	85	14	stated	state	VERB
ejpam-4706	85	15	as	as	SCONJ
ejpam-4706	85	16	follows	follow	VERB
ejpam-4706	85	17	:	:	PUNCT
ejpam-4706	85	18	w(f	w(f	ADJ
ejpam-4706	85	19	2(p	2(p	NUM
ejpam-4706	85	20	)	)	PUNCT
ejpam-4706	85	21	)	)	PUNCT
ejpam-4706	86	1	≤1	≤1	PROPN
ejpam-4706	86	2	4	4	NUM
ejpam-4706	86	3	(	(	PUNCT
ejpam-4706	86	4	w(bm	w(bm	PROPN
ejpam-4706	86	5	)	)	PUNCT
ejpam-4706	86	6	+	+	CCONJ
ejpam-4706	86	7	w(am−1	w(am−1	PUNCT
ejpam-4706	86	8	)	)	PUNCT
ejpam-4706	87	1	+	+	CCONJ
ejpam-4706	87	2	γ	γ	X
ejpam-4706	87	3	)	)	PUNCT
ejpam-4706	87	4	+	+	NUM
ejpam-4706	87	5	cos2	cos2	NOUN
ejpam-4706	87	6	(	(	PUNCT
ejpam-4706	87	7	π	π	NOUN
ejpam-4706	87	8	mn−	mn−	PROPN
ejpam-4706	87	9	1	1	NUM
ejpam-4706	87	10	)	)	PUNCT
ejpam-4706	87	11	+	+	CCONJ
ejpam-4706	87	12	1	1	NUM
ejpam-4706	87	13	2	2	NUM
ejpam-4706	87	14	+	+	CCONJ
ejpam-4706	87	15	1	1	NUM
ejpam-4706	87	16	2	2	NUM
ejpam-4706	87	17	√	√	NUM
ejpam-4706	87	18	1	1	NUM
ejpam-4706	87	19	4	4	NUM
ejpam-4706	87	20	(	(	PUNCT
ejpam-4706	87	21	w	w	PROPN
ejpam-4706	87	22	(	(	PUNCT
ejpam-4706	87	23	bm	bm	PROPN
ejpam-4706	87	24	)	)	PUNCT
ejpam-4706	87	25	+	+	CCONJ
ejpam-4706	87	26	w	w	PROPN
ejpam-4706	87	27	(	(	PUNCT
ejpam-4706	87	28	am−1	am−1	PROPN
ejpam-4706	87	29	)	)	PUNCT
ejpam-4706	87	30	+	+	NUM
ejpam-4706	87	31	γ)2	γ)2	NOUN
ejpam-4706	87	32	+	+	CCONJ
ejpam-4706	87	33	1	1	NUM
ejpam-4706	87	34	2	2	NUM
ejpam-4706	87	35	(	(	PUNCT
ejpam-4706	87	36	α+	α+	X
ejpam-4706	87	37	η	η	PROPN
ejpam-4706	87	38	+	+	NOUN
ejpam-4706	87	39	√	√	PROPN
ejpam-4706	87	40	(	(	PUNCT
ejpam-4706	87	41	α−	α−	ADP
ejpam-4706	87	42	η)2	η)2	NOUN
ejpam-4706	87	43	+	+	CCONJ
ejpam-4706	87	44	4β2	4β2	NUM
ejpam-4706	87	45	)	)	PUNCT
ejpam-4706	88	1	+	+	CCONJ
ejpam-4706	88	2	1	1	NUM
ejpam-4706	88	3	2	2	NUM
ejpam-4706	88	4	√	√	NUM
ejpam-4706	88	5	(	(	PUNCT
ejpam-4706	88	6	2	2	NUM
ejpam-4706	88	7	cos2	cos2	NOUN
ejpam-4706	88	8	(	(	PUNCT
ejpam-4706	88	9	π	π	NOUN
ejpam-4706	88	10	mn−	mn−	PROPN
ejpam-4706	88	11	1	1	NUM
ejpam-4706	88	12	)	)	PUNCT
ejpam-4706	88	13	+	+	CCONJ
ejpam-4706	88	14	1	1	NUM
ejpam-4706	88	15	)	)	SYM
ejpam-4706	88	16	2	2	NUM
ejpam-4706	88	17	+	+	CCONJ
ejpam-4706	88	18	1	1	NUM
ejpam-4706	88	19	2	2	NUM
ejpam-4706	88	20	(	(	PUNCT
ejpam-4706	88	21	α+	α+	X
ejpam-4706	88	22	η	η	PROPN
ejpam-4706	88	23	+	+	NOUN
ejpam-4706	88	24	√	√	PROPN
ejpam-4706	88	25	(	(	PUNCT
ejpam-4706	88	26	α−	α−	ADP
ejpam-4706	88	27	η)2	η)2	NOUN
ejpam-4706	88	28	+	+	CCONJ
ejpam-4706	88	29	4β2	4β2	NUM
ejpam-4706	88	30	)	)	PUNCT
ejpam-4706	88	31	,	,	PUNCT
ejpam-4706	88	32	where	where	SCONJ
ejpam-4706	88	33	α	α	PROPN
ejpam-4706	88	34	=	=	PROPN
ejpam-4706	88	35	w2	w2	PROPN
ejpam-4706	88	36	(	(	PUNCT
ejpam-4706	88	37	t	t	PROPN
ejpam-4706	88	38	(	(	PUNCT
ejpam-4706	88	39	i	i	NOUN
ejpam-4706	88	40	,	,	PUNCT
ejpam-4706	88	41	bm−2	bm−2	PROPN
ejpam-4706	88	42	)	)	PUNCT
ejpam-4706	88	43	)	)	PUNCT
ejpam-4706	89	1	+	+	CCONJ
ejpam-4706	89	2	1	1	NUM
ejpam-4706	89	3	4	4	NUM
ejpam-4706	89	4	m−3∑	m−3∑	NUM
ejpam-4706	89	5	i=1	i=1	PROPN
ejpam-4706	89	6	∥bi∥2	∥bi∥2	PROPN
ejpam-4706	89	7	,	,	PUNCT
ejpam-4706	89	8	η	η	PROPN
ejpam-4706	89	9	=	=	SYM
ejpam-4706	89	10	w2(t	w2(t	PROPN
ejpam-4706	89	11	(	(	PUNCT
ejpam-4706	89	12	i	i	PROPN
ejpam-4706	89	13	,	,	PUNCT
ejpam-4706	89	14	am−3	am−3	PROPN
ejpam-4706	89	15	)	)	PUNCT
ejpam-4706	89	16	)	)	PUNCT
ejpam-4706	90	1	+	+	CCONJ
ejpam-4706	90	2	1	1	NUM
ejpam-4706	90	3	4	4	NUM
ejpam-4706	90	4	∥am−2∥2	∥am−2∥2	ADJ
ejpam-4706	90	5	+	+	CCONJ
ejpam-4706	90	6	1	1	NUM
ejpam-4706	90	7	4	4	NUM
ejpam-4706	90	8	m−4∑	m−4∑	NOUN
ejpam-4706	90	9	i=1	i=1	PRON
ejpam-4706	90	10	∥ai∥2	∥ai∥2	PROPN
ejpam-4706	90	11	,	,	PUNCT
ejpam-4706	90	12	β	β	X
ejpam-4706	90	13	=	=	SYM
ejpam-4706	90	14	w	w	PROPN
ejpam-4706	90	15	(	(	PUNCT
ejpam-4706	90	16	t	t	PROPN
ejpam-4706	90	17	(	(	PUNCT
ejpam-4706	90	18	bm−2	bm−2	PROPN
ejpam-4706	90	19	,	,	PUNCT
ejpam-4706	90	20	i	i	NOUN
ejpam-4706	90	21	)	)	PUNCT
ejpam-4706	90	22	)	)	PUNCT
ejpam-4706	91	1	∥am−2∥	∥am−2∥	ADP
ejpam-4706	91	2	2	2	NUM
ejpam-4706	92	1	+	+	CCONJ
ejpam-4706	92	2	w	w	PROPN
ejpam-4706	92	3	(	(	PUNCT
ejpam-4706	92	4	t	t	PROPN
ejpam-4706	92	5	(	(	PUNCT
ejpam-4706	92	6	am−3	am−3	PROPN
ejpam-4706	92	7	,	,	PUNCT
ejpam-4706	92	8	i	i	NOUN
ejpam-4706	92	9	)	)	PUNCT
ejpam-4706	92	10	)	)	PUNCT
ejpam-4706	93	1	∥bm−3∥	∥bm−3∥	ADP
ejpam-4706	93	2	2	2	NUM
ejpam-4706	94	1	+	+	CCONJ
ejpam-4706	94	2	1	1	NUM
ejpam-4706	94	3	4	4	NUM
ejpam-4706	94	4	m−4∑	m−4∑	NOUN
ejpam-4706	94	5	i=1	i=1	PROPN
ejpam-4706	94	6	(	(	PUNCT
ejpam-4706	94	7	∥ai∥∥bi∥	∥ai∥∥bi∥	NOUN
ejpam-4706	94	8	)	)	PUNCT
ejpam-4706	94	9	,	,	PUNCT
ejpam-4706	94	10	γ	γ	X
ejpam-4706	94	11	=	=	SYM
ejpam-4706	94	12	√	√	PROPN
ejpam-4706	94	13	(	(	PUNCT
ejpam-4706	94	14	w	w	PROPN
ejpam-4706	94	15	(	(	PUNCT
ejpam-4706	94	16	bm)−	bm)−	NOUN
ejpam-4706	94	17	w	w	PROPN
ejpam-4706	94	18	(	(	PUNCT
ejpam-4706	94	19	am−1	am−1	PROPN
ejpam-4706	94	20	)	)	PUNCT
ejpam-4706	94	21	)	)	PUNCT
ejpam-4706	94	22	2	2	NUM
ejpam-4706	95	1	+	+	CCONJ
ejpam-4706	95	2	4w2	4w2	NUM
ejpam-4706	95	3	(	(	PUNCT
ejpam-4706	95	4	t	t	PROPN
ejpam-4706	95	5	(	(	PUNCT
ejpam-4706	95	6	bm−1,−am	bm−1,−am	PROPN
ejpam-4706	95	7	)	)	PUNCT
ejpam-4706	95	8	)	)	PUNCT
ejpam-4706	95	9	.	.	PUNCT
ejpam-4706	96	1	proof	proof	NOUN
ejpam-4706	96	2	.	.	PUNCT
ejpam-4706	97	1	for	for	ADP
ejpam-4706	97	2	any	any	DET
ejpam-4706	97	3	two	two	NUM
ejpam-4706	97	4	matrices	matrix	NOUN
ejpam-4706	97	5	,	,	PUNCT
ejpam-4706	97	6	c	c	X
ejpam-4706	97	7	,	,	PUNCT
ejpam-4706	97	8	d	d	PROPN
ejpam-4706	97	9	∈	∈	PROPN
ejpam-4706	97	10	mn(c	mn(c	X
ejpam-4706	97	11	)	)	PUNCT
ejpam-4706	97	12	,	,	PUNCT
ejpam-4706	97	13	let	let	VERB
ejpam-4706	97	14	t	t	PROPN
ejpam-4706	97	15	(	(	PUNCT
ejpam-4706	97	16	c	c	X
ejpam-4706	97	17	,	,	PUNCT
ejpam-4706	97	18	d	d	NOUN
ejpam-4706	97	19	)	)	PUNCT
ejpam-4706	97	20	=	=	NOUN
ejpam-4706	98	1	[	[	PUNCT
ejpam-4706	98	2	0	0	NUM
ejpam-4706	98	3	c	c	NOUN
ejpam-4706	98	4	d	d	NOUN
ejpam-4706	98	5	0	0	NUM
ejpam-4706	98	6	]	]	PUNCT
ejpam-4706	98	7	.	.	PUNCT
ejpam-4706	99	1	by	by	ADP
ejpam-4706	99	2	applying	apply	VERB
ejpam-4706	99	3	lemma	lemma	PROPN
ejpam-4706	99	4	1	1	NUM
ejpam-4706	99	5	on	on	ADP
ejpam-4706	99	6	f	f	PROPN
ejpam-4706	99	7	2(p	2(p	NUM
ejpam-4706	99	8	)	)	PUNCT
ejpam-4706	99	9	,	,	PUNCT
ejpam-4706	99	10	we	we	PRON
ejpam-4706	99	11	have	have	VERB
ejpam-4706	99	12	w(f	w(f	PROPN
ejpam-4706	99	13	2(p	2(p	NUM
ejpam-4706	99	14	)	)	PUNCT
ejpam-4706	99	15	)	)	PUNCT
ejpam-4706	99	16	≤	≤	PROPN
ejpam-4706	100	1	w(r	w(r	PROPN
ejpam-4706	100	2	)	)	PUNCT
ejpam-4706	100	3	,	,	PUNCT
ejpam-4706	100	4	where	where	SCONJ
ejpam-4706	100	5	r	r	NOUN
ejpam-4706	100	6	is	be	AUX
ejpam-4706	100	7	mn×mn	mn×mn	ADJ
ejpam-4706	100	8	matrix	matrix	NOUN
ejpam-4706	100	9	given	give	VERB
ejpam-4706	100	10	by	by	PROPN
ejpam-4706	100	11	w(bm	w(bm	PROPN
ejpam-4706	100	12	)	)	PUNCT
ejpam-4706	100	13	w(t	w(t	PROPN
ejpam-4706	100	14	(	(	PUNCT
ejpam-4706	100	15	bm−1,−am	bm−1,−am	PROPN
ejpam-4706	100	16	)	)	PUNCT
ejpam-4706	100	17	)	)	PUNCT
ejpam-4706	101	1	w(t	w(t	PROPN
ejpam-4706	101	2	(	(	PUNCT
ejpam-4706	101	3	bm−2	bm−2	PROPN
ejpam-4706	101	4	,	,	PUNCT
ejpam-4706	101	5	i	i	NOUN
ejpam-4706	101	6	)	)	PUNCT
ejpam-4706	101	7	)	)	PUNCT
ejpam-4706	101	8	w(t	w(t	PROPN
ejpam-4706	101	9	(	(	PUNCT
ejpam-4706	101	10	bm−3	bm−3	PROPN
ejpam-4706	101	11	,	,	PUNCT
ejpam-4706	101	12	0	0	NUM
ejpam-4706	101	13	)	)	PUNCT
ejpam-4706	101	14	)	)	PUNCT
ejpam-4706	102	1	w(t	w(t	PROPN
ejpam-4706	102	2	(	(	PUNCT
ejpam-4706	102	3	bm−4	bm−4	PROPN
ejpam-4706	102	4	,	,	PUNCT
ejpam-4706	102	5	0	0	NUM
ejpam-4706	102	6	)	)	PUNCT
ejpam-4706	102	7	)	)	PUNCT
ejpam-4706	102	8	.	.	PUNCT
ejpam-4706	102	9	.	.	PUNCT
ejpam-4706	102	10	.	.	PUNCT
ejpam-4706	103	1	w(t	w(t	PROPN
ejpam-4706	103	2	(	(	PUNCT
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ejpam-4706	104	15	w(am−1	w(am−1	PUNCT
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ejpam-4706	104	17	w(t	w(t	PROPN
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ejpam-4706	104	20	,	,	PUNCT
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ejpam-4706	105	2	(	(	PUNCT
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ejpam-4706	106	2	(	(	PUNCT
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ejpam-4706	108	2	(	(	PUNCT
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ejpam-4706	109	2	(	(	PUNCT
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ejpam-4706	110	3	i	i	PROPN
ejpam-4706	110	4	,	,	PUNCT
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ejpam-4706	110	7	w(t	w(t	PUNCT
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ejpam-4706	111	3	w(t	w(t	PROPN
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ejpam-4706	117	2	(	(	PUNCT
ejpam-4706	117	3	i	i	PROPN
ejpam-4706	117	4	,	,	PUNCT
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ejpam-4706	118	3	w(t	w(t	PROPN
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ejpam-4706	125	5	.	.	PUNCT
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ejpam-4706	128	13	.	.	PUNCT
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ejpam-4706	129	10	0,−a3	0,−a3	NOUN
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ejpam-4706	130	1	w(t	w(t	PROPN
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ejpam-4706	133	3	w(t	w(t	PROPN
ejpam-4706	133	4	(	(	PUNCT
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ejpam-4706	135	9	(	(	PUNCT
ejpam-4706	135	10	0,−a2	0,−a2	NOUN
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ejpam-4706	137	1	w(t	w(t	PROPN
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ejpam-4706	138	1	w(t	w(t	PROPN
ejpam-4706	138	2	(	(	PUNCT
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ejpam-4706	139	2	(	(	PUNCT
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ejpam-4706	140	1	w(0	w(0	PROPN
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ejpam-4706	140	3	w(t	w(t	PROPN
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ejpam-4706	141	10	0,−a1	0,−a1	NUM
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ejpam-4706	145	1	w(t	w(t	PROPN
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ejpam-4706	145	8	w(t	w(t	PROPN
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ejpam-4706	146	3			NUM
ejpam-4706	146	4			NOUN
ejpam-4706	146	5	w(bm	w(bm	PROPN
ejpam-4706	146	6	)	)	PUNCT
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ejpam-4706	146	8	(	(	PUNCT
ejpam-4706	146	9	bm−1,−am	bm−1,−am	PROPN
ejpam-4706	146	10	)	)	PUNCT
ejpam-4706	146	11	)	)	PUNCT
ejpam-4706	147	1	w(t	w(t	PROPN
ejpam-4706	147	2	(	(	PUNCT
ejpam-4706	147	3	bm−2	bm−2	PROPN
ejpam-4706	147	4	,	,	PUNCT
ejpam-4706	147	5	i	i	NOUN
ejpam-4706	147	6	)	)	PUNCT
ejpam-4706	147	7	)	)	PUNCT
ejpam-4706	148	1	w(t	w(t	PROPN
ejpam-4706	148	2	(	(	PUNCT
ejpam-4706	148	3	bm−3	bm−3	PROPN
ejpam-4706	148	4	,	,	PUNCT
ejpam-4706	148	5	0	0	NUM
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ejpam-4706	148	7	)	)	PUNCT
ejpam-4706	148	8	w(t	w(t	PROPN
ejpam-4706	148	9	(	(	PUNCT
ejpam-4706	148	10	bm−4	bm−4	PROPN
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ejpam-4706	148	15	.	.	PUNCT
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ejpam-4706	148	17	.	.	PUNCT
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ejpam-4706	149	2	(	(	PUNCT
ejpam-4706	149	3	b3	b3	PROPN
ejpam-4706	149	4	,	,	PUNCT
ejpam-4706	149	5	0	0	NUM
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ejpam-4706	149	7	)	)	PUNCT
ejpam-4706	149	8	w(t	w(t	PROPN
ejpam-4706	149	9	(	(	PUNCT
ejpam-4706	149	10	b2	b2	NOUN
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ejpam-4706	149	14	)	)	PUNCT
ejpam-4706	150	1	w(t	w(t	PROPN
ejpam-4706	150	2	(	(	PUNCT
ejpam-4706	150	3	b1	b1	NOUN
ejpam-4706	150	4	,	,	PUNCT
ejpam-4706	150	5	0	0	NUM
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ejpam-4706	150	7	)	)	PUNCT
ejpam-4706	150	8	w(t	w(t	PROPN
ejpam-4706	150	9	(	(	PUNCT
ejpam-4706	150	10	−am	−am	PROPN
ejpam-4706	150	11	,	,	PUNCT
ejpam-4706	150	12	bm−1	bm−1	NOUN
ejpam-4706	150	13	)	)	PUNCT
ejpam-4706	150	14	)	)	PUNCT
ejpam-4706	150	15	w(am−1	w(am−1	PUNCT
ejpam-4706	150	16	)	)	PUNCT
ejpam-4706	150	17	w(t	w(t	PROPN
ejpam-4706	150	18	(	(	PUNCT
ejpam-4706	150	19	0	0	NUM
ejpam-4706	150	20	,	,	PUNCT
ejpam-4706	150	21	am−2	am−2	NOUN
ejpam-4706	150	22	)	)	PUNCT
ejpam-4706	150	23	)	)	PUNCT
ejpam-4706	151	1	w(t	w(t	PROPN
ejpam-4706	151	2	(	(	PUNCT
ejpam-4706	151	3	am−3	am−3	PROPN
ejpam-4706	151	4	,	,	PUNCT
ejpam-4706	151	5	i	i	NOUN
ejpam-4706	151	6	)	)	PUNCT
ejpam-4706	151	7	)	)	PUNCT
ejpam-4706	152	1	w(t	w(t	PROPN
ejpam-4706	152	2	(	(	PUNCT
ejpam-4706	152	3	am−4	am−4	ADV
ejpam-4706	152	4	,	,	PUNCT
ejpam-4706	152	5	0	0	NUM
ejpam-4706	152	6	)	)	PUNCT
ejpam-4706	152	7	)	)	PUNCT
ejpam-4706	152	8	.	.	PUNCT
ejpam-4706	152	9	.	.	PUNCT
ejpam-4706	152	10	.	.	PUNCT
ejpam-4706	153	1	w(t	w(t	PROPN
ejpam-4706	153	2	(	(	PUNCT
ejpam-4706	153	3	−a3	−a3	PROPN
ejpam-4706	153	4	,	,	PUNCT
ejpam-4706	153	5	0	0	NUM
ejpam-4706	153	6	)	)	PUNCT
ejpam-4706	153	7	)	)	PUNCT
ejpam-4706	154	1	w(t	w(t	PROPN
ejpam-4706	154	2	(	(	PUNCT
ejpam-4706	154	3	−a2	−a2	PROPN
ejpam-4706	154	4	,	,	PUNCT
ejpam-4706	154	5	0	0	NUM
ejpam-4706	154	6	)	)	PUNCT
ejpam-4706	154	7	)	)	PUNCT
ejpam-4706	155	1	w(t	w(t	PROPN
ejpam-4706	155	2	(	(	PUNCT
ejpam-4706	155	3	−a1	−a1	PROPN
ejpam-4706	155	4	,	,	PUNCT
ejpam-4706	155	5	0	0	NUM
ejpam-4706	155	6	)	)	PUNCT
ejpam-4706	155	7	)	)	PUNCT
ejpam-4706	156	1	w(t	w(t	PROPN
ejpam-4706	156	2	(	(	PUNCT
ejpam-4706	156	3	i	i	PROPN
ejpam-4706	156	4	,	,	PUNCT
ejpam-4706	156	5	bm−2	bm−2	PROPN
ejpam-4706	156	6	)	)	PUNCT
ejpam-4706	156	7	w(t	w(t	PUNCT
ejpam-4706	156	8	(	(	PUNCT
ejpam-4706	156	9	0	0	NUM
ejpam-4706	156	10	,	,	PUNCT
ejpam-4706	156	11	am−2	am−2	NOUN
ejpam-4706	156	12	)	)	PUNCT
ejpam-4706	156	13	)	)	PUNCT
ejpam-4706	157	1	w(0	w(0	PROPN
ejpam-4706	157	2	)	)	PUNCT
ejpam-4706	157	3	w(t	w(t	PROPN
ejpam-4706	157	4	(	(	PUNCT
ejpam-4706	157	5	0	0	NUM
ejpam-4706	157	6	,	,	PUNCT
ejpam-4706	157	7	0	0	NUM
ejpam-4706	157	8	)	)	PUNCT
ejpam-4706	157	9	)	)	PUNCT
ejpam-4706	158	1	w(t	w(t	PROPN
ejpam-4706	158	2	(	(	PUNCT
ejpam-4706	158	3	0	0	NUM
ejpam-4706	158	4	,	,	PUNCT
ejpam-4706	158	5	i	i	NOUN
ejpam-4706	158	6	)	)	PUNCT
ejpam-4706	158	7	)	)	PUNCT
ejpam-4706	158	8	.	.	PUNCT
ejpam-4706	158	9	.	.	PUNCT
ejpam-4706	158	10	.	.	PUNCT
ejpam-4706	159	1	w(t	w(t	PROPN
ejpam-4706	159	2	(	(	PUNCT
ejpam-4706	159	3	0	0	NUM
ejpam-4706	159	4	,	,	PUNCT
ejpam-4706	159	5	0	0	NUM
ejpam-4706	159	6	)	)	PUNCT
ejpam-4706	159	7	)	)	PUNCT
ejpam-4706	160	1	w(t	w(t	PROPN
ejpam-4706	160	2	(	(	PUNCT
ejpam-4706	160	3	0	0	NUM
ejpam-4706	160	4	,	,	PUNCT
ejpam-4706	160	5	0	0	NUM
ejpam-4706	160	6	)	)	PUNCT
ejpam-4706	160	7	)	)	PUNCT
ejpam-4706	161	1	w(t	w(t	PROPN
ejpam-4706	161	2	(	(	PUNCT
ejpam-4706	161	3	0	0	NUM
ejpam-4706	161	4	,	,	PUNCT
ejpam-4706	161	5	0	0	NUM
ejpam-4706	161	6	)	)	PUNCT
ejpam-4706	161	7	)	)	PUNCT
ejpam-4706	162	1	w(t	w(t	PROPN
ejpam-4706	162	2	(	(	PUNCT
ejpam-4706	162	3	0	0	NUM
ejpam-4706	162	4	,	,	PUNCT
ejpam-4706	162	5	bm−3	bm−3	NOUN
ejpam-4706	162	6	)	)	PUNCT
ejpam-4706	162	7	)	)	PUNCT
ejpam-4706	163	1	w(t	w(t	PROPN
ejpam-4706	163	2	(	(	PUNCT
ejpam-4706	163	3	i	i	PROPN
ejpam-4706	163	4	,	,	PUNCT
ejpam-4706	163	5	am−3	am−3	PROPN
ejpam-4706	163	6	)	)	PUNCT
ejpam-4706	163	7	)	)	PUNCT
ejpam-4706	163	8	w(t	w(t	PROPN
ejpam-4706	163	9	(	(	PUNCT
ejpam-4706	163	10	0	0	NUM
ejpam-4706	163	11	,	,	PUNCT
ejpam-4706	163	12	0	0	NUM
ejpam-4706	163	13	)	)	PUNCT
ejpam-4706	163	14	)	)	PUNCT
ejpam-4706	164	1	w(0	w(0	PROPN
ejpam-4706	164	2	)	)	PUNCT
ejpam-4706	164	3	w(t	w(t	PROPN
ejpam-4706	164	4	(	(	PUNCT
ejpam-4706	164	5	0	0	NUM
ejpam-4706	164	6	,	,	PUNCT
ejpam-4706	164	7	0	0	NUM
ejpam-4706	164	8	)	)	PUNCT
ejpam-4706	164	9	)	)	PUNCT
ejpam-4706	164	10	.	.	PUNCT
ejpam-4706	164	11	.	.	PUNCT
ejpam-4706	164	12	.	.	PUNCT
ejpam-4706	165	1	w(t	w(t	PROPN
ejpam-4706	165	2	(	(	PUNCT
ejpam-4706	165	3	0	0	NUM
ejpam-4706	165	4	,	,	PUNCT
ejpam-4706	165	5	0	0	NUM
ejpam-4706	165	6	)	)	PUNCT
ejpam-4706	165	7	)	)	PUNCT
ejpam-4706	166	1	w(t	w(t	PROPN
ejpam-4706	166	2	(	(	PUNCT
ejpam-4706	166	3	0	0	NUM
ejpam-4706	166	4	,	,	PUNCT
ejpam-4706	166	5	0	0	NUM
ejpam-4706	166	6	)	)	PUNCT
ejpam-4706	166	7	)	)	PUNCT
ejpam-4706	167	1	w(t	w(t	PROPN
ejpam-4706	167	2	(	(	PUNCT
ejpam-4706	167	3	0	0	NUM
ejpam-4706	167	4	,	,	PUNCT
ejpam-4706	167	5	0	0	NUM
ejpam-4706	167	6	)	)	PUNCT
ejpam-4706	167	7	)	)	PUNCT
ejpam-4706	168	1	w(t	w(t	PROPN
ejpam-4706	168	2	(	(	PUNCT
ejpam-4706	168	3	0	0	NUM
ejpam-4706	168	4	,	,	PUNCT
ejpam-4706	168	5	bm−4	bm−4	PROPN
ejpam-4706	168	6	)	)	PUNCT
ejpam-4706	168	7	)	)	PUNCT
ejpam-4706	169	1	w(t	w(t	PROPN
ejpam-4706	169	2	(	(	PUNCT
ejpam-4706	169	3	0	0	NUM
ejpam-4706	169	4	,	,	PUNCT
ejpam-4706	169	5	am−4	am−4	ADV
ejpam-4706	169	6	)	)	PUNCT
ejpam-4706	169	7	)	)	PUNCT
ejpam-4706	170	1	w(t	w(t	PROPN
ejpam-4706	170	2	(	(	PUNCT
ejpam-4706	170	3	i	i	NOUN
ejpam-4706	170	4	,	,	PUNCT
ejpam-4706	170	5	0	0	NUM
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ejpam-4706	170	7	)	)	PUNCT
ejpam-4706	170	8	w(t	w(t	PROPN
ejpam-4706	170	9	(	(	PUNCT
ejpam-4706	170	10	0	0	NUM
ejpam-4706	170	11	,	,	PUNCT
ejpam-4706	170	12	0	0	NUM
ejpam-4706	170	13	)	)	PUNCT
ejpam-4706	170	14	)	)	PUNCT
ejpam-4706	171	1	w(0	w(0	PROPN
ejpam-4706	171	2	)	)	PUNCT
ejpam-4706	171	3	.	.	PUNCT
ejpam-4706	171	4	.	.	PUNCT
ejpam-4706	171	5	.	.	PUNCT
ejpam-4706	172	1	w(t	w(t	PROPN
ejpam-4706	172	2	(	(	PUNCT
ejpam-4706	172	3	0	0	NUM
ejpam-4706	172	4	,	,	PUNCT
ejpam-4706	172	5	0	0	NUM
ejpam-4706	172	6	)	)	PUNCT
ejpam-4706	172	7	)	)	PUNCT
ejpam-4706	173	1	w(t	w(t	PROPN
ejpam-4706	173	2	(	(	PUNCT
ejpam-4706	173	3	0	0	NUM
ejpam-4706	173	4	,	,	PUNCT
ejpam-4706	173	5	0	0	NUM
ejpam-4706	173	6	)	)	PUNCT
ejpam-4706	173	7	)	)	PUNCT
ejpam-4706	174	1	w(t	w(t	PROPN
ejpam-4706	174	2	(	(	PUNCT
ejpam-4706	174	3	0	0	NUM
ejpam-4706	174	4	,	,	PUNCT
ejpam-4706	174	5	0	0	NUM
ejpam-4706	174	6	)	)	PUNCT
ejpam-4706	174	7	)	)	PUNCT
ejpam-4706	174	8	...	...	PUNCT
ejpam-4706	174	9	...	...	PUNCT
ejpam-4706	174	10	...	...	PUNCT
ejpam-4706	174	11	...	...	PUNCT
ejpam-4706	174	12	...	...	PUNCT
ejpam-4706	174	13	.	.	PUNCT
ejpam-4706	174	14	.	.	PUNCT
ejpam-4706	174	15	.	.	PUNCT
ejpam-4706	174	16	...	...	PUNCT
ejpam-4706	174	17	...	...	PUNCT
ejpam-4706	174	18	...	...	PUNCT
ejpam-4706	175	1	w(t	w(t	X
ejpam-4706	175	2	(	(	PUNCT
ejpam-4706	175	3	0	0	NUM
ejpam-4706	175	4	,	,	PUNCT
ejpam-4706	175	5	b3	b3	PROPN
ejpam-4706	175	6	)	)	PUNCT
ejpam-4706	175	7	)	)	PUNCT
ejpam-4706	175	8	w(t	w(t	PROPN
ejpam-4706	175	9	(	(	PUNCT
ejpam-4706	175	10	0,−a3	0,−a3	NOUN
ejpam-4706	175	11	)	)	PUNCT
ejpam-4706	175	12	)	)	PUNCT
ejpam-4706	176	1	w(t	w(t	PROPN
ejpam-4706	176	2	(	(	PUNCT
ejpam-4706	176	3	0	0	NUM
ejpam-4706	176	4	,	,	PUNCT
ejpam-4706	176	5	0	0	NUM
ejpam-4706	176	6	)	)	PUNCT
ejpam-4706	176	7	)	)	PUNCT
ejpam-4706	177	1	w(t	w(t	PROPN
ejpam-4706	177	2	(	(	PUNCT
ejpam-4706	177	3	0	0	NUM
ejpam-4706	177	4	,	,	PUNCT
ejpam-4706	177	5	0	0	NUM
ejpam-4706	177	6	)	)	PUNCT
ejpam-4706	177	7	)	)	PUNCT
ejpam-4706	178	1	w(t	w(t	PROPN
ejpam-4706	178	2	(	(	PUNCT
ejpam-4706	178	3	0	0	NUM
ejpam-4706	178	4	,	,	PUNCT
ejpam-4706	178	5	0	0	NUM
ejpam-4706	178	6	)	)	PUNCT
ejpam-4706	178	7	)	)	PUNCT
ejpam-4706	178	8	.	.	PUNCT
ejpam-4706	178	9	.	.	PUNCT
ejpam-4706	178	10	.	.	PUNCT
ejpam-4706	179	1	w(0	w(0	PROPN
ejpam-4706	179	2	)	)	PUNCT
ejpam-4706	179	3	w(t	w(t	PROPN
ejpam-4706	179	4	(	(	PUNCT
ejpam-4706	179	5	0	0	NUM
ejpam-4706	179	6	,	,	PUNCT
ejpam-4706	179	7	0	0	NUM
ejpam-4706	179	8	)	)	PUNCT
ejpam-4706	179	9	)	)	PUNCT
ejpam-4706	180	1	w(t	w(t	PROPN
ejpam-4706	180	2	(	(	PUNCT
ejpam-4706	180	3	0	0	NUM
ejpam-4706	180	4	,	,	PUNCT
ejpam-4706	180	5	i	i	NOUN
ejpam-4706	180	6	)	)	PUNCT
ejpam-4706	180	7	)	)	PUNCT
ejpam-4706	181	1	w(t	w(t	PROPN
ejpam-4706	181	2	(	(	PUNCT
ejpam-4706	181	3	0	0	NUM
ejpam-4706	181	4	,	,	PUNCT
ejpam-4706	181	5	b2	b2	NOUN
ejpam-4706	181	6	)	)	PUNCT
ejpam-4706	181	7	)	)	PUNCT
ejpam-4706	181	8	w(t	w(t	PROPN
ejpam-4706	181	9	(	(	PUNCT
ejpam-4706	181	10	0,−a2	0,−a2	NOUN
ejpam-4706	181	11	)	)	PUNCT
ejpam-4706	181	12	)	)	PUNCT
ejpam-4706	182	1	w(t	w(t	PROPN
ejpam-4706	182	2	(	(	PUNCT
ejpam-4706	182	3	0	0	NUM
ejpam-4706	182	4	,	,	PUNCT
ejpam-4706	182	5	0	0	NUM
ejpam-4706	182	6	)	)	PUNCT
ejpam-4706	182	7	)	)	PUNCT
ejpam-4706	183	1	w(t	w(t	PROPN
ejpam-4706	183	2	(	(	PUNCT
ejpam-4706	183	3	0	0	NUM
ejpam-4706	183	4	,	,	PUNCT
ejpam-4706	183	5	0	0	NUM
ejpam-4706	183	6	)	)	PUNCT
ejpam-4706	183	7	)	)	PUNCT
ejpam-4706	184	1	w(t	w(t	PROPN
ejpam-4706	184	2	(	(	PUNCT
ejpam-4706	184	3	0	0	NUM
ejpam-4706	184	4	,	,	PUNCT
ejpam-4706	184	5	0	0	NUM
ejpam-4706	184	6	)	)	PUNCT
ejpam-4706	184	7	)	)	PUNCT
ejpam-4706	184	8	.	.	PUNCT
ejpam-4706	184	9	.	.	PUNCT
ejpam-4706	184	10	.	.	PUNCT
ejpam-4706	185	1	w(t	w(t	PROPN
ejpam-4706	185	2	(	(	PUNCT
ejpam-4706	185	3	0	0	NUM
ejpam-4706	185	4	,	,	PUNCT
ejpam-4706	185	5	0	0	NUM
ejpam-4706	185	6	)	)	PUNCT
ejpam-4706	185	7	)	)	PUNCT
ejpam-4706	186	1	w(0	w(0	PROPN
ejpam-4706	186	2	)	)	PUNCT
ejpam-4706	186	3	w(t	w(t	PROPN
ejpam-4706	186	4	(	(	PUNCT
ejpam-4706	186	5	0	0	NUM
ejpam-4706	186	6	,	,	PUNCT
ejpam-4706	186	7	0	0	NUM
ejpam-4706	186	8	)	)	PUNCT
ejpam-4706	186	9	)	)	PUNCT
ejpam-4706	187	1	w(t	w(t	PROPN
ejpam-4706	187	2	(	(	PUNCT
ejpam-4706	187	3	0	0	NUM
ejpam-4706	187	4	,	,	PUNCT
ejpam-4706	187	5	b1	b1	NOUN
ejpam-4706	187	6	)	)	PUNCT
ejpam-4706	187	7	)	)	PUNCT
ejpam-4706	187	8	w(t	w(t	PROPN
ejpam-4706	187	9	(	(	PUNCT
ejpam-4706	187	10	0,−a1	0,−a1	NUM
ejpam-4706	187	11	)	)	PUNCT
ejpam-4706	187	12	)	)	PUNCT
ejpam-4706	188	1	w(t	w(t	PROPN
ejpam-4706	188	2	(	(	PUNCT
ejpam-4706	188	3	0	0	NUM
ejpam-4706	188	4	,	,	PUNCT
ejpam-4706	188	5	0	0	NUM
ejpam-4706	188	6	)	)	PUNCT
ejpam-4706	188	7	)	)	PUNCT
ejpam-4706	189	1	w(t	w(t	PROPN
ejpam-4706	189	2	(	(	PUNCT
ejpam-4706	189	3	0	0	NUM
ejpam-4706	189	4	,	,	PUNCT
ejpam-4706	189	5	0	0	NUM
ejpam-4706	189	6	)	)	PUNCT
ejpam-4706	189	7	)	)	PUNCT
ejpam-4706	190	1	w(t	w(t	PROPN
ejpam-4706	190	2	(	(	PUNCT
ejpam-4706	190	3	0	0	NUM
ejpam-4706	190	4	,	,	PUNCT
ejpam-4706	190	5	0	0	NUM
ejpam-4706	190	6	)	)	PUNCT
ejpam-4706	190	7	)	)	PUNCT
ejpam-4706	190	8	.	.	PUNCT
ejpam-4706	190	9	.	.	PUNCT
ejpam-4706	190	10	.	.	PUNCT
ejpam-4706	191	1	w(t	w(t	PROPN
ejpam-4706	191	2	(	(	PUNCT
ejpam-4706	191	3	i	i	NOUN
ejpam-4706	191	4	,	,	PUNCT
ejpam-4706	191	5	0	0	NUM
ejpam-4706	191	6	)	)	PUNCT
ejpam-4706	191	7	)	)	PUNCT
ejpam-4706	191	8	w(t	w(t	PROPN
ejpam-4706	191	9	(	(	PUNCT
ejpam-4706	191	10	0	0	NUM
ejpam-4706	191	11	,	,	PUNCT
ejpam-4706	191	12	0	0	NUM
ejpam-4706	191	13	)	)	PUNCT
ejpam-4706	191	14	)	)	PUNCT
ejpam-4706	192	1	w(0	w(0	PROPN
ejpam-4706	192	2	)	)	PUNCT
ejpam-4706	192	3			NUM
ejpam-4706	192	4	using	use	VERB
ejpam-4706	192	5	the	the	DET
ejpam-4706	192	6	fact	fact	NOUN
ejpam-4706	192	7	that	that	SCONJ
ejpam-4706	192	8	w	w	INTJ
ejpam-4706	192	9	(	(	PUNCT
ejpam-4706	192	10	[	[	PUNCT
ejpam-4706	192	11	0	0	NUM
ejpam-4706	192	12	a	a	DET
ejpam-4706	192	13	0	0	NUM
ejpam-4706	192	14	0	0	NUM
ejpam-4706	192	15	]	]	PUNCT
ejpam-4706	192	16	)	)	PUNCT
ejpam-4706	193	1	=	=	SYM
ejpam-4706	193	2	w	w	X
ejpam-4706	193	3	(	(	PUNCT
ejpam-4706	193	4	[	[	PUNCT
ejpam-4706	193	5	0	0	NUM
ejpam-4706	193	6	0	0	NUM
ejpam-4706	193	7	a	a	DET
ejpam-4706	193	8	0	0	NUM
ejpam-4706	193	9	]	]	PUNCT
ejpam-4706	193	10	)	)	PUNCT
ejpam-4706	193	11	=	=	SYM
ejpam-4706	193	12	∥a∥	∥a∥	VERB
ejpam-4706	193	13	2	2	NUM
ejpam-4706	193	14	,	,	PUNCT
ejpam-4706	193	15	for	for	ADP
ejpam-4706	193	16	every	every	DET
ejpam-4706	193	17	matrix	matrix	NOUN
ejpam-4706	193	18	a	a	DET
ejpam-4706	193	19	∈	∈	NOUN
ejpam-4706	193	20	mn(c	mn(c	X
ejpam-4706	193	21	)	)	PUNCT
ejpam-4706	193	22	,	,	PUNCT
ejpam-4706	193	23	then	then	ADV
ejpam-4706	193	24	r	r	NOUN
ejpam-4706	193	25	is	be	AUX
ejpam-4706	193	26	equal	equal	ADJ
ejpam-4706	193	27	to	to	ADP
ejpam-4706	193	28	a.	a.	PROPN
ejpam-4706	193	29	burqan	burqan	PROPN
ejpam-4706	193	30	et	et	PROPN
ejpam-4706	194	1	al	al	PROPN
ejpam-4706	194	2	.	.	PUNCT
ejpam-4706	194	3	/	/	SYM
ejpam-4706	194	4	eur	eur	PROPN
ejpam-4706	194	5	.	.	PUNCT
ejpam-4706	195	1	j.	j.	PROPN
ejpam-4706	195	2	pure	pure	PROPN
ejpam-4706	195	3	appl	appl	PROPN
ejpam-4706	195	4	.	.	PROPN
ejpam-4706	195	5	math	math	PROPN
ejpam-4706	195	6	,	,	PUNCT
ejpam-4706	195	7	16	16	NUM
ejpam-4706	195	8	(	(	PUNCT
ejpam-4706	195	9	2	2	NUM
ejpam-4706	195	10	)	)	PUNCT
ejpam-4706	195	11	(	(	PUNCT
ejpam-4706	195	12	2023	2023	NUM
ejpam-4706	195	13	)	)	PUNCT
ejpam-4706	195	14	,	,	PUNCT
ejpam-4706	195	15	806	806	NUM
ejpam-4706	195	16	-	-	SYM
ejpam-4706	195	17	818	818	NUM
ejpam-4706	195	18	810	810	PROPN
ejpam-4706	195	19	w(bm	w(bm	PROPN
ejpam-4706	195	20	)	)	PUNCT
ejpam-4706	195	21	w(t	w(t	PROPN
ejpam-4706	195	22	(	(	PUNCT
ejpam-4706	195	23	bm−1,−am	bm−1,−am	PROPN
ejpam-4706	195	24	)	)	PUNCT
ejpam-4706	195	25	)	)	PUNCT
ejpam-4706	196	1	w(t	w(t	PROPN
ejpam-4706	196	2	(	(	PUNCT
ejpam-4706	196	3	bm−2	bm−2	PROPN
ejpam-4706	196	4	,	,	PUNCT
ejpam-4706	196	5	i	i	NOUN
ejpam-4706	196	6	)	)	PUNCT
ejpam-4706	196	7	)	)	PUNCT
ejpam-4706	196	8	∥bm−3∥	∥bm−3∥	ADP
ejpam-4706	196	9	2	2	NUM
ejpam-4706	196	10	∥bm−4∥	∥bm−4∥	NOUN
ejpam-4706	196	11	2	2	NUM
ejpam-4706	196	12	.	.	PUNCT
ejpam-4706	196	13	.	.	PUNCT
ejpam-4706	196	14	.	.	PUNCT
ejpam-4706	197	1	∥b3∥	∥b3∥	PROPN
ejpam-4706	197	2	2	2	NUM
ejpam-4706	197	3	∥b2∥	∥b2∥	PROPN
ejpam-4706	197	4	2	2	NUM
ejpam-4706	197	5	∥b1∥	∥b1∥	PROPN
ejpam-4706	197	6	2	2	NUM
ejpam-4706	197	7	w(t	w(t	PROPN
ejpam-4706	197	8	(	(	PUNCT
ejpam-4706	197	9	−am	−am	PROPN
ejpam-4706	197	10	,	,	PUNCT
ejpam-4706	197	11	bm−1	bm−1	NOUN
ejpam-4706	197	12	)	)	PUNCT
ejpam-4706	197	13	)	)	PUNCT
ejpam-4706	197	14	w(am−1	w(am−1	PUNCT
ejpam-4706	197	15	)	)	PUNCT
ejpam-4706	197	16	∥am−2∥	∥am−2∥	X
ejpam-4706	197	17	2	2	NUM
ejpam-4706	197	18	w(t	w(t	PROPN
ejpam-4706	197	19	(	(	PUNCT
ejpam-4706	197	20	am−3	am−3	PROPN
ejpam-4706	197	21	,	,	PUNCT
ejpam-4706	197	22	i	i	NOUN
ejpam-4706	197	23	)	)	PUNCT
ejpam-4706	197	24	)	)	PUNCT
ejpam-4706	197	25	∥am−4∥	∥am−4∥	NUM
ejpam-4706	197	26	2	2	NUM
ejpam-4706	197	27	.	.	PUNCT
ejpam-4706	197	28	.	.	PUNCT
ejpam-4706	197	29	.	.	PUNCT
ejpam-4706	198	1	∥a3∥	∥a3∥	ADJ
ejpam-4706	198	2	2	2	NUM
ejpam-4706	198	3	∥a2∥	∥a2∥	PROPN
ejpam-4706	198	4	2	2	NUM
ejpam-4706	198	5	∥a1∥	∥a1∥	PROPN
ejpam-4706	198	6	2	2	NUM
ejpam-4706	198	7	w(t	w(t	PROPN
ejpam-4706	198	8	(	(	PUNCT
ejpam-4706	198	9	bm−2	bm−2	PROPN
ejpam-4706	198	10	,	,	PUNCT
ejpam-4706	198	11	i	i	PROPN
ejpam-4706	198	12	)	)	PUNCT
ejpam-4706	198	13	∥am−2∥	∥am−2∥	X
ejpam-4706	198	14	2	2	NUM
ejpam-4706	198	15	0	0	SYM
ejpam-4706	198	16	0	0	NUM
ejpam-4706	198	17	1	1	NUM
ejpam-4706	198	18	2	2	NUM
ejpam-4706	198	19	.	.	PUNCT
ejpam-4706	198	20	.	.	PUNCT
ejpam-4706	198	21	.	.	PUNCT
ejpam-4706	199	1	0	0	NUM
ejpam-4706	200	1	0	0	NUM
ejpam-4706	200	2	0	0	NUM
ejpam-4706	200	3	∥bm−3∥	∥bm−3∥	NUM
ejpam-4706	200	4	2	2	NUM
ejpam-4706	200	5	w(t	w(t	PROPN
ejpam-4706	200	6	(	(	PUNCT
ejpam-4706	200	7	am−3	am−3	PROPN
ejpam-4706	200	8	,	,	PUNCT
ejpam-4706	200	9	i	i	NOUN
ejpam-4706	200	10	)	)	PUNCT
ejpam-4706	200	11	)	)	PUNCT
ejpam-4706	200	12	0	0	NUM
ejpam-4706	200	13	0	0	NUM
ejpam-4706	200	14	0	0	NUM
ejpam-4706	200	15	.	.	PUNCT
ejpam-4706	200	16	.	.	PUNCT
ejpam-4706	200	17	.	.	PUNCT
ejpam-4706	201	1	0	0	NUM
ejpam-4706	201	2	0	0	NUM
ejpam-4706	201	3	0	0	NUM
ejpam-4706	201	4	∥bm−4∥	∥bm−4∥	NOUN
ejpam-4706	201	5	2	2	NUM
ejpam-4706	201	6	∥am−4∥	∥am−4∥	NUM
ejpam-4706	201	7	2	2	NUM
ejpam-4706	201	8	1	1	NUM
ejpam-4706	201	9	2	2	NUM
ejpam-4706	201	10	0	0	NUM
ejpam-4706	201	11	0	0	NUM
ejpam-4706	201	12	.	.	PUNCT
ejpam-4706	201	13	.	.	PUNCT
ejpam-4706	201	14	.	.	PUNCT
ejpam-4706	202	1	0	0	NUM
ejpam-4706	203	1	0	0	NUM
ejpam-4706	203	2	0	0	NUM
ejpam-4706	203	3	...	...	PUNCT
ejpam-4706	203	4	...	...	PUNCT
ejpam-4706	203	5	...	...	PUNCT
ejpam-4706	203	6	...	...	PUNCT
ejpam-4706	203	7	...	...	PUNCT
ejpam-4706	203	8	.	.	PUNCT
ejpam-4706	203	9	.	.	PUNCT
ejpam-4706	203	10	.	.	PUNCT
ejpam-4706	204	1	...	...	PUNCT
ejpam-4706	204	2	...	...	PUNCT
ejpam-4706	205	1	...	...	PUNCT
ejpam-4706	206	1	∥b3∥	∥b3∥	PROPN
ejpam-4706	206	2	2	2	NUM
ejpam-4706	206	3	∥a3∥	∥a3∥	PROPN
ejpam-4706	206	4	2	2	NUM
ejpam-4706	206	5	0	0	NUM
ejpam-4706	206	6	1	1	NUM
ejpam-4706	206	7	2	2	NUM
ejpam-4706	206	8	0	0	NUM
ejpam-4706	206	9	.	.	PUNCT
ejpam-4706	206	10	.	.	PUNCT
ejpam-4706	207	1	.	.	PUNCT
ejpam-4706	208	1	0	0	NUM
ejpam-4706	208	2	0	0	NUM
ejpam-4706	208	3	1	1	NUM
ejpam-4706	208	4	2	2	NUM
ejpam-4706	208	5	∥b2∥	∥b2∥	PROPN
ejpam-4706	208	6	2	2	NUM
ejpam-4706	208	7	∥a2∥	∥a2∥	PROPN
ejpam-4706	208	8	2	2	NUM
ejpam-4706	208	9	0	0	NUM
ejpam-4706	208	10	0	0	NUM
ejpam-4706	208	11	1	1	NUM
ejpam-4706	208	12	2	2	NUM
ejpam-4706	208	13	.	.	PUNCT
ejpam-4706	208	14	.	.	PUNCT
ejpam-4706	208	15	.	.	PUNCT
ejpam-4706	209	1	0	0	NUM
ejpam-4706	210	1	0	0	NUM
ejpam-4706	210	2	0	0	X
ejpam-4706	211	1	∥b1∥	∥b1∥	NOUN
ejpam-4706	211	2	2	2	NUM
ejpam-4706	211	3	∥a1∥	∥a1∥	PROPN
ejpam-4706	211	4	2	2	NUM
ejpam-4706	211	5	0	0	NUM
ejpam-4706	211	6	0	0	NUM
ejpam-4706	211	7	0	0	NUM
ejpam-4706	211	8	.	.	PUNCT
ejpam-4706	211	9	.	.	PUNCT
ejpam-4706	211	10	.	.	PUNCT
ejpam-4706	212	1	1	1	NUM
ejpam-4706	212	2	2	2	NUM
ejpam-4706	212	3	0	0	NUM
ejpam-4706	212	4	0	0	NUM
ejpam-4706	212	5			NUM
ejpam-4706	212	6	.	.	PUNCT
ejpam-4706	213	1	to	to	PART
ejpam-4706	213	2	find	find	VERB
ejpam-4706	213	3	w(r	w(r	PROPN
ejpam-4706	213	4	)	)	PUNCT
ejpam-4706	213	5	we	we	PRON
ejpam-4706	213	6	need	need	VERB
ejpam-4706	213	7	to	to	PART
ejpam-4706	213	8	partition	partition	VERB
ejpam-4706	213	9	the	the	DET
ejpam-4706	213	10	new	new	ADJ
ejpam-4706	213	11	form	form	NOUN
ejpam-4706	213	12	of	of	ADP
ejpam-4706	213	13	r	r	NOUN
ejpam-4706	213	14	as	as	ADP
ejpam-4706	213	15	r	r	NOUN
ejpam-4706	213	16	=	=	PUNCT
ejpam-4706	213	17	[	[	PUNCT
ejpam-4706	213	18	r11	r11	NOUN
ejpam-4706	213	19	r12	r12	NOUN
ejpam-4706	213	20	r21	r21	NOUN
ejpam-4706	213	21	r22	r22	NOUN
ejpam-4706	213	22	]	]	PUNCT
ejpam-4706	213	23	,	,	PUNCT
ejpam-4706	213	24	where	where	SCONJ
ejpam-4706	213	25	r11	r11	NOUN
ejpam-4706	213	26	=	=	SYM
ejpam-4706	213	27	[	[	PUNCT
ejpam-4706	213	28	w(bm	w(bm	PROPN
ejpam-4706	213	29	)	)	PUNCT
ejpam-4706	213	30	w	w	PROPN
ejpam-4706	213	31	(	(	PUNCT
ejpam-4706	213	32	t	t	PROPN
ejpam-4706	213	33	(	(	PUNCT
ejpam-4706	213	34	bm−1,−am	bm−1,−am	PROPN
ejpam-4706	213	35	)	)	PUNCT
ejpam-4706	213	36	)	)	PUNCT
ejpam-4706	214	1	w	w	X
ejpam-4706	214	2	(	(	PUNCT
ejpam-4706	214	3	t	t	PROPN
ejpam-4706	214	4	(	(	PUNCT
ejpam-4706	214	5	−am	−am	PROPN
ejpam-4706	214	6	,	,	PUNCT
ejpam-4706	214	7	bm−1	bm−1	PROPN
ejpam-4706	214	8	)	)	PUNCT
ejpam-4706	214	9	)	)	PUNCT
ejpam-4706	214	10	w(am−1	w(am−1	PUNCT
ejpam-4706	214	11	)	)	PUNCT
ejpam-4706	214	12	]	]	PUNCT
ejpam-4706	214	13	,	,	PUNCT
ejpam-4706	214	14	r12	r12	NOUN
ejpam-4706	214	15	=	=	SYM
ejpam-4706	214	16	[	[	PUNCT
ejpam-4706	214	17	w(t	w(t	PROPN
ejpam-4706	214	18	(	(	PUNCT
ejpam-4706	214	19	bm−2	bm−2	PROPN
ejpam-4706	214	20	,	,	PUNCT
ejpam-4706	214	21	i	i	NOUN
ejpam-4706	214	22	)	)	PUNCT
ejpam-4706	214	23	)	)	PUNCT
ejpam-4706	214	24	∥bm−3∥	∥bm−3∥	ADP
ejpam-4706	214	25	2	2	NUM
ejpam-4706	214	26	∥bm−4∥	∥bm−4∥	NOUN
ejpam-4706	214	27	2	2	NUM
ejpam-4706	214	28	.	.	PUNCT
ejpam-4706	214	29	.	.	PUNCT
ejpam-4706	214	30	.	.	PUNCT
ejpam-4706	215	1	∥b3∥	∥b3∥	PROPN
ejpam-4706	215	2	2	2	NUM
ejpam-4706	215	3	∥b2∥	∥b2∥	PROPN
ejpam-4706	215	4	2	2	NUM
ejpam-4706	215	5	∥b1∥	∥b1∥	PROPN
ejpam-4706	215	6	2	2	NUM
ejpam-4706	215	7	∥am−2∥	∥am−2∥	X
ejpam-4706	215	8	2	2	NUM
ejpam-4706	215	9	w(t	w(t	PROPN
ejpam-4706	215	10	(	(	PUNCT
ejpam-4706	215	11	am−3	am−3	PROPN
ejpam-4706	215	12	,	,	PUNCT
ejpam-4706	215	13	i	i	NOUN
ejpam-4706	215	14	)	)	PUNCT
ejpam-4706	215	15	)	)	PUNCT
ejpam-4706	215	16	∥am−4∥	∥am−4∥	NUM
ejpam-4706	215	17	2	2	NUM
ejpam-4706	215	18	.	.	PUNCT
ejpam-4706	215	19	.	.	PUNCT
ejpam-4706	215	20	.	.	PUNCT
ejpam-4706	216	1	∥a3∥	∥a3∥	ADJ
ejpam-4706	216	2	2	2	NUM
ejpam-4706	216	3	∥a2∥	∥a2∥	PROPN
ejpam-4706	216	4	2	2	NUM
ejpam-4706	216	5	∥a1∥	∥a1∥	PROPN
ejpam-4706	216	6	2	2	NUM
ejpam-4706	216	7	]	]	PUNCT
ejpam-4706	216	8	,	,	PUNCT
ejpam-4706	216	9	r21	r21	NOUN
ejpam-4706	216	10	=	=	SYM
ejpam-4706	216	11	[	[	PUNCT
ejpam-4706	216	12	w(t	w(t	PROPN
ejpam-4706	216	13	(	(	PUNCT
ejpam-4706	216	14	bm−2	bm−2	PROPN
ejpam-4706	216	15	,	,	PUNCT
ejpam-4706	216	16	i	i	NOUN
ejpam-4706	216	17	)	)	PUNCT
ejpam-4706	216	18	)	)	PUNCT
ejpam-4706	216	19	∥bm−3∥	∥bm−3∥	ADP
ejpam-4706	216	20	2	2	NUM
ejpam-4706	216	21	∥bm−4∥	∥bm−4∥	NOUN
ejpam-4706	216	22	2	2	NUM
ejpam-4706	216	23	.	.	PUNCT
ejpam-4706	216	24	.	.	PUNCT
ejpam-4706	216	25	.	.	PUNCT
ejpam-4706	217	1	∥b3∥	∥b3∥	PROPN
ejpam-4706	217	2	2	2	NUM
ejpam-4706	217	3	∥b2∥	∥b2∥	PROPN
ejpam-4706	217	4	2	2	NUM
ejpam-4706	217	5	∥b1∥	∥b1∥	PROPN
ejpam-4706	217	6	2	2	NUM
ejpam-4706	217	7	∥am−2∥	∥am−2∥	X
ejpam-4706	217	8	2	2	NUM
ejpam-4706	217	9	w(t	w(t	PROPN
ejpam-4706	217	10	(	(	PUNCT
ejpam-4706	217	11	am−3	am−3	PROPN
ejpam-4706	217	12	,	,	PUNCT
ejpam-4706	217	13	i	i	NOUN
ejpam-4706	217	14	)	)	PUNCT
ejpam-4706	217	15	)	)	PUNCT
ejpam-4706	217	16	∥am−4∥	∥am−4∥	NUM
ejpam-4706	217	17	2	2	NUM
ejpam-4706	217	18	.	.	PUNCT
ejpam-4706	217	19	.	.	PUNCT
ejpam-4706	217	20	.	.	PUNCT
ejpam-4706	218	1	∥a3∥	∥a3∥	ADJ
ejpam-4706	219	1	2	2	NUM
ejpam-4706	219	2	∥a2∥	∥a2∥	PROPN
ejpam-4706	219	3	2	2	NUM
ejpam-4706	219	4	∥a1∥	∥a1∥	PROPN
ejpam-4706	219	5	2	2	NUM
ejpam-4706	219	6	]	]	SYM
ejpam-4706	219	7	t	t	NOUN
ejpam-4706	219	8	,	,	PUNCT
ejpam-4706	219	9	r22	r22	NOUN
ejpam-4706	219	10	=	=	SYM
ejpam-4706	219	11			ADJ
ejpam-4706	219	12	0	0	NUM
ejpam-4706	219	13	0	0	NUM
ejpam-4706	219	14	1	1	NUM
ejpam-4706	219	15	2	2	NUM
ejpam-4706	219	16	0	0	NUM
ejpam-4706	219	17	0	0	NUM
ejpam-4706	219	18	.	.	PUNCT
ejpam-4706	219	19	.	.	PUNCT
ejpam-4706	219	20	.	.	PUNCT
ejpam-4706	220	1	0	0	NUM
ejpam-4706	221	1	0	0	NUM
ejpam-4706	221	2	0	0	NUM
ejpam-4706	221	3	0	0	NUM
ejpam-4706	221	4	1	1	NUM
ejpam-4706	221	5	2	2	NUM
ejpam-4706	221	6	0	0	NUM
ejpam-4706	221	7	.	.	PUNCT
ejpam-4706	221	8	.	.	PUNCT
ejpam-4706	222	1	.	.	PUNCT
ejpam-4706	223	1	0	0	NUM
ejpam-4706	224	1	1	1	NUM
ejpam-4706	224	2	2	2	NUM
ejpam-4706	224	3	0	0	NUM
ejpam-4706	224	4	0	0	NUM
ejpam-4706	224	5	.	.	PUNCT
ejpam-4706	224	6	.	.	PUNCT
ejpam-4706	224	7	.	.	PUNCT
ejpam-4706	225	1	1	1	NUM
ejpam-4706	225	2	2	2	NUM
ejpam-4706	225	3	.	.	PUNCT
ejpam-4706	225	4	.	.	PUNCT
ejpam-4706	225	5	.	.	PUNCT
ejpam-4706	226	1	0	0	NUM
ejpam-4706	226	2	0	0	NUM
ejpam-4706	226	3	1	1	NUM
ejpam-4706	226	4	2	2	NUM
ejpam-4706	226	5	.	.	PUNCT
ejpam-4706	226	6	.	.	PUNCT
ejpam-4706	226	7	.	.	PUNCT
ejpam-4706	226	8	.	.	PUNCT
ejpam-4706	226	9	.	.	PUNCT
ejpam-4706	226	10	.	.	PUNCT
ejpam-4706	226	11	.	.	PUNCT
ejpam-4706	226	12	.	.	PUNCT
ejpam-4706	226	13	.	.	PUNCT
ejpam-4706	227	1	...	...	PUNCT
ejpam-4706	227	2	...	...	PUNCT
ejpam-4706	227	3	.	.	PUNCT
ejpam-4706	227	4	.	.	PUNCT
ejpam-4706	228	1	.	.	PUNCT
ejpam-4706	229	1	...	...	PUNCT
ejpam-4706	230	1	0	0	NUM
ejpam-4706	230	2	0	0	NUM
ejpam-4706	230	3	1	1	NUM
ejpam-4706	230	4	2	2	NUM
ejpam-4706	230	5	.	.	PUNCT
ejpam-4706	230	6	.	.	PUNCT
ejpam-4706	230	7	.	.	PUNCT
ejpam-4706	230	8	.	.	PUNCT
ejpam-4706	230	9	.	.	PUNCT
ejpam-4706	231	1	.	.	PUNCT
ejpam-4706	232	1	0	0	NUM
ejpam-4706	232	2	0	0	NUM
ejpam-4706	232	3	1	1	NUM
ejpam-4706	232	4	2	2	NUM
ejpam-4706	232	5	...	...	PUNCT
ejpam-4706	232	6	...	...	PUNCT
ejpam-4706	232	7	...	...	PUNCT
ejpam-4706	232	8	.	.	PUNCT
ejpam-4706	232	9	.	.	PUNCT
ejpam-4706	232	10	.	.	PUNCT
ejpam-4706	232	11	.	.	PUNCT
ejpam-4706	232	12	.	.	PUNCT
ejpam-4706	232	13	.	.	PUNCT
ejpam-4706	233	1	0	0	NUM
ejpam-4706	234	1	0	0	NUM
ejpam-4706	234	2	0	0	NUM
ejpam-4706	234	3	0	0	NUM
ejpam-4706	234	4	0	0	NUM
ejpam-4706	234	5	0	0	NUM
ejpam-4706	234	6	.	.	PUNCT
ejpam-4706	234	7	.	.	PUNCT
ejpam-4706	234	8	.	.	PUNCT
ejpam-4706	235	1	1	1	NUM
ejpam-4706	235	2	2	2	NUM
ejpam-4706	235	3	0	0	NUM
ejpam-4706	235	4	0	0	NUM
ejpam-4706	235	5			NOUN
ejpam-4706	235	6	.	.	PUNCT
ejpam-4706	236	1	(	(	PUNCT
ejpam-4706	236	2	mn−2)×(mn−2	mn−2)×(mn−2	NOUN
ejpam-4706	236	3	)	)	PUNCT
ejpam-4706	236	4	to	to	PART
ejpam-4706	236	5	achieve	achieve	VERB
ejpam-4706	236	6	our	our	PRON
ejpam-4706	236	7	goal	goal	NOUN
ejpam-4706	236	8	,	,	PUNCT
ejpam-4706	236	9	we	we	PRON
ejpam-4706	236	10	apply	apply	VERB
ejpam-4706	236	11	lemma	lemma	PROPN
ejpam-4706	236	12	4	4	NUM
ejpam-4706	236	13	on	on	ADP
ejpam-4706	236	14	the	the	DET
ejpam-4706	236	15	matrix	matrix	NOUN
ejpam-4706	236	16	r.	r.	PROPN
ejpam-4706	237	1	so	so	ADV
ejpam-4706	237	2	,	,	PUNCT
ejpam-4706	237	3	we	we	PRON
ejpam-4706	237	4	need	need	VERB
ejpam-4706	237	5	to	to	PART
ejpam-4706	237	6	estimate	estimate	VERB
ejpam-4706	237	7	w(r11),w(r22	w(r11),w(r22	NOUN
ejpam-4706	237	8	)	)	PUNCT
ejpam-4706	237	9	,	,	PUNCT
ejpam-4706	237	10	∥r12∥	∥r12∥	NUM
ejpam-4706	237	11	and	and	CCONJ
ejpam-4706	237	12	∥r21∥.	∥r21∥.	VERB
ejpam-4706	237	13	a	a	DET
ejpam-4706	237	14	matrix	matrix	NOUN
ejpam-4706	237	15	a	a	DET
ejpam-4706	237	16	∈	∈	NOUN
ejpam-4706	237	17	mn(c	mn(c	X
ejpam-4706	237	18	)	)	PUNCT
ejpam-4706	237	19	is	be	AUX
ejpam-4706	237	20	called	call	VERB
ejpam-4706	237	21	hermitian	hermitian	ADJ
ejpam-4706	237	22	if	if	SCONJ
ejpam-4706	237	23	a	a	DET
ejpam-4706	237	24	=	=	NOUN
ejpam-4706	237	25	a∗.	a∗.	NOUN
ejpam-4706	237	26	since	since	SCONJ
ejpam-4706	237	27	r11	r11	NOUN
ejpam-4706	237	28	is	be	AUX
ejpam-4706	237	29	hermitian	hermitian	ADJ
ejpam-4706	237	30	,	,	PUNCT
ejpam-4706	237	31	lemma	lemma	PROPN
ejpam-4706	237	32	3	3	NUM
ejpam-4706	237	33	yields	yield	NOUN
ejpam-4706	237	34	that	that	PRON
ejpam-4706	237	35	w(r11	w(r11	VERB
ejpam-4706	237	36	)	)	PUNCT
ejpam-4706	237	37	=	=	SYM
ejpam-4706	237	38	r(r11	r(r11	NOUN
ejpam-4706	237	39	)	)	PUNCT
ejpam-4706	237	40	=	=	SYM
ejpam-4706	237	41	1	1	NUM
ejpam-4706	237	42	2	2	NUM
ejpam-4706	237	43	(	(	PUNCT
ejpam-4706	237	44	w(bm	w(bm	PROPN
ejpam-4706	237	45	)	)	PUNCT
ejpam-4706	237	46	+	+	CCONJ
ejpam-4706	237	47	w(am−1	w(am−1	PUNCT
ejpam-4706	237	48	)	)	PUNCT
ejpam-4706	238	1	+	+	CCONJ
ejpam-4706	238	2	√	√	NUM
ejpam-4706	238	3	(	(	PUNCT
ejpam-4706	238	4	w(bm)−	w(bm)−	INTJ
ejpam-4706	238	5	w(am−1	w(am−1	NOUN
ejpam-4706	238	6	)	)	PUNCT
ejpam-4706	238	7	)	)	PUNCT
ejpam-4706	238	8	2	2	NUM
ejpam-4706	239	1	+	+	X
ejpam-4706	239	2	4w2(t	4w2(t	NOUN
ejpam-4706	239	3	(	(	PUNCT
ejpam-4706	239	4	bm−1,−am	bm−1,−am	PROPN
ejpam-4706	239	5	)	)	PUNCT
ejpam-4706	239	6	)	)	PUNCT
ejpam-4706	239	7	.	.	PUNCT
ejpam-4706	240	1	the	the	DET
ejpam-4706	240	2	matrix	matrix	NOUN
ejpam-4706	240	3	r22	r22	NOUN
ejpam-4706	240	4	can	can	AUX
ejpam-4706	240	5	be	be	AUX
ejpam-4706	240	6	written	write	VERB
ejpam-4706	240	7	as	as	ADP
ejpam-4706	240	8	r22	r22	NOUN
ejpam-4706	240	9	=	=	SYM
ejpam-4706	240	10	2	2	NUM
ejpam-4706	240	11	(	(	PUNCT
ejpam-4706	240	12	a2	a2	PROPN
ejpam-4706	240	13	−	−	PROPN
ejpam-4706	240	14	diag	diag	NOUN
ejpam-4706	240	15	(	(	PUNCT
ejpam-4706	240	16	1	1	NUM
ejpam-4706	240	17	4	4	NUM
ejpam-4706	240	18	,	,	PUNCT
ejpam-4706	240	19	1	1	NUM
ejpam-4706	240	20	2	2	NUM
ejpam-4706	240	21	,	,	PUNCT
ejpam-4706	240	22	.	.	PUNCT
ejpam-4706	240	23	.	.	PUNCT
ejpam-4706	241	1	.	.	PUNCT
ejpam-4706	242	1	,	,	PUNCT
ejpam-4706	242	2	1	1	NUM
ejpam-4706	242	3	2	2	NUM
ejpam-4706	242	4	,	,	PUNCT
ejpam-4706	242	5	1	1	NUM
ejpam-4706	242	6	4	4	NUM
ejpam-4706	242	7	)	)	PUNCT
ejpam-4706	242	8	)	)	PUNCT
ejpam-4706	242	9	,	,	PUNCT
ejpam-4706	243	1	a.	a.	NOUN
ejpam-4706	243	2	burqan	burqan	PROPN
ejpam-4706	243	3	et	et	PROPN
ejpam-4706	243	4	al	al	PROPN
ejpam-4706	243	5	.	.	PUNCT
ejpam-4706	243	6	/	/	SYM
ejpam-4706	243	7	eur	eur	PROPN
ejpam-4706	243	8	.	.	PUNCT
ejpam-4706	244	1	j.	j.	PROPN
ejpam-4706	244	2	pure	pure	PROPN
ejpam-4706	244	3	appl	appl	PROPN
ejpam-4706	244	4	.	.	PROPN
ejpam-4706	244	5	math	math	PROPN
ejpam-4706	244	6	,	,	PUNCT
ejpam-4706	244	7	16	16	NUM
ejpam-4706	244	8	(	(	PUNCT
ejpam-4706	244	9	2	2	NUM
ejpam-4706	244	10	)	)	PUNCT
ejpam-4706	244	11	(	(	PUNCT
ejpam-4706	244	12	2023	2023	NUM
ejpam-4706	244	13	)	)	PUNCT
ejpam-4706	244	14	,	,	PUNCT
ejpam-4706	244	15	806	806	NUM
ejpam-4706	244	16	-	-	SYM
ejpam-4706	244	17	818	818	NUM
ejpam-4706	244	18	811	811	NUM
ejpam-4706	244	19	where	where	SCONJ
ejpam-4706	244	20	a	a	DET
ejpam-4706	244	21	=	=	NOUN
ejpam-4706	244	22			NOUN
ejpam-4706	244	23	0	0	NUM
ejpam-4706	245	1	1	1	NUM
ejpam-4706	245	2	2	2	NUM
ejpam-4706	245	3	0	0	NUM
ejpam-4706	245	4	.	.	PUNCT
ejpam-4706	245	5	.	.	PUNCT
ejpam-4706	245	6	.	.	PUNCT
ejpam-4706	246	1	0	0	NUM
ejpam-4706	246	2	1	1	NUM
ejpam-4706	246	3	2	2	NUM
ejpam-4706	246	4	0	0	NUM
ejpam-4706	246	5	1	1	NUM
ejpam-4706	246	6	2	2	NUM
ejpam-4706	246	7	.	.	PUNCT
ejpam-4706	246	8	.	.	PUNCT
ejpam-4706	246	9	.	.	PUNCT
ejpam-4706	247	1	0	0	NUM
ejpam-4706	247	2	0	0	NUM
ejpam-4706	248	1	1	1	NUM
ejpam-4706	248	2	2	2	NUM
ejpam-4706	248	3	0	0	NUM
ejpam-4706	248	4	.	.	PUNCT
ejpam-4706	248	5	.	.	PUNCT
ejpam-4706	248	6	.	.	PUNCT
ejpam-4706	249	1	0	0	NUM
ejpam-4706	250	1	...	...	PUNCT
ejpam-4706	250	2	0	0	NUM
ejpam-4706	250	3	...	...	PUNCT
ejpam-4706	250	4	.	.	PUNCT
ejpam-4706	250	5	.	.	PUNCT
ejpam-4706	251	1	.	.	PUNCT
ejpam-4706	252	1	1	1	NUM
ejpam-4706	252	2	2	2	NUM
ejpam-4706	252	3	0	0	NUM
ejpam-4706	252	4	0	0	NUM
ejpam-4706	252	5	.	.	PUNCT
ejpam-4706	252	6	.	.	PUNCT
ejpam-4706	252	7	.	.	PUNCT
ejpam-4706	253	1	1	1	NUM
ejpam-4706	253	2	2	2	NUM
ejpam-4706	253	3	0	0	NUM
ejpam-4706	253	4			NOUN
ejpam-4706	253	5	.	.	PUNCT
ejpam-4706	254	1	thus	thus	ADV
ejpam-4706	254	2	w	w	X
ejpam-4706	254	3	(	(	PUNCT
ejpam-4706	254	4	r22	r22	NOUN
ejpam-4706	254	5	)	)	PUNCT
ejpam-4706	254	6	≤	≤	NOUN
ejpam-4706	254	7	2	2	NUM
ejpam-4706	254	8	(	(	PUNCT
ejpam-4706	254	9	w	w	PROPN
ejpam-4706	254	10	(	(	PUNCT
ejpam-4706	254	11	a2	a2	PROPN
ejpam-4706	254	12	)	)	PUNCT
ejpam-4706	255	1	+	+	CCONJ
ejpam-4706	255	2	w(diag	w(diag	NOUN
ejpam-4706	255	3	(	(	PUNCT
ejpam-4706	255	4	1	1	NUM
ejpam-4706	255	5	4	4	NUM
ejpam-4706	255	6	,	,	PUNCT
ejpam-4706	255	7	1	1	NUM
ejpam-4706	255	8	2	2	NUM
ejpam-4706	255	9	,	,	PUNCT
ejpam-4706	255	10	.	.	PUNCT
ejpam-4706	255	11	.	.	PUNCT
ejpam-4706	255	12	.	.	PUNCT
ejpam-4706	256	1	,	,	PUNCT
ejpam-4706	256	2	1	1	NUM
ejpam-4706	256	3	2	2	NUM
ejpam-4706	256	4	,	,	PUNCT
ejpam-4706	256	5	1	1	NUM
ejpam-4706	256	6	4	4	NUM
ejpam-4706	256	7	)	)	PUNCT
ejpam-4706	256	8	)	)	PUNCT
ejpam-4706	256	9	.	.	PUNCT
ejpam-4706	257	1	since	since	SCONJ
ejpam-4706	257	2	a	a	PRON
ejpam-4706	257	3	is	be	AUX
ejpam-4706	257	4	normal	normal	ADJ
ejpam-4706	257	5	and	and	CCONJ
ejpam-4706	257	6	by	by	ADP
ejpam-4706	257	7	using	use	VERB
ejpam-4706	257	8	the	the	DET
ejpam-4706	257	9	fact	fact	NOUN
ejpam-4706	257	10	w	w	PROPN
ejpam-4706	257	11	(	(	PUNCT
ejpam-4706	257	12	a2	a2	PROPN
ejpam-4706	257	13	)	)	PUNCT
ejpam-4706	257	14	=	=	SYM
ejpam-4706	257	15	w2(a	w2(a	PROPN
ejpam-4706	257	16	)	)	PUNCT
ejpam-4706	257	17	,	,	PUNCT
ejpam-4706	257	18	we	we	PRON
ejpam-4706	257	19	get	get	VERB
ejpam-4706	257	20	w	w	NOUN
ejpam-4706	257	21	(	(	PUNCT
ejpam-4706	257	22	r22	r22	NOUN
ejpam-4706	257	23	)	)	PUNCT
ejpam-4706	257	24	≤	≤	NOUN
ejpam-4706	257	25	2w2	2w2	NUM
ejpam-4706	257	26	(	(	PUNCT
ejpam-4706	257	27	a	a	X
ejpam-4706	257	28	)	)	PUNCT
ejpam-4706	257	29	+	+	NOUN
ejpam-4706	257	30	1	1	X
ejpam-4706	257	31	.	.	X
ejpam-4706	257	32	lemma	lemma	PROPN
ejpam-4706	257	33	2	2	NUM
ejpam-4706	257	34	yields	yield	NOUN
ejpam-4706	257	35	that	that	PRON
ejpam-4706	257	36	w	w	PROPN
ejpam-4706	257	37	(	(	PUNCT
ejpam-4706	257	38	r22	r22	NOUN
ejpam-4706	257	39	)	)	PUNCT
ejpam-4706	257	40	≤	≤	NUM
ejpam-4706	257	41	2	2	NUM
ejpam-4706	257	42	cos2	cos2	NOUN
ejpam-4706	257	43	(	(	PUNCT
ejpam-4706	257	44	π	π	NOUN
ejpam-4706	257	45	mn−	mn−	PROPN
ejpam-4706	257	46	1	1	NUM
ejpam-4706	257	47	)	)	PUNCT
ejpam-4706	258	1	+	+	CCONJ
ejpam-4706	258	2	1	1	X
ejpam-4706	258	3	.	.	PUNCT
ejpam-4706	258	4	now	now	ADV
ejpam-4706	258	5	,	,	PUNCT
ejpam-4706	258	6	to	to	PART
ejpam-4706	258	7	estimate	estimate	VERB
ejpam-4706	258	8	the	the	DET
ejpam-4706	258	9	spectral	spectral	ADJ
ejpam-4706	258	10	norm	norm	NOUN
ejpam-4706	258	11	of	of	ADP
ejpam-4706	258	12	r12	r12	NOUN
ejpam-4706	258	13	,	,	PUNCT
ejpam-4706	258	14	r21	r21	NOUN
ejpam-4706	258	15	consider	consider	VERB
ejpam-4706	258	16	r∗	r∗	NOUN
ejpam-4706	258	17	21r21	21r21	NUM
ejpam-4706	259	1	=	=	PUNCT
ejpam-4706	259	2	[	[	PUNCT
ejpam-4706	259	3	α	α	X
ejpam-4706	259	4	β	β	X
ejpam-4706	259	5	β	β	X
ejpam-4706	259	6	η	η	PROPN
ejpam-4706	259	7	]	]	PUNCT
ejpam-4706	259	8	,	,	PUNCT
ejpam-4706	259	9	where	where	SCONJ
ejpam-4706	259	10	α	α	PROPN
ejpam-4706	259	11	=	=	PROPN
ejpam-4706	259	12	w2	w2	PROPN
ejpam-4706	259	13	(	(	PUNCT
ejpam-4706	259	14	t	t	PROPN
ejpam-4706	259	15	(	(	PUNCT
ejpam-4706	259	16	bm−2	bm−2	PROPN
ejpam-4706	259	17	,	,	PUNCT
ejpam-4706	259	18	i	i	NOUN
ejpam-4706	259	19	)	)	PUNCT
ejpam-4706	259	20	)	)	PUNCT
ejpam-4706	260	1	+	+	CCONJ
ejpam-4706	260	2	1	1	NUM
ejpam-4706	260	3	4	4	NUM
ejpam-4706	260	4	m−3∑	m−3∑	NUM
ejpam-4706	260	5	i=1	i=1	PROPN
ejpam-4706	261	1	∥bi∥2	∥bi∥2	PROPN
ejpam-4706	261	2	,	,	PUNCT
ejpam-4706	261	3	β	β	X
ejpam-4706	261	4	=	=	SYM
ejpam-4706	261	5	w	w	PROPN
ejpam-4706	261	6	(	(	PUNCT
ejpam-4706	261	7	t	t	PROPN
ejpam-4706	261	8	(	(	PUNCT
ejpam-4706	261	9	bm−2	bm−2	PROPN
ejpam-4706	261	10	,	,	PUNCT
ejpam-4706	261	11	i	i	NOUN
ejpam-4706	261	12	)	)	PUNCT
ejpam-4706	261	13	)	)	PUNCT
ejpam-4706	262	1	∥am−2∥	∥am−2∥	ADP
ejpam-4706	262	2	2	2	NUM
ejpam-4706	263	1	+	+	CCONJ
ejpam-4706	263	2	w	w	PROPN
ejpam-4706	263	3	(	(	PUNCT
ejpam-4706	263	4	t	t	PROPN
ejpam-4706	263	5	(	(	PUNCT
ejpam-4706	263	6	am−3	am−3	PROPN
ejpam-4706	263	7	,	,	PUNCT
ejpam-4706	263	8	i	i	NOUN
ejpam-4706	263	9	)	)	PUNCT
ejpam-4706	263	10	)	)	PUNCT
ejpam-4706	264	1	∥bm−3∥	∥bm−3∥	ADP
ejpam-4706	264	2	2	2	NUM
ejpam-4706	265	1	+	+	CCONJ
ejpam-4706	265	2	1	1	NUM
ejpam-4706	265	3	4	4	NUM
ejpam-4706	265	4	m−4∑	m−4∑	NOUN
ejpam-4706	265	5	i=1	i=1	PROPN
ejpam-4706	265	6	(	(	PUNCT
ejpam-4706	265	7	∥ai∥∥bi∥	∥ai∥∥bi∥	NOUN
ejpam-4706	265	8	)	)	PUNCT
ejpam-4706	265	9	,	,	PUNCT
ejpam-4706	265	10	η	η	PROPN
ejpam-4706	265	11	=	=	SYM
ejpam-4706	265	12	w2(t	w2(t	PROPN
ejpam-4706	265	13	(	(	PUNCT
ejpam-4706	265	14	am−3	am−3	PROPN
ejpam-4706	265	15	,	,	PUNCT
ejpam-4706	265	16	i	i	NOUN
ejpam-4706	265	17	)	)	PUNCT
ejpam-4706	265	18	)	)	PUNCT
ejpam-4706	266	1	+	+	CCONJ
ejpam-4706	266	2	1	1	NUM
ejpam-4706	266	3	4	4	NUM
ejpam-4706	266	4	∥am−2∥2	∥am−2∥2	ADJ
ejpam-4706	266	5	+	+	CCONJ
ejpam-4706	266	6	1	1	NUM
ejpam-4706	266	7	4	4	NUM
ejpam-4706	266	8	m−4∑	m−4∑	NOUN
ejpam-4706	266	9	i=1	i=1	PRON
ejpam-4706	266	10	∥ai∥2	∥ai∥2	PROPN
ejpam-4706	266	11	.	.	PUNCT
ejpam-4706	267	1	so	so	ADV
ejpam-4706	267	2	,	,	PUNCT
ejpam-4706	267	3	∥r21∥2	∥r21∥2	ADJ
ejpam-4706	267	4	=	=	SYM
ejpam-4706	267	5	∥r21r	∥r21r	PROPN
ejpam-4706	267	6	∗	∗	NOUN
ejpam-4706	267	7	21∥	21∥	NUM
ejpam-4706	268	1	=	=	SYM
ejpam-4706	268	2	r	r	NOUN
ejpam-4706	268	3	(	(	PUNCT
ejpam-4706	268	4	r21r	r21r	PROPN
ejpam-4706	268	5	∗	∗	NOUN
ejpam-4706	268	6	21	21	NUM
ejpam-4706	268	7	)	)	PUNCT
ejpam-4706	268	8	=	=	SYM
ejpam-4706	268	9	1	1	NUM
ejpam-4706	268	10	2	2	NUM
ejpam-4706	268	11	(	(	PUNCT
ejpam-4706	268	12	α+	α+	X
ejpam-4706	268	13	η	η	PROPN
ejpam-4706	268	14	+	+	NOUN
ejpam-4706	268	15	√	√	PROPN
ejpam-4706	268	16	(	(	PUNCT
ejpam-4706	268	17	α−	α−	ADP
ejpam-4706	268	18	η)2	η)2	NOUN
ejpam-4706	268	19	+	+	CCONJ
ejpam-4706	268	20	4β2	4β2	NUM
ejpam-4706	268	21	)	)	PUNCT
ejpam-4706	268	22	.	.	PUNCT
ejpam-4706	269	1	since	since	SCONJ
ejpam-4706	269	2	r21	r21	NOUN
ejpam-4706	269	3	=	=	SYM
ejpam-4706	269	4	rt	rt	NOUN
ejpam-4706	269	5	12	12	NUM
ejpam-4706	269	6	,	,	PUNCT
ejpam-4706	269	7	then	then	ADV
ejpam-4706	269	8	∥r12∥	∥r12∥	VERB
ejpam-4706	269	9	=	=	PUNCT
ejpam-4706	269	10	∥r21∥.	∥r21∥.	VERB
ejpam-4706	269	11	now	now	ADV
ejpam-4706	269	12	,	,	PUNCT
ejpam-4706	269	13	by	by	ADP
ejpam-4706	269	14	applying	apply	VERB
ejpam-4706	269	15	lemma	lemma	PROPN
ejpam-4706	269	16	4	4	NUM
ejpam-4706	269	17	,	,	PUNCT
ejpam-4706	269	18	we	we	PRON
ejpam-4706	269	19	have	have	VERB
ejpam-4706	269	20	w(f	w(f	PROPN
ejpam-4706	269	21	2(p	2(p	NUM
ejpam-4706	269	22	)	)	PUNCT
ejpam-4706	269	23	)	)	PUNCT
ejpam-4706	269	24	≤	≤	PROPN
ejpam-4706	270	1	w(r	w(r	PROPN
ejpam-4706	270	2	)	)	PUNCT
ejpam-4706	270	3	≤	≤	NOUN
ejpam-4706	270	4	1	1	NUM
ejpam-4706	270	5	2	2	NUM
ejpam-4706	270	6	2∑	2∑	NUM
ejpam-4706	270	7	l=1	l=1	NOUN
ejpam-4706	270	8	w(rkk	w(rkk	NUM
ejpam-4706	270	9	)	)	PUNCT
ejpam-4706	270	10	+	+	CCONJ
ejpam-4706	270	11	√√√√√w2(rkk	√√√√√w2(rkk	NOUN
ejpam-4706	270	12	)	)	PUNCT
ejpam-4706	271	1	+	+	NUM
ejpam-4706	272	1	2∑	2∑	NUM
ejpam-4706	272	2	m=1	m=1	SYM
ejpam-4706	272	3	m	m	VERB
ejpam-4706	272	4	̸=k	̸=k	PROPN
ejpam-4706	272	5	∥rkm∥2	∥rkm∥2	PROPN
ejpam-4706	272	6			PROPN
ejpam-4706	272	7	.	.	PUNCT
ejpam-4706	273	1	this	this	PRON
ejpam-4706	273	2	completes	complete	VERB
ejpam-4706	273	3	the	the	DET
ejpam-4706	273	4	proof	proof	NOUN
ejpam-4706	273	5	.	.	PUNCT
ejpam-4706	274	1	a.	a.	PROPN
ejpam-4706	274	2	burqan	burqan	PROPN
ejpam-4706	274	3	et	et	PROPN
ejpam-4706	274	4	al	al	PROPN
ejpam-4706	274	5	.	.	PUNCT
ejpam-4706	274	6	/	/	SYM
ejpam-4706	274	7	eur	eur	PROPN
ejpam-4706	274	8	.	.	PUNCT
ejpam-4706	275	1	j.	j.	PROPN
ejpam-4706	275	2	pure	pure	PROPN
ejpam-4706	275	3	appl	appl	PROPN
ejpam-4706	275	4	.	.	PROPN
ejpam-4706	275	5	math	math	PROPN
ejpam-4706	275	6	,	,	PUNCT
ejpam-4706	275	7	16	16	NUM
ejpam-4706	275	8	(	(	PUNCT
ejpam-4706	275	9	2	2	NUM
ejpam-4706	275	10	)	)	PUNCT
ejpam-4706	275	11	(	(	PUNCT
ejpam-4706	275	12	2023	2023	NUM
ejpam-4706	275	13	)	)	PUNCT
ejpam-4706	275	14	,	,	PUNCT
ejpam-4706	275	15	806	806	NUM
ejpam-4706	275	16	-	-	SYM
ejpam-4706	275	17	818	818	NUM
ejpam-4706	275	18	812	812	NUM
ejpam-4706	275	19	from	from	ADP
ejpam-4706	275	20	theorem	theorem	ADJ
ejpam-4706	275	21	1	1	NUM
ejpam-4706	275	22	,	,	PUNCT
ejpam-4706	275	23	we	we	PRON
ejpam-4706	275	24	obtain	obtain	VERB
ejpam-4706	275	25	the	the	DET
ejpam-4706	275	26	first	first	ADJ
ejpam-4706	275	27	new	new	ADJ
ejpam-4706	275	28	bound	bind	VERB
ejpam-4706	275	29	of	of	ADP
ejpam-4706	275	30	the	the	DET
ejpam-4706	275	31	eigenvalues	eigenvalue	NOUN
ejpam-4706	275	32	of	of	ADP
ejpam-4706	275	33	p	p	NOUN
ejpam-4706	275	34	(	(	PUNCT
ejpam-4706	275	35	z	z	NOUN
ejpam-4706	275	36	)	)	PUNCT
ejpam-4706	275	37	.	.	PUNCT
ejpam-4706	276	1	in	in	ADP
ejpam-4706	276	2	fact	fact	NOUN
ejpam-4706	276	3	,	,	PUNCT
ejpam-4706	276	4	if	if	SCONJ
ejpam-4706	276	5	λ	λ	PROPN
ejpam-4706	276	6	is	be	AUX
ejpam-4706	276	7	an	an	DET
ejpam-4706	276	8	eigenvalue	eigenvalue	NOUN
ejpam-4706	276	9	of	of	ADP
ejpam-4706	276	10	p	p	PROPN
ejpam-4706	276	11	(	(	PUNCT
ejpam-4706	276	12	z	z	NOUN
ejpam-4706	276	13	)	)	PUNCT
ejpam-4706	276	14	,	,	PUNCT
ejpam-4706	276	15	then	then	ADV
ejpam-4706	276	16	|λ|2	|λ|2	PROPN
ejpam-4706	276	17	≤	≤	NUM
ejpam-4706	276	18	r(f	r(f	PROPN
ejpam-4706	276	19	2(p	2(p	NUM
ejpam-4706	276	20	)	)	PUNCT
ejpam-4706	276	21	)	)	PUNCT
ejpam-4706	277	1	≤	≤	NOUN
ejpam-4706	277	2	w(f	w(f	ADJ
ejpam-4706	277	3	2(p	2(p	NUM
ejpam-4706	277	4	)	)	PUNCT
ejpam-4706	277	5	)	)	PUNCT
ejpam-4706	277	6	.	.	PUNCT
ejpam-4706	278	1	on	on	ADP
ejpam-4706	278	2	the	the	DET
ejpam-4706	278	3	other	other	ADJ
ejpam-4706	278	4	hand	hand	NOUN
ejpam-4706	278	5	,	,	PUNCT
ejpam-4706	278	6	we	we	PRON
ejpam-4706	278	7	derive	derive	VERB
ejpam-4706	278	8	a	a	DET
ejpam-4706	278	9	new	new	ADJ
ejpam-4706	278	10	bound	bind	VERB
ejpam-4706	278	11	for	for	ADP
ejpam-4706	278	12	the	the	DET
ejpam-4706	278	13	eigenvalues	eigenvalue	NOUN
ejpam-4706	278	14	of	of	ADP
ejpam-4706	278	15	matrix	matrix	NOUN
ejpam-4706	278	16	polynomials	polynomial	NOUN
ejpam-4706	278	17	using	use	VERB
ejpam-4706	278	18	a	a	DET
ejpam-4706	278	19	similar	similar	ADJ
ejpam-4706	278	20	matrix	matrix	NOUN
ejpam-4706	278	21	to	to	ADP
ejpam-4706	278	22	f	f	PROPN
ejpam-4706	278	23	2(p	2(p	NUM
ejpam-4706	278	24	)	)	PUNCT
ejpam-4706	278	25	.	.	PUNCT
ejpam-4706	279	1	consider	consider	VERB
ejpam-4706	279	2	the	the	DET
ejpam-4706	279	3	invertible	invertible	ADJ
ejpam-4706	279	4	matrix	matrix	NOUN
ejpam-4706	279	5	b	b	NOUN
ejpam-4706	280	1	=	=	NOUN
ejpam-4706	280	2			NOUN
ejpam-4706	281	1	i	i	INTJ
ejpam-4706	281	2	i	i	PRON
ejpam-4706	281	3	i	i	PRON
ejpam-4706	281	4	.	.	PUNCT
ejpam-4706	281	5	.	.	PUNCT
ejpam-4706	281	6	.	.	PUNCT
ejpam-4706	282	1	i	i	PRON
ejpam-4706	282	2	0	0	PUNCT
ejpam-4706	283	1	i	i	PRON
ejpam-4706	283	2	i	i	PRON
ejpam-4706	283	3	.	.	PUNCT
ejpam-4706	283	4	.	.	PUNCT
ejpam-4706	283	5	.	.	PUNCT
ejpam-4706	284	1	i	i	PRON
ejpam-4706	284	2	0	0	PUNCT
ejpam-4706	284	3	0	0	PUNCT
ejpam-4706	285	1	i	i	PRON
ejpam-4706	285	2	.	.	PUNCT
ejpam-4706	285	3	.	.	PUNCT
ejpam-4706	285	4	.	.	PUNCT
ejpam-4706	286	1	i	i	PRON
ejpam-4706	286	2	...	...	PUNCT
ejpam-4706	286	3	...	...	PUNCT
ejpam-4706	287	1	0	0	PUNCT
ejpam-4706	287	2	.	.	PUNCT
ejpam-4706	287	3	.	.	PUNCT
ejpam-4706	287	4	.	.	PUNCT
ejpam-4706	288	1	...	...	PUNCT
ejpam-4706	289	1	0	0	NUM
ejpam-4706	289	2	0	0	NUM
ejpam-4706	289	3	0	0	NUM
ejpam-4706	289	4	0	0	NUM
ejpam-4706	290	1	i	i	PRON
ejpam-4706	290	2			NOUN
ejpam-4706	290	3	,	,	PUNCT
ejpam-4706	290	4	where	where	SCONJ
ejpam-4706	290	5	b−1	b−1	PROPN
ejpam-4706	290	6	=	=	SYM
ejpam-4706	290	7			NOUN
ejpam-4706	290	8	i	i	PRON
ejpam-4706	290	9	−i	−i	PROPN
ejpam-4706	290	10	0	0	PUNCT
ejpam-4706	290	11	.	.	PUNCT
ejpam-4706	290	12	.	.	PUNCT
ejpam-4706	290	13	.	.	PUNCT
ejpam-4706	291	1	0	0	NUM
ejpam-4706	291	2	0	0	NUM
ejpam-4706	292	1	i	i	PRON
ejpam-4706	292	2	−i	−i	PROPN
ejpam-4706	292	3	.	.	PUNCT
ejpam-4706	292	4	.	.	PUNCT
ejpam-4706	292	5	.	.	PUNCT
ejpam-4706	293	1	0	0	NUM
ejpam-4706	293	2	0	0	NUM
ejpam-4706	293	3	0	0	NUM
ejpam-4706	294	1	i	i	PRON
ejpam-4706	294	2	.	.	PUNCT
ejpam-4706	294	3	.	.	PUNCT
ejpam-4706	294	4	.	.	PUNCT
ejpam-4706	295	1	0	0	NUM
ejpam-4706	295	2	...	...	PUNCT
ejpam-4706	295	3	...	...	PUNCT
ejpam-4706	295	4	...	...	PUNCT
ejpam-4706	295	5	.	.	PUNCT
ejpam-4706	295	6	.	.	PUNCT
ejpam-4706	295	7	.	.	PUNCT
ejpam-4706	296	1	−i	−i	NOUN
ejpam-4706	296	2	0	0	NUM
ejpam-4706	296	3	0	0	NUM
ejpam-4706	296	4	0	0	NUM
ejpam-4706	296	5	·	·	PUNCT
ejpam-4706	296	6	·	·	PUNCT
ejpam-4706	296	7	·	·	PUNCT
ejpam-4706	297	1	i	i	PRON
ejpam-4706	297	2			NUM
ejpam-4706	297	3	.	.	PUNCT
ejpam-4706	298	1	consider	consider	VERB
ejpam-4706	298	2	the	the	DET
ejpam-4706	298	3	mn×mn	mn×mn	PROPN
ejpam-4706	298	4	matrix	matrix	NOUN
ejpam-4706	298	5	h	h	NOUN
ejpam-4706	298	6	,	,	PUNCT
ejpam-4706	298	7	where	where	SCONJ
ejpam-4706	298	8	h	h	NOUN
ejpam-4706	298	9	=	=	NOUN
ejpam-4706	298	10	bf	bf	NOUN
ejpam-4706	298	11	2(p	2(p	NUM
ejpam-4706	298	12	)	)	PUNCT
ejpam-4706	299	1	b−1	b−1	NOUN
ejpam-4706	299	2	;	;	PUNCT
ejpam-4706	299	3	h=	h=	NOUN
ejpam-4706	299	4			PROPN
ejpam-4706	299	5	bm	bm	PROPN
ejpam-4706	299	6	−am	−am	PROPN
ejpam-4706	299	7	+	+	PROPN
ejpam-4706	299	8	i	i	PROPN
ejpam-4706	299	9	bm−1	bm−1	NOUN
ejpam-4706	299	10	−bm	−bm	NOUN
ejpam-4706	299	11	+	+	NOUN
ejpam-4706	299	12	am	be	AUX
ejpam-4706	299	13	−am−1	−am−1	X
ejpam-4706	299	14	bm−2	bm−2	ADP
ejpam-4706	299	15	−bm−1	−bm−1	NOUN
ejpam-4706	299	16	+	+	PROPN
ejpam-4706	299	17	am−1	am−1	PROPN
ejpam-4706	299	18	−am−2	−am−2	X
ejpam-4706	299	19	.	.	PUNCT
ejpam-4706	299	20	.	.	PUNCT
ejpam-4706	299	21	.	.	PUNCT
ejpam-4706	300	1	b2	b2	NOUN
ejpam-4706	300	2	−b3	−b3	PROPN
ejpam-4706	300	3	+	+	PROPN
ejpam-4706	300	4	a3	a3	NOUN
ejpam-4706	300	5	−a2	−a2	NOUN
ejpam-4706	300	6	b1	b1	NOUN
ejpam-4706	300	7	−b2	−b2	PROPN
ejpam-4706	300	8	+	+	PROPN
ejpam-4706	300	9	a2	a2	PROPN
ejpam-4706	300	10	−a1	−a1	VERB
ejpam-4706	300	11	i	i	PRON
ejpam-4706	300	12	−am	−am	PROPN
ejpam-4706	300	13	am	be	AUX
ejpam-4706	300	14	−am−1	−am−1	NUM
ejpam-4706	300	15	am−1	am−1	PROPN
ejpam-4706	300	16	−am−2	−am−2	X
ejpam-4706	300	17	.	.	PUNCT
ejpam-4706	300	18	.	.	PUNCT
ejpam-4706	300	19	.	.	PUNCT
ejpam-4706	301	1	a3	a3	PROPN
ejpam-4706	301	2	−a2	−a2	NOUN
ejpam-4706	301	3	−	−	PROPN
ejpam-4706	302	1	i	i	PRON
ejpam-4706	302	2	a2	a2	PROPN
ejpam-4706	302	3	−a1	−a1	VERB
ejpam-4706	302	4	i	i	PRON
ejpam-4706	302	5	0	0	NUM
ejpam-4706	302	6	0	0	NUM
ejpam-4706	302	7	.	.	PUNCT
ejpam-4706	302	8	.	.	PUNCT
ejpam-4706	302	9	.	.	PUNCT
ejpam-4706	303	1	−i	−i	NOUN
ejpam-4706	303	2	0	0	NUM
ejpam-4706	303	3	0	0	PUNCT
ejpam-4706	304	1	i	i	NOUN
ejpam-4706	304	2	0	0	NUM
ejpam-4706	304	3	.	.	PUNCT
ejpam-4706	304	4	.	.	PUNCT
ejpam-4706	304	5	.	.	PUNCT
ejpam-4706	305	1	−i	−i	NOUN
ejpam-4706	305	2	0	0	NUM
ejpam-4706	305	3	0	0	NUM
ejpam-4706	305	4	0	0	NUM
ejpam-4706	305	5	.	.	PUNCT
ejpam-4706	305	6	.	.	PUNCT
ejpam-4706	305	7	.	.	PUNCT
ejpam-4706	305	8	.	.	PUNCT
ejpam-4706	305	9	.	.	PUNCT
ejpam-4706	305	10	.	.	PUNCT
ejpam-4706	306	1	−i	−i	NOUN
ejpam-4706	306	2	0	0	NUM
ejpam-4706	306	3	...	...	PUNCT
ejpam-4706	306	4	...	...	PUNCT
ejpam-4706	306	5	...	...	PUNCT
ejpam-4706	306	6	.	.	PUNCT
ejpam-4706	306	7	.	.	PUNCT
ejpam-4706	306	8	.	.	PUNCT
ejpam-4706	307	1	...	...	PUNCT
ejpam-4706	308	1	...	...	PUNCT
ejpam-4706	309	1	0	0	NUM
ejpam-4706	309	2	0	0	NUM
ejpam-4706	309	3	0	0	NUM
ejpam-4706	309	4	.	.	PUNCT
ejpam-4706	309	5	.	.	PUNCT
ejpam-4706	309	6	.	.	PUNCT
ejpam-4706	310	1	−i	−i	PROPN
ejpam-4706	310	2	0	0	NUM
ejpam-4706	310	3			PUNCT
ejpam-4706	310	4	since	since	SCONJ
ejpam-4706	310	5	h	h	NOUN
ejpam-4706	310	6	is	be	AUX
ejpam-4706	310	7	similar	similar	ADJ
ejpam-4706	310	8	to	to	ADP
ejpam-4706	310	9	f	f	PROPN
ejpam-4706	310	10	2(p	2(p	NUM
ejpam-4706	310	11	)	)	PUNCT
ejpam-4706	310	12	,	,	PUNCT
ejpam-4706	310	13	if	if	SCONJ
ejpam-4706	310	14	λ	λ	PROPN
ejpam-4706	310	15	is	be	AUX
ejpam-4706	310	16	an	an	DET
ejpam-4706	310	17	eigenvalue	eigenvalue	NOUN
ejpam-4706	310	18	of	of	ADP
ejpam-4706	310	19	p(z	p(z	NOUN
ejpam-4706	310	20	)	)	PUNCT
ejpam-4706	310	21	,	,	PUNCT
ejpam-4706	310	22	we	we	PRON
ejpam-4706	310	23	obtain	obtain	VERB
ejpam-4706	310	24	|λ|2	|λ|2	PROPN
ejpam-4706	310	25	≤	≤	NUM
ejpam-4706	310	26	r(h	r(h	NOUN
ejpam-4706	310	27	)	)	PUNCT
ejpam-4706	310	28	≤	≤	NOUN
ejpam-4706	310	29	w(h	w(h	PROPN
ejpam-4706	310	30	)	)	PUNCT
ejpam-4706	310	31	.	.	PUNCT
ejpam-4706	311	1	in	in	ADP
ejpam-4706	311	2	the	the	DET
ejpam-4706	311	3	following	following	NOUN
ejpam-4706	311	4	,	,	PUNCT
ejpam-4706	311	5	we	we	PRON
ejpam-4706	311	6	provide	provide	VERB
ejpam-4706	311	7	an	an	DET
ejpam-4706	311	8	estimate	estimate	NOUN
ejpam-4706	311	9	of	of	ADP
ejpam-4706	311	10	the	the	DET
ejpam-4706	311	11	numerical	numerical	ADJ
ejpam-4706	311	12	radius	radius	NOUN
ejpam-4706	311	13	of	of	ADP
ejpam-4706	311	14	h	h	NOUN
ejpam-4706	311	15	in	in	ADP
ejpam-4706	311	16	order	order	NOUN
ejpam-4706	311	17	to	to	PART
ejpam-4706	311	18	extract	extract	VERB
ejpam-4706	311	19	a	a	DET
ejpam-4706	311	20	new	new	ADJ
ejpam-4706	311	21	upper	upper	ADJ
ejpam-4706	311	22	bound	bind	VERB
ejpam-4706	311	23	for	for	ADP
ejpam-4706	311	24	the	the	DET
ejpam-4706	311	25	eigenvalues	eigenvalue	NOUN
ejpam-4706	311	26	of	of	ADP
ejpam-4706	311	27	p	p	NOUN
ejpam-4706	311	28	(	(	PUNCT
ejpam-4706	311	29	z	z	NOUN
ejpam-4706	311	30	)	)	PUNCT
ejpam-4706	311	31	.	.	PUNCT
ejpam-4706	312	1	theorem	theorem	NOUN
ejpam-4706	312	2	2	2	NUM
ejpam-4706	312	3	.	.	PUNCT
ejpam-4706	313	1	an	an	DET
ejpam-4706	313	2	upper	upper	ADJ
ejpam-4706	313	3	bound	bound	NOUN
ejpam-4706	313	4	of	of	ADP
ejpam-4706	313	5	the	the	DET
ejpam-4706	313	6	numerical	numerical	ADJ
ejpam-4706	313	7	radius	radius	PROPN
ejpam-4706	313	8	of	of	ADP
ejpam-4706	313	9	h	h	NOUN
ejpam-4706	313	10	can	can	AUX
ejpam-4706	313	11	be	be	AUX
ejpam-4706	313	12	stated	state	VERB
ejpam-4706	313	13	as	as	SCONJ
ejpam-4706	313	14	follows	follow	VERB
ejpam-4706	313	15	:	:	PUNCT
ejpam-4706	313	16	w(h	w(h	PROPN
ejpam-4706	313	17	)	)	PUNCT
ejpam-4706	313	18	≤	≤	NUM
ejpam-4706	313	19	1	1	NUM
ejpam-4706	313	20	2	2	NUM
ejpam-4706	313	21	ξ	ξ	NUM
ejpam-4706	313	22	+	+	CCONJ
ejpam-4706	313	23	2	2	NUM
ejpam-4706	313	24	cos2	cos2	NOUN
ejpam-4706	313	25	(	(	PUNCT
ejpam-4706	313	26	π	π	PROPN
ejpam-4706	313	27	mn−	mn−	PROPN
ejpam-4706	313	28	3	3	NUM
ejpam-4706	313	29	)	)	PUNCT
ejpam-4706	313	30	+	+	CCONJ
ejpam-4706	313	31	1	1	NUM
ejpam-4706	313	32	+	+	NUM
ejpam-4706	313	33	2	2	NUM
ejpam-4706	313	34	+	+	CCONJ
ejpam-4706	313	35	√	√	NUM
ejpam-4706	313	36	5	5	NUM
ejpam-4706	313	37	4	4	NUM
ejpam-4706	313	38	+	+	CCONJ
ejpam-4706	313	39	√	√	PROPN
ejpam-4706	313	40	ξ2	ξ2	NOUN
ejpam-4706	313	41	+	+	CCONJ
ejpam-4706	313	42	(	(	PUNCT
ejpam-4706	313	43	1	1	NUM
ejpam-4706	313	44	2	2	NUM
ejpam-4706	313	45	(	(	PUNCT
ejpam-4706	313	46	α+	α+	X
ejpam-4706	313	47	η	η	PROPN
ejpam-4706	313	48	+	+	NOUN
ejpam-4706	313	49	√	√	PROPN
ejpam-4706	313	50	(	(	PUNCT
ejpam-4706	313	51	α−	α−	ADP
ejpam-4706	313	52	η)2	η)2	NOUN
ejpam-4706	313	53	+	+	CCONJ
ejpam-4706	313	54	4β2	4β2	NUM
ejpam-4706	313	55	)	)	PUNCT
ejpam-4706	313	56	)	)	PUNCT
ejpam-4706	314	1	2	2	NUM
ejpam-4706	315	1	+	+	X
ejpam-4706	315	2	τ2	τ2	NOUN
ejpam-4706	315	3	+	+	CCONJ
ejpam-4706	315	4	√	√	NUM
ejpam-4706	315	5	(	(	PUNCT
ejpam-4706	315	6	2	2	NUM
ejpam-4706	315	7	cos2	cos2	NOUN
ejpam-4706	315	8	(	(	PUNCT
ejpam-4706	315	9	π	π	PROPN
ejpam-4706	315	10	mn−	mn−	PROPN
ejpam-4706	315	11	3	3	NUM
ejpam-4706	315	12	)	)	PUNCT
ejpam-4706	316	1	+	+	CCONJ
ejpam-4706	316	2	1	1	NUM
ejpam-4706	316	3	)	)	SYM
ejpam-4706	316	4	2	2	NUM
ejpam-4706	317	1	+	+	CCONJ
ejpam-4706	317	2	(	(	PUNCT
ejpam-4706	317	3	1	1	NUM
ejpam-4706	317	4	2	2	NUM
ejpam-4706	317	5	(	(	PUNCT
ejpam-4706	317	6	α+	α+	X
ejpam-4706	317	7	η	η	PROPN
ejpam-4706	317	8	+	+	NOUN
ejpam-4706	317	9	√	√	PROPN
ejpam-4706	317	10	(	(	PUNCT
ejpam-4706	317	11	α−	α−	ADP
ejpam-4706	317	12	η)2	η)2	NOUN
ejpam-4706	317	13	+	+	CCONJ
ejpam-4706	317	14	4β2	4β2	NUM
ejpam-4706	317	15	)	)	PUNCT
ejpam-4706	317	16	)	)	PUNCT
ejpam-4706	318	1	2	2	NUM
ejpam-4706	318	2	+	+	SYM
ejpam-4706	318	3	µ	µ	X
ejpam-4706	318	4	+	+	NUM
ejpam-4706	318	5	√√√√(2	√√√√(2	PROPN
ejpam-4706	318	6	+	+	CCONJ
ejpam-4706	318	7	√	√	NUM
ejpam-4706	318	8	5	5	NUM
ejpam-4706	318	9	4	4	NUM
ejpam-4706	318	10	)	)	SYM
ejpam-4706	318	11	2	2	NUM
ejpam-4706	318	12	+	+	X
ejpam-4706	318	13	τ2	τ2	NOUN
ejpam-4706	318	14	+	+	NUM
ejpam-4706	318	15	µ	µ	NOUN
ejpam-4706	318	16	)	)	PUNCT
ejpam-4706	318	17	,	,	PUNCT
ejpam-4706	318	18	a.	a.	NOUN
ejpam-4706	318	19	burqan	burqan	PROPN
ejpam-4706	318	20	et	et	PROPN
ejpam-4706	318	21	al	al	PROPN
ejpam-4706	318	22	.	.	PUNCT
ejpam-4706	318	23	/	/	SYM
ejpam-4706	318	24	eur	eur	PROPN
ejpam-4706	318	25	.	.	PUNCT
ejpam-4706	319	1	j.	j.	PROPN
ejpam-4706	319	2	pure	pure	PROPN
ejpam-4706	319	3	appl	appl	PROPN
ejpam-4706	319	4	.	.	PROPN
ejpam-4706	319	5	math	math	PROPN
ejpam-4706	319	6	,	,	PUNCT
ejpam-4706	319	7	16	16	NUM
ejpam-4706	319	8	(	(	PUNCT
ejpam-4706	319	9	2	2	NUM
ejpam-4706	319	10	)	)	PUNCT
ejpam-4706	319	11	(	(	PUNCT
ejpam-4706	319	12	2023	2023	NUM
ejpam-4706	319	13	)	)	PUNCT
ejpam-4706	319	14	,	,	PUNCT
ejpam-4706	319	15	806	806	NUM
ejpam-4706	319	16	-	-	SYM
ejpam-4706	319	17	818	818	NUM
ejpam-4706	319	18	813	813	NUM
ejpam-4706	319	19	where	where	SCONJ
ejpam-4706	319	20	ξ	ξ	PROPN
ejpam-4706	319	21	=	=	SYM
ejpam-4706	319	22	1	1	NUM
ejpam-4706	319	23	2	2	NUM
ejpam-4706	319	24	(	(	PUNCT
ejpam-4706	319	25	w(bm	w(bm	PROPN
ejpam-4706	319	26	−am+i	−am+i	PROPN
ejpam-4706	319	27	)	)	PUNCT
ejpam-4706	319	28	+	+	CCONJ
ejpam-4706	319	29	w(am	w(am	PROPN
ejpam-4706	319	30	−am−1	−am−1	NUM
ejpam-4706	319	31	)	)	PUNCT
ejpam-4706	320	1	+	+	CCONJ
ejpam-4706	320	2	√	√	ADJ
ejpam-4706	320	3	(	(	PUNCT
ejpam-4706	320	4	w(bm	w(bm	PROPN
ejpam-4706	320	5	−am+i)−	−am+i)−	PROPN
ejpam-4706	320	6	w(am	w(am	PROPN
ejpam-4706	320	7	−am−1	−am−1	NUM
ejpam-4706	320	8	)	)	PUNCT
ejpam-4706	320	9	)	)	PUNCT
ejpam-4706	320	10	2	2	NUM
ejpam-4706	320	11	+4w2(t	+4w2(t	X
ejpam-4706	320	12	(	(	PUNCT
ejpam-4706	320	13	bm−1	bm−1	NOUN
ejpam-4706	320	14	−bm	−bm	NOUN
ejpam-4706	320	15	+	+	NOUN
ejpam-4706	320	16	am	be	AUX
ejpam-4706	320	17	−am−1	−am−1	NUM
ejpam-4706	320	18	,	,	PUNCT
ejpam-4706	320	19	i	i	PRON
ejpam-4706	320	20	−am	−am	PROPN
ejpam-4706	320	21	)	)	PUNCT
ejpam-4706	320	22	)	)	PUNCT
ejpam-4706	320	23	)	)	PUNCT
ejpam-4706	320	24	,	,	PUNCT
ejpam-4706	320	25	α	α	NOUN
ejpam-4706	320	26	=	=	PROPN
ejpam-4706	320	27	w2	w2	PROPN
ejpam-4706	320	28	(	(	PUNCT
ejpam-4706	320	29	t	t	PROPN
ejpam-4706	320	30	(	(	PUNCT
ejpam-4706	320	31	bm−2	bm−2	PROPN
ejpam-4706	320	32	−bm−1	−bm−1	NOUN
ejpam-4706	320	33	+	+	PROPN
ejpam-4706	320	34	am−1	am−1	PROPN
ejpam-4706	320	35	−am−2	−am−2	PRON
ejpam-4706	320	36	,	,	PUNCT
ejpam-4706	320	37	i	i	NOUN
ejpam-4706	320	38	)	)	PUNCT
ejpam-4706	320	39	)	)	PUNCT
ejpam-4706	321	1	+	+	CCONJ
ejpam-4706	321	2	1	1	NUM
ejpam-4706	321	3	4	4	NUM
ejpam-4706	321	4	m∑	m∑	NOUN
ejpam-4706	321	5	j=6	j=6	VERB
ejpam-4706	321	6	∥bj−3	∥bj−3	NUM
ejpam-4706	321	7	−bj−2	−bj−2	X
ejpam-4706	321	8	+	+	ADJ
ejpam-4706	321	9	aj−2	aj−2	PROPN
ejpam-4706	321	10	−aj−3∥2	−aj−3∥2	PROPN
ejpam-4706	321	11	,	,	PUNCT
ejpam-4706	321	12	η	η	PROPN
ejpam-4706	321	13	=	=	SYM
ejpam-4706	321	14	1	1	NUM
ejpam-4706	321	15	4	4	NUM
ejpam-4706	321	16	∥am−1	∥am−1	NOUN
ejpam-4706	321	17	−am−2∥2	−am−2∥2	ADP
ejpam-4706	321	18	+	+	CCONJ
ejpam-4706	321	19	w2(t	w2(t	PROPN
ejpam-4706	321	20	(	(	PUNCT
ejpam-4706	321	21	am−2	am−2	PROPN
ejpam-4706	321	22	−am−3	−am−3	PROPN
ejpam-4706	321	23	,	,	PUNCT
ejpam-4706	321	24	i	i	PRON
ejpam-4706	321	25	)	)	PUNCT
ejpam-4706	322	1	+	+	CCONJ
ejpam-4706	322	2	1	1	NUM
ejpam-4706	322	3	4	4	NUM
ejpam-4706	322	4	m∑	m∑	VERB
ejpam-4706	322	5	i=7	i=7	PRON
ejpam-4706	322	6	∥aj−3	∥aj−3	PROPN
ejpam-4706	322	7	−aj−4∥2	−aj−4∥2	PROPN
ejpam-4706	322	8	,	,	PUNCT
ejpam-4706	322	9	β	β	X
ejpam-4706	322	10	=	=	SYM
ejpam-4706	322	11	1	1	NUM
ejpam-4706	322	12	2	2	NUM
ejpam-4706	322	13	w	w	NOUN
ejpam-4706	322	14	(	(	PUNCT
ejpam-4706	322	15	t	t	PROPN
ejpam-4706	322	16	(	(	PUNCT
ejpam-4706	322	17	bm−2	bm−2	PROPN
ejpam-4706	322	18	−bm−1	−bm−1	NOUN
ejpam-4706	322	19	+	+	PROPN
ejpam-4706	322	20	am−1	am−1	PROPN
ejpam-4706	322	21	−am−2	−am−2	PRON
ejpam-4706	322	22	,	,	PUNCT
ejpam-4706	322	23	i	i	NOUN
ejpam-4706	322	24	)	)	PUNCT
ejpam-4706	322	25	)	)	PUNCT
ejpam-4706	323	1	∥am−1	∥am−1	PROPN
ejpam-4706	323	2	−am−2∥	−am−2∥	NOUN
ejpam-4706	323	3	+	+	CCONJ
ejpam-4706	323	4	1	1	NUM
ejpam-4706	323	5	2	2	NUM
ejpam-4706	323	6	∥bm−3	∥bm−3	NOUN
ejpam-4706	323	7	−bm−2	−bm−2	ADP
ejpam-4706	323	8	+	+	ADJ
ejpam-4706	323	9	am−2	am−2	PROPN
ejpam-4706	323	10	−am−3∥w(t	−am−3∥w(t	PROPN
ejpam-4706	323	11	(	(	PUNCT
ejpam-4706	323	12	am−2	am−2	PROPN
ejpam-4706	323	13	−am−3	−am−3	PROPN
ejpam-4706	323	14	,	,	PUNCT
ejpam-4706	323	15	i	i	NOUN
ejpam-4706	323	16	)	)	PUNCT
ejpam-4706	323	17	)	)	PUNCT
ejpam-4706	324	1	+	+	CCONJ
ejpam-4706	324	2	1	1	NUM
ejpam-4706	324	3	4	4	NUM
ejpam-4706	324	4	m∑	m∑	NOUN
ejpam-4706	324	5	j=7	j=7	PROPN
ejpam-4706	324	6	∥bj−4	∥bj−4	NOUN
ejpam-4706	324	7	−bj−3	−bj−3	X
ejpam-4706	325	1	+	+	SCONJ
ejpam-4706	325	2	aj−3	aj−3	PROPN
ejpam-4706	325	3	−aj−4∥∥aj−3	−aj−4∥∥aj−3	NOUN
ejpam-4706	325	4	−aj−4∥	−aj−4∥	ADP
ejpam-4706	325	5	,	,	PUNCT
ejpam-4706	325	6	τ	τ	PROPN
ejpam-4706	325	7	=	=	SYM
ejpam-4706	325	8	1	1	NUM
ejpam-4706	325	9	2	2	NUM
ejpam-4706	325	10	(	(	PUNCT
ejpam-4706	325	11	∥b2	∥b2	VERB
ejpam-4706	325	12	−b3	−b3	PROPN
ejpam-4706	325	13	+	+	NOUN
ejpam-4706	325	14	a3	a3	NOUN
ejpam-4706	325	15	−a2∥2	−a2∥2	VERB
ejpam-4706	325	16	4	4	NUM
ejpam-4706	325	17	+	+	CCONJ
ejpam-4706	325	18	∥a3	∥a3	X
ejpam-4706	325	19	−a2	−a2	NOUN
ejpam-4706	325	20	−	−	PROPN
ejpam-4706	325	21	i∥2	i∥2	NOUN
ejpam-4706	325	22	4	4	NUM
ejpam-4706	325	23	−	−	NOUN
ejpam-4706	325	24	∥b1	∥b1	ADJ
ejpam-4706	325	25	−b2	−b2	PROPN
ejpam-4706	325	26	+	+	PROPN
ejpam-4706	325	27	a2	a2	PROPN
ejpam-4706	325	28	−a1∥2	−a1∥2	ADJ
ejpam-4706	325	29	4	4	NUM
ejpam-4706	325	30	−	−	NOUN
ejpam-4706	325	31	∥a2	∥a2	VERB
ejpam-4706	325	32	−a1∥2	−a1∥2	ADJ
ejpam-4706	325	33	4	4	NUM
ejpam-4706	325	34	)	)	PUNCT
ejpam-4706	325	35	√√√√	√√√√	ADP
ejpam-4706	325	36	(	(	PUNCT
ejpam-4706	325	37	∥b2−b3+a3−a2∥2	∥b2−b3+a3−a2∥2	X
ejpam-4706	325	38	4	4	NUM
ejpam-4706	325	39	+	+	NUM
ejpam-4706	325	40	∥a3−a2−i∥2	∥a3−a2−i∥2	NOUN
ejpam-4706	325	41	4	4	NUM
ejpam-4706	325	42	−	−	NOUN
ejpam-4706	325	43	∥b1−b2+a2−a1∥2	∥b1−b2+a2−a1∥2	PROPN
ejpam-4706	325	44	4	4	NUM
ejpam-4706	325	45	−	−	NOUN
ejpam-4706	325	46	∥a2−a1∥2	∥a2−a1∥2	PROPN
ejpam-4706	325	47	4	4	NUM
ejpam-4706	325	48	)	)	SYM
ejpam-4706	325	49	2	2	NUM
ejpam-4706	325	50	+1	+1	NOUN
ejpam-4706	325	51	4	4	NUM
ejpam-4706	325	52	(	(	PUNCT
ejpam-4706	325	53	∥b2	∥b2	VERB
ejpam-4706	325	54	−b3	−b3	PROPN
ejpam-4706	325	55	+	+	NOUN
ejpam-4706	325	56	a3	a3	NOUN
ejpam-4706	325	57	−a2∥∥b1	−a2∥∥b1	NOUN
ejpam-4706	325	58	−b2	−b2	PROPN
ejpam-4706	325	59	+	+	NOUN
ejpam-4706	325	60	a2	a2	PROPN
ejpam-4706	325	61	−a1∥+	−a1∥+	NOUN
ejpam-4706	325	62	∥a3	∥a3	X
ejpam-4706	325	63	−a2	−a2	NOUN
ejpam-4706	326	1	−	−	PROPN
ejpam-4706	326	2	i∥∥a2	i∥∥a2	INTJ
ejpam-4706	326	3	−a1∥)2	−a1∥)2	NOUN
ejpam-4706	326	4	.	.	PUNCT
ejpam-4706	327	1	proof	proof	NOUN
ejpam-4706	327	2	.	.	PUNCT
ejpam-4706	328	1	for	for	ADP
ejpam-4706	328	2	any	any	DET
ejpam-4706	328	3	two	two	NUM
ejpam-4706	328	4	matrices	matrix	NOUN
ejpam-4706	328	5	,	,	PUNCT
ejpam-4706	328	6	d	d	PROPN
ejpam-4706	328	7	∈	∈	PROPN
ejpam-4706	328	8	mn	mn	PROPN
ejpam-4706	328	9	(	(	PUNCT
ejpam-4706	328	10	c	c	NOUN
ejpam-4706	328	11	)	)	PUNCT
ejpam-4706	328	12	,	,	PUNCT
ejpam-4706	328	13	let	let	VERB
ejpam-4706	328	14	t	t	PROPN
ejpam-4706	328	15	(	(	PUNCT
ejpam-4706	328	16	c	c	X
ejpam-4706	328	17	,	,	PUNCT
ejpam-4706	328	18	d	d	NOUN
ejpam-4706	328	19	)	)	PUNCT
ejpam-4706	328	20	=	=	NOUN
ejpam-4706	329	1	[	[	PUNCT
ejpam-4706	329	2	0	0	NUM
ejpam-4706	329	3	c	c	NOUN
ejpam-4706	329	4	d	d	NOUN
ejpam-4706	329	5	0	0	NUM
ejpam-4706	329	6	]	]	PUNCT
ejpam-4706	329	7	.	.	PUNCT
ejpam-4706	330	1	applying	apply	VERB
ejpam-4706	330	2	lemma	lemma	PROPN
ejpam-4706	330	3	1	1	NUM
ejpam-4706	330	4	for	for	ADP
ejpam-4706	330	5	the	the	DET
ejpam-4706	330	6	matrix	matrix	NOUN
ejpam-4706	330	7	h	h	NOUN
ejpam-4706	330	8	,	,	PUNCT
ejpam-4706	330	9	we	we	PRON
ejpam-4706	330	10	have	have	VERB
ejpam-4706	330	11	w	w	PROPN
ejpam-4706	330	12	(	(	PUNCT
ejpam-4706	330	13	h	h	NOUN
ejpam-4706	330	14	)	)	PUNCT
ejpam-4706	330	15	≤	≤	NOUN
ejpam-4706	331	1	w	w	ADP
ejpam-4706	331	2	(	(	PUNCT
ejpam-4706	331	3	s	s	NOUN
ejpam-4706	331	4	)	)	PUNCT
ejpam-4706	331	5	where	where	SCONJ
ejpam-4706	331	6	the	the	DET
ejpam-4706	331	7	block	block	NOUN
ejpam-4706	331	8	matrix	matrix	NOUN
ejpam-4706	331	9	s	s	VERB
ejpam-4706	331	10	is	be	AUX
ejpam-4706	331	11	given	give	VERB
ejpam-4706	331	12	by	by	ADP
ejpam-4706	331	13	s	s	NOUN
ejpam-4706	331	14	=	=	SYM
ejpam-4706	331	15	s11	s11	PROPN
ejpam-4706	331	16	s12	s12	PROPN
ejpam-4706	331	17	s13	s13	PROPN
ejpam-4706	331	18	s21	s21	PROPN
ejpam-4706	331	19	s22	s22	PROPN
ejpam-4706	331	20	s23	s23	PROPN
ejpam-4706	331	21	s31	s31	NOUN
ejpam-4706	331	22	s32	s32	NOUN
ejpam-4706	331	23	s33	s33	NOUN
ejpam-4706	331	24			NOUN
ejpam-4706	331	25	,	,	PUNCT
ejpam-4706	331	26	s11	s11	NOUN
ejpam-4706	331	27	=	=	SYM
ejpam-4706	331	28	[	[	PUNCT
ejpam-4706	331	29	w(bm	w(bm	PROPN
ejpam-4706	331	30	−am	−am	PROPN
ejpam-4706	331	31	+	+	X
ejpam-4706	331	32	i	i	NOUN
ejpam-4706	331	33	)	)	PUNCT
ejpam-4706	331	34	w(t	w(t	PROPN
ejpam-4706	331	35	(	(	PUNCT
ejpam-4706	331	36	bm−1	bm−1	NOUN
ejpam-4706	331	37	−bm	−bm	NOUN
ejpam-4706	332	1	+	+	NOUN
ejpam-4706	332	2	am	be	AUX
ejpam-4706	332	3	−am−1	−am−1	NUM
ejpam-4706	332	4	,	,	PUNCT
ejpam-4706	332	5	i	i	PRON
ejpam-4706	332	6	−am	−am	PROPN
ejpam-4706	332	7	)	)	PUNCT
ejpam-4706	332	8	)	)	PUNCT
ejpam-4706	333	1	w(t	w(t	PROPN
ejpam-4706	333	2	(	(	PUNCT
ejpam-4706	333	3	i	i	PRON
ejpam-4706	333	4	−am	−am	PROPN
ejpam-4706	333	5	,	,	PUNCT
ejpam-4706	333	6	bm−1	bm−1	NOUN
ejpam-4706	333	7	−bm	−bm	NOUN
ejpam-4706	334	1	+	+	NOUN
ejpam-4706	334	2	am	be	AUX
ejpam-4706	334	3	−am−1	−am−1	NUM
ejpam-4706	334	4	)	)	PUNCT
ejpam-4706	334	5	)	)	PUNCT
ejpam-4706	335	1	w	w	X
ejpam-4706	335	2	(	(	PUNCT
ejpam-4706	335	3	am	be	AUX
ejpam-4706	335	4	−am−1	−am−1	NUM
ejpam-4706	335	5	)	)	PUNCT
ejpam-4706	335	6	]	]	PUNCT
ejpam-4706	335	7	2×2	2×2	NUM
ejpam-4706	335	8	,	,	PUNCT
ejpam-4706	335	9	s12	s12	NOUN
ejpam-4706	335	10	=	=	SYM
ejpam-4706	335	11			NOUN
ejpam-4706	335	12			NOUN
ejpam-4706	335	13	w(t	w(t	PROPN
ejpam-4706	335	14	(	(	PUNCT
ejpam-4706	335	15	i	i	NOUN
ejpam-4706	335	16	,	,	PUNCT
ejpam-4706	335	17	bm−2	bm−2	PROPN
ejpam-4706	335	18	−bm−1	−bm−1	NOUN
ejpam-4706	335	19	+	+	PROPN
ejpam-4706	335	20	am−1	am−1	PROPN
ejpam-4706	335	21	−am−2	−am−2	NUM
ejpam-4706	335	22	)	)	PUNCT
ejpam-4706	335	23	)	)	PUNCT
ejpam-4706	336	1	w(t	w(t	PROPN
ejpam-4706	336	2	(	(	PUNCT
ejpam-4706	336	3	0	0	NUM
ejpam-4706	336	4	,	,	PUNCT
ejpam-4706	336	5	am−1	am−1	PROPN
ejpam-4706	336	6	−am−2	−am−2	NUM
ejpam-4706	336	7	)	)	PUNCT
ejpam-4706	336	8	)	)	PUNCT
ejpam-4706	337	1	w(t	w(t	PROPN
ejpam-4706	337	2	(	(	PUNCT
ejpam-4706	337	3	0	0	NUM
ejpam-4706	337	4	,	,	PUNCT
ejpam-4706	337	5	bm−3	bm−3	PROPN
ejpam-4706	337	6	−bm−2	−bm−2	ADP
ejpam-4706	337	7	+	+	PROPN
ejpam-4706	337	8	am−2	am−2	PROPN
ejpam-4706	337	9	−am−3	−am−3	NOUN
ejpam-4706	337	10	)	)	PUNCT
ejpam-4706	337	11	)	)	PUNCT
ejpam-4706	338	1	w(t	w(t	PROPN
ejpam-4706	338	2	(	(	PUNCT
ejpam-4706	338	3	i	i	NOUN
ejpam-4706	338	4	,	,	PUNCT
ejpam-4706	338	5	am−2	am−2	PROPN
ejpam-4706	338	6	−am−3	−am−3	NOUN
ejpam-4706	338	7	)	)	PUNCT
ejpam-4706	338	8	)	)	PUNCT
ejpam-4706	338	9	...	...	PUNCT
ejpam-4706	339	1	w(t	w(t	PROPN
ejpam-4706	339	2	(	(	PUNCT
ejpam-4706	339	3	0	0	NUM
ejpam-4706	339	4	,	,	PUNCT
ejpam-4706	339	5	am−3	am−3	PROPN
ejpam-4706	339	6	−am−4	−am−4	NUM
ejpam-4706	339	7	)	)	PUNCT
ejpam-4706	339	8	)	)	PUNCT
ejpam-4706	339	9	...	...	PUNCT
ejpam-4706	339	10	...	...	PUNCT
ejpam-4706	340	1	w(t	w(t	X
ejpam-4706	340	2	(	(	PUNCT
ejpam-4706	340	3	0	0	NUM
ejpam-4706	340	4	,	,	PUNCT
ejpam-4706	340	5	b3	b3	PROPN
ejpam-4706	340	6	−b4	−b4	PROPN
ejpam-4706	340	7	+	+	PROPN
ejpam-4706	340	8	a4	a4	PROPN
ejpam-4706	340	9	−a3	−a3	NOUN
ejpam-4706	340	10	)	)	PUNCT
ejpam-4706	340	11	)	)	PUNCT
ejpam-4706	341	1	w(t	w(t	PROPN
ejpam-4706	341	2	(	(	PUNCT
ejpam-4706	341	3	0	0	NUM
ejpam-4706	341	4	,	,	PUNCT
ejpam-4706	341	5	a4	a4	PROPN
ejpam-4706	341	6	−a3	−a3	NOUN
ejpam-4706	341	7	)	)	PUNCT
ejpam-4706	341	8	)	)	PUNCT
ejpam-4706	341	9			NUM
ejpam-4706	341	10	t	t	NOUN
ejpam-4706	341	11	2×(mn−4	2×(mn−4	NUM
ejpam-4706	341	12	)	)	PUNCT
ejpam-4706	341	13	,	,	PUNCT
ejpam-4706	341	14	a.	a.	NOUN
ejpam-4706	341	15	burqan	burqan	PROPN
ejpam-4706	341	16	et	et	PROPN
ejpam-4706	341	17	al	al	PROPN
ejpam-4706	341	18	.	.	PUNCT
ejpam-4706	341	19	/	/	SYM
ejpam-4706	341	20	eur	eur	PROPN
ejpam-4706	341	21	.	.	PUNCT
ejpam-4706	342	1	j.	j.	PROPN
ejpam-4706	342	2	pure	pure	PROPN
ejpam-4706	342	3	appl	appl	PROPN
ejpam-4706	342	4	.	.	PROPN
ejpam-4706	342	5	math	math	PROPN
ejpam-4706	342	6	,	,	PUNCT
ejpam-4706	342	7	16	16	NUM
ejpam-4706	342	8	(	(	PUNCT
ejpam-4706	342	9	2	2	NUM
ejpam-4706	342	10	)	)	PUNCT
ejpam-4706	342	11	(	(	PUNCT
ejpam-4706	342	12	2023	2023	NUM
ejpam-4706	342	13	)	)	PUNCT
ejpam-4706	342	14	,	,	PUNCT
ejpam-4706	342	15	806	806	NUM
ejpam-4706	342	16	-	-	SYM
ejpam-4706	342	17	818	818	NUM
ejpam-4706	342	18	814	814	NUM
ejpam-4706	342	19	s13	s13	NOUN
ejpam-4706	342	20	=	=	PROPN
ejpam-4706	342	21	[	[	PUNCT
ejpam-4706	342	22	w(t	w(t	PROPN
ejpam-4706	342	23	(	(	PUNCT
ejpam-4706	342	24	b2	b2	NOUN
ejpam-4706	342	25	−b3	−b3	PROPN
ejpam-4706	342	26	+	+	PROPN
ejpam-4706	342	27	a3	a3	NOUN
ejpam-4706	342	28	−a2	−a2	NOUN
ejpam-4706	342	29	,	,	PUNCT
ejpam-4706	342	30	0	0	NUM
ejpam-4706	342	31	)	)	PUNCT
ejpam-4706	342	32	)	)	PUNCT
ejpam-4706	343	1	w(t	w(t	PROPN
ejpam-4706	343	2	(	(	PUNCT
ejpam-4706	343	3	b1	b1	VERB
ejpam-4706	343	4	−b2	−b2	PROPN
ejpam-4706	343	5	+	+	PROPN
ejpam-4706	343	6	a2	a2	PROPN
ejpam-4706	343	7	−a1	−a1	VERB
ejpam-4706	343	8	,	,	PUNCT
ejpam-4706	343	9	0	0	NUM
ejpam-4706	343	10	)	)	PUNCT
ejpam-4706	343	11	)	)	PUNCT
ejpam-4706	344	1	w(t	w(t	PROPN
ejpam-4706	344	2	(	(	PUNCT
ejpam-4706	344	3	a3	a3	NOUN
ejpam-4706	344	4	−a2	−a2	NOUN
ejpam-4706	344	5	−	−	PROPN
ejpam-4706	345	1	i	i	PRON
ejpam-4706	345	2	,	,	PUNCT
ejpam-4706	345	3	0	0	NUM
ejpam-4706	345	4	)	)	PUNCT
ejpam-4706	345	5	)	)	PUNCT
ejpam-4706	346	1	w(t	w(t	PROPN
ejpam-4706	346	2	(	(	PUNCT
ejpam-4706	346	3	a2	a2	PROPN
ejpam-4706	346	4	−a1	−a1	PROPN
ejpam-4706	346	5	,	,	PUNCT
ejpam-4706	346	6	0	0	NUM
ejpam-4706	346	7	)	)	PUNCT
ejpam-4706	346	8	)	)	PUNCT
ejpam-4706	346	9	]	]	PUNCT
ejpam-4706	346	10	2×2	2×2	NUM
ejpam-4706	346	11	,	,	PUNCT
ejpam-4706	346	12	s21	s21	NOUN
ejpam-4706	346	13	=	=	SYM
ejpam-4706	346	14			NOUN
ejpam-4706	346	15	w(t	w(t	PROPN
ejpam-4706	346	16	(	(	PUNCT
ejpam-4706	346	17	i	i	NOUN
ejpam-4706	346	18	,	,	PUNCT
ejpam-4706	346	19	bm−2	bm−2	PROPN
ejpam-4706	346	20	−bm−1	−bm−1	NOUN
ejpam-4706	346	21	+	+	PROPN
ejpam-4706	346	22	am−1	am−1	PROPN
ejpam-4706	346	23	−am−2	−am−2	NUM
ejpam-4706	346	24	)	)	PUNCT
ejpam-4706	346	25	)	)	PUNCT
ejpam-4706	347	1	w(t	w(t	PROPN
ejpam-4706	347	2	(	(	PUNCT
ejpam-4706	347	3	0	0	NUM
ejpam-4706	347	4	,	,	PUNCT
ejpam-4706	347	5	am−1	am−1	PROPN
ejpam-4706	347	6	−am−2	−am−2	NUM
ejpam-4706	347	7	)	)	PUNCT
ejpam-4706	347	8	)	)	PUNCT
ejpam-4706	348	1	w(t	w(t	PROPN
ejpam-4706	348	2	(	(	PUNCT
ejpam-4706	348	3	0	0	NUM
ejpam-4706	348	4	,	,	PUNCT
ejpam-4706	348	5	bm−3	bm−3	PROPN
ejpam-4706	348	6	−bm−2	−bm−2	ADP
ejpam-4706	348	7	+	+	PROPN
ejpam-4706	348	8	am−2	am−2	PROPN
ejpam-4706	348	9	−am−3	−am−3	NOUN
ejpam-4706	348	10	)	)	PUNCT
ejpam-4706	348	11	)	)	PUNCT
ejpam-4706	349	1	w(t	w(t	PROPN
ejpam-4706	349	2	(	(	PUNCT
ejpam-4706	349	3	i	i	NOUN
ejpam-4706	349	4	,	,	PUNCT
ejpam-4706	349	5	am−2	am−2	PROPN
ejpam-4706	349	6	−am−3	−am−3	NOUN
ejpam-4706	349	7	)	)	PUNCT
ejpam-4706	349	8	)	)	PUNCT
ejpam-4706	349	9	...	...	PUNCT
ejpam-4706	350	1	w(t	w(t	PROPN
ejpam-4706	350	2	(	(	PUNCT
ejpam-4706	350	3	0	0	NUM
ejpam-4706	350	4	,	,	PUNCT
ejpam-4706	350	5	am−3	am−3	PROPN
ejpam-4706	350	6	−am−4	−am−4	NUM
ejpam-4706	350	7	)	)	PUNCT
ejpam-4706	350	8	)	)	PUNCT
ejpam-4706	350	9	...	...	PUNCT
ejpam-4706	350	10	...	...	PUNCT
ejpam-4706	351	1	w(t	w(t	X
ejpam-4706	351	2	(	(	PUNCT
ejpam-4706	351	3	0	0	NUM
ejpam-4706	351	4	,	,	PUNCT
ejpam-4706	351	5	b3	b3	PROPN
ejpam-4706	351	6	−b4	−b4	PROPN
ejpam-4706	351	7	+	+	PROPN
ejpam-4706	351	8	a4	a4	PROPN
ejpam-4706	351	9	−a3	−a3	NOUN
ejpam-4706	351	10	)	)	PUNCT
ejpam-4706	351	11	)	)	PUNCT
ejpam-4706	351	12	w(t	w(t	PROPN
ejpam-4706	351	13	(	(	PUNCT
ejpam-4706	351	14	0	0	NUM
ejpam-4706	351	15	,	,	PUNCT
ejpam-4706	351	16	a4	a4	PROPN
ejpam-4706	351	17	−a3	−a3	NOUN
ejpam-4706	351	18	)	)	PUNCT
ejpam-4706	351	19	)	)	PUNCT
ejpam-4706	351	20			NUM
ejpam-4706	351	21	(	(	PUNCT
ejpam-4706	351	22	mn−4)×2	mn−4)×2	NUM
ejpam-4706	351	23	,	,	PUNCT
ejpam-4706	351	24	s22	s22	NOUN
ejpam-4706	351	25	=	=	SYM
ejpam-4706	351	26			NOUN
ejpam-4706	351	27	w(0	w(0	PROPN
ejpam-4706	351	28	)	)	PUNCT
ejpam-4706	351	29	w(t	w(t	PROPN
ejpam-4706	351	30	(	(	PUNCT
ejpam-4706	351	31	0.0	0.0	NUM
ejpam-4706	351	32	)	)	PUNCT
ejpam-4706	351	33	)	)	PUNCT
ejpam-4706	352	1	w(t	w(t	PROPN
ejpam-4706	352	2	(	(	PUNCT
ejpam-4706	352	3	0.i	0.i	PROPN
ejpam-4706	352	4	)	)	PUNCT
ejpam-4706	352	5	)	)	PUNCT
ejpam-4706	353	1	w(t	w(t	PROPN
ejpam-4706	353	2	(	(	PUNCT
ejpam-4706	353	3	0.0	0.0	NUM
ejpam-4706	353	4	)	)	PUNCT
ejpam-4706	353	5	)	)	PUNCT
ejpam-4706	353	6	.	.	PUNCT
ejpam-4706	353	7	.	.	PUNCT
ejpam-4706	353	8	.	.	PUNCT
ejpam-4706	354	1	w(t	w(t	PROPN
ejpam-4706	354	2	(	(	PUNCT
ejpam-4706	354	3	0.0	0.0	NUM
ejpam-4706	354	4	)	)	PUNCT
ejpam-4706	354	5	)	)	PUNCT
ejpam-4706	355	1	w(t	w(t	PROPN
ejpam-4706	355	2	(	(	PUNCT
ejpam-4706	355	3	0.0	0.0	NUM
ejpam-4706	355	4	)	)	PUNCT
ejpam-4706	355	5	)	)	PUNCT
ejpam-4706	356	1	w(t	w(t	PROPN
ejpam-4706	356	2	(	(	PUNCT
ejpam-4706	356	3	0.0	0.0	NUM
ejpam-4706	356	4	)	)	PUNCT
ejpam-4706	356	5	)	)	PUNCT
ejpam-4706	357	1	w(0	w(0	PROPN
ejpam-4706	357	2	)	)	PUNCT
ejpam-4706	357	3	w(t	w(t	PROPN
ejpam-4706	357	4	(	(	PUNCT
ejpam-4706	357	5	0.0	0.0	NUM
ejpam-4706	357	6	)	)	PUNCT
ejpam-4706	357	7	)	)	PUNCT
ejpam-4706	358	1	w(t	w(t	PROPN
ejpam-4706	358	2	(	(	PUNCT
ejpam-4706	358	3	0.i	0.i	PROPN
ejpam-4706	358	4	)	)	PUNCT
ejpam-4706	358	5	)	)	PUNCT
ejpam-4706	358	6	.	.	PUNCT
ejpam-4706	358	7	.	.	PUNCT
ejpam-4706	358	8	.	.	PUNCT
ejpam-4706	359	1	w(t	w(t	PROPN
ejpam-4706	359	2	(	(	PUNCT
ejpam-4706	359	3	0.0	0.0	NUM
ejpam-4706	359	4	)	)	PUNCT
ejpam-4706	359	5	)	)	PUNCT
ejpam-4706	360	1	w(t	w(t	PROPN
ejpam-4706	360	2	(	(	PUNCT
ejpam-4706	360	3	0.0	0.0	NUM
ejpam-4706	360	4	)	)	PUNCT
ejpam-4706	360	5	)	)	PUNCT
ejpam-4706	361	1	w(t	w(t	PROPN
ejpam-4706	361	2	(	(	PUNCT
ejpam-4706	361	3	i.0	i.0	NOUN
ejpam-4706	361	4	)	)	PUNCT
ejpam-4706	361	5	)	)	PUNCT
ejpam-4706	362	1	w(t	w(t	PROPN
ejpam-4706	362	2	(	(	PUNCT
ejpam-4706	362	3	0.0	0.0	NUM
ejpam-4706	362	4	)	)	PUNCT
ejpam-4706	362	5	)	)	PUNCT
ejpam-4706	363	1	w(0	w(0	PROPN
ejpam-4706	363	2	)	)	PUNCT
ejpam-4706	363	3	w(t	w(t	PROPN
ejpam-4706	363	4	(	(	PUNCT
ejpam-4706	363	5	0.0	0.0	NUM
ejpam-4706	363	6	)	)	PUNCT
ejpam-4706	363	7	)	)	PUNCT
ejpam-4706	363	8	.	.	PUNCT
ejpam-4706	363	9	.	.	PUNCT
ejpam-4706	363	10	.	.	PUNCT
ejpam-4706	364	1	w(t	w(t	PROPN
ejpam-4706	364	2	(	(	PUNCT
ejpam-4706	364	3	0.0	0.0	NUM
ejpam-4706	364	4	)	)	PUNCT
ejpam-4706	364	5	)	)	PUNCT
ejpam-4706	365	1	w(t	w(t	PROPN
ejpam-4706	365	2	(	(	PUNCT
ejpam-4706	365	3	0.0	0.0	NUM
ejpam-4706	365	4	)	)	PUNCT
ejpam-4706	365	5	)	)	PUNCT
ejpam-4706	366	1	w(t	w(t	PROPN
ejpam-4706	366	2	(	(	PUNCT
ejpam-4706	366	3	0.0	0.0	NUM
ejpam-4706	366	4	)	)	PUNCT
ejpam-4706	366	5	)	)	PUNCT
ejpam-4706	367	1	w(t	w(t	PROPN
ejpam-4706	367	2	(	(	PUNCT
ejpam-4706	367	3	i.0	i.0	NOUN
ejpam-4706	367	4	)	)	PUNCT
ejpam-4706	367	5	)	)	PUNCT
ejpam-4706	368	1	w(t	w(t	PROPN
ejpam-4706	368	2	(	(	PUNCT
ejpam-4706	368	3	0.0	0.0	NUM
ejpam-4706	368	4	)	)	PUNCT
ejpam-4706	368	5	)	)	PUNCT
ejpam-4706	369	1	w(0	w(0	PROPN
ejpam-4706	369	2	)	)	PUNCT
ejpam-4706	369	3	.	.	PUNCT
ejpam-4706	369	4	.	.	PUNCT
ejpam-4706	369	5	.	.	PUNCT
ejpam-4706	370	1	w(t	w(t	PROPN
ejpam-4706	370	2	(	(	PUNCT
ejpam-4706	370	3	0.i	0.i	PROPN
ejpam-4706	370	4	)	)	PUNCT
ejpam-4706	370	5	)	)	PUNCT
ejpam-4706	371	1	w(t	w(t	PROPN
ejpam-4706	371	2	(	(	PUNCT
ejpam-4706	371	3	0.0	0.0	NUM
ejpam-4706	371	4	)	)	PUNCT
ejpam-4706	371	5	)	)	PUNCT
ejpam-4706	372	1	w(t	w(t	PROPN
ejpam-4706	372	2	(	(	PUNCT
ejpam-4706	372	3	0.0	0.0	NUM
ejpam-4706	372	4	)	)	PUNCT
ejpam-4706	372	5	)	)	PUNCT
ejpam-4706	373	1	w(t	w(t	PROPN
ejpam-4706	373	2	(	(	PUNCT
ejpam-4706	373	3	0.0	0.0	NUM
ejpam-4706	373	4	)	)	PUNCT
ejpam-4706	373	5	)	)	PUNCT
ejpam-4706	374	1	w(t	w(t	PROPN
ejpam-4706	374	2	(	(	PUNCT
ejpam-4706	374	3	i.0	i.0	NOUN
ejpam-4706	374	4	)	)	PUNCT
ejpam-4706	374	5	)	)	PUNCT
ejpam-4706	375	1	w(t	w(t	PROPN
ejpam-4706	375	2	(	(	PUNCT
ejpam-4706	375	3	0.0	0.0	NUM
ejpam-4706	375	4	)	)	PUNCT
ejpam-4706	375	5	)	)	PUNCT
ejpam-4706	375	6	.	.	PUNCT
ejpam-4706	375	7	.	.	PUNCT
ejpam-4706	375	8	.	.	PUNCT
ejpam-4706	376	1	w(t	w(t	PROPN
ejpam-4706	376	2	(	(	PUNCT
ejpam-4706	376	3	0.0	0.0	NUM
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ejpam-4706	376	5	)	)	PUNCT
ejpam-4706	376	6	w(t	w(t	PROPN
ejpam-4706	376	7	(	(	PUNCT
ejpam-4706	376	8	0.i	0.i	PROPN
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ejpam-4706	376	10	)	)	PUNCT
ejpam-4706	376	11	...	...	PUNCT
ejpam-4706	376	12	...	...	PUNCT
ejpam-4706	376	13	...	...	PUNCT
ejpam-4706	376	14	.	.	PUNCT
ejpam-4706	376	15	.	.	PUNCT
ejpam-4706	376	16	.	.	PUNCT
ejpam-4706	376	17	.	.	PUNCT
ejpam-4706	376	18	.	.	PUNCT
ejpam-4706	376	19	.	.	PUNCT
ejpam-4706	377	1	w(0	w(0	PROPN
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ejpam-4706	377	3	w(t	w(t	PROPN
ejpam-4706	377	4	(	(	PUNCT
ejpam-4706	377	5	0.0	0.0	NUM
ejpam-4706	377	6	)	)	PUNCT
ejpam-4706	377	7	)	)	PUNCT
ejpam-4706	378	1	w(t	w(t	PROPN
ejpam-4706	378	2	(	(	PUNCT
ejpam-4706	378	3	0.0	0.0	NUM
ejpam-4706	378	4	)	)	PUNCT
ejpam-4706	378	5	)	)	PUNCT
ejpam-4706	379	1	w(t	w(t	PROPN
ejpam-4706	379	2	(	(	PUNCT
ejpam-4706	379	3	0.0	0.0	NUM
ejpam-4706	379	4	)	)	PUNCT
ejpam-4706	379	5	)	)	PUNCT
ejpam-4706	379	6	·	·	PUNCT
ejpam-4706	379	7	·	·	PUNCT
ejpam-4706	379	8	·	·	PUNCT
ejpam-4706	379	9	w(t	w(t	X
ejpam-4706	379	10	(	(	PUNCT
ejpam-4706	379	11	0.0	0.0	NUM
ejpam-4706	379	12	)	)	PUNCT
ejpam-4706	379	13	)	)	PUNCT
ejpam-4706	380	1	w(t	w(t	PROPN
ejpam-4706	380	2	(	(	PUNCT
ejpam-4706	380	3	i.0	i.0	NOUN
ejpam-4706	380	4	)	)	PUNCT
ejpam-4706	380	5	)	)	PUNCT
ejpam-4706	381	1	w(t	w(t	PROPN
ejpam-4706	381	2	(	(	PUNCT
ejpam-4706	381	3	0.0	0.0	NUM
ejpam-4706	381	4	)	)	PUNCT
ejpam-4706	381	5	)	)	PUNCT
ejpam-4706	382	1	w(0	w(0	PROPN
ejpam-4706	382	2	)	)	PUNCT
ejpam-4706	382	3			NOUN
ejpam-4706	382	4	(	(	PUNCT
ejpam-4706	382	5	mn−4)×(mn−4	mn−4)×(mn−4	X
ejpam-4706	382	6	)	)	PUNCT
ejpam-4706	382	7	,	,	PUNCT
ejpam-4706	382	8	s23	s23	NOUN
ejpam-4706	382	9	=	=	SYM
ejpam-4706	382	10			PROPN
ejpam-4706	382	11	w(t	w(t	PROPN
ejpam-4706	382	12	(	(	PUNCT
ejpam-4706	382	13	−i	−i	PROPN
ejpam-4706	382	14	,	,	PUNCT
ejpam-4706	382	15	0	0	NUM
ejpam-4706	382	16	)	)	PUNCT
ejpam-4706	382	17	)	)	PUNCT
ejpam-4706	382	18	w(t	w(t	PROPN
ejpam-4706	382	19	(	(	PUNCT
ejpam-4706	382	20	0	0	NUM
ejpam-4706	382	21	,	,	PUNCT
ejpam-4706	382	22	0	0	NUM
ejpam-4706	382	23	)	)	PUNCT
ejpam-4706	382	24	)	)	PUNCT
ejpam-4706	383	1	w(t	w(t	PROPN
ejpam-4706	383	2	(	(	PUNCT
ejpam-4706	383	3	−i	−i	PROPN
ejpam-4706	383	4	,	,	PUNCT
ejpam-4706	383	5	0	0	NUM
ejpam-4706	383	6	)	)	PUNCT
ejpam-4706	383	7	)	)	PUNCT
ejpam-4706	383	8	w(t	w(t	PROPN
ejpam-4706	383	9	(	(	PUNCT
ejpam-4706	383	10	0	0	NUM
ejpam-4706	383	11	,	,	PUNCT
ejpam-4706	383	12	0	0	NUM
ejpam-4706	383	13	)	)	PUNCT
ejpam-4706	383	14	)	)	PUNCT
ejpam-4706	383	15	...	...	PUNCT
ejpam-4706	383	16	...	...	PUNCT
ejpam-4706	384	1	w(t	w(t	PROPN
ejpam-4706	384	2	(	(	PUNCT
ejpam-4706	384	3	−i	−i	PROPN
ejpam-4706	384	4	,	,	PUNCT
ejpam-4706	384	5	0	0	NUM
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ejpam-4706	384	8	w(t	w(t	PROPN
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ejpam-4706	384	10	0	0	NUM
ejpam-4706	384	11	,	,	PUNCT
ejpam-4706	384	12	0	0	NUM
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ejpam-4706	384	14	)	)	PUNCT
ejpam-4706	384	15			PROPN
ejpam-4706	384	16	(	(	PUNCT
ejpam-4706	384	17	mn−4)×2	mn−4)×2	NUM
ejpam-4706	384	18	,	,	PUNCT
ejpam-4706	384	19	s31	s31	NOUN
ejpam-4706	384	20	=	=	PUNCT
ejpam-4706	384	21	[	[	PUNCT
ejpam-4706	384	22	w	w	PROPN
ejpam-4706	384	23	(	(	PUNCT
ejpam-4706	384	24	t	t	PROPN
ejpam-4706	384	25	(	(	PUNCT
ejpam-4706	384	26	0	0	NUM
ejpam-4706	384	27	,	,	PUNCT
ejpam-4706	384	28	b2	b2	NOUN
ejpam-4706	384	29	−b3	−b3	PROPN
ejpam-4706	384	30	+	+	PROPN
ejpam-4706	384	31	a3	a3	NOUN
ejpam-4706	384	32	−a2	−a2	NOUN
ejpam-4706	384	33	)	)	PUNCT
ejpam-4706	384	34	)	)	PUNCT
ejpam-4706	385	1	w(t	w(t	PROPN
ejpam-4706	385	2	(	(	PUNCT
ejpam-4706	385	3	0	0	NUM
ejpam-4706	385	4	,	,	PUNCT
ejpam-4706	385	5	a3	a3	NOUN
ejpam-4706	385	6	−a2	−a2	NOUN
ejpam-4706	385	7	−	−	PROPN
ejpam-4706	385	8	i	i	NOUN
ejpam-4706	385	9	)	)	PUNCT
ejpam-4706	385	10	)	)	PUNCT
ejpam-4706	386	1	w	w	X
ejpam-4706	386	2	(	(	PUNCT
ejpam-4706	386	3	t	t	PROPN
ejpam-4706	386	4	(	(	PUNCT
ejpam-4706	386	5	0	0	NUM
ejpam-4706	386	6	,	,	PUNCT
ejpam-4706	386	7	b1	b1	NOUN
ejpam-4706	386	8	−b2	−b2	PROPN
ejpam-4706	386	9	+	+	PROPN
ejpam-4706	386	10	a2	a2	PROPN
ejpam-4706	386	11	−a1	−a1	VERB
ejpam-4706	386	12	)	)	PUNCT
ejpam-4706	386	13	)	)	PUNCT
ejpam-4706	386	14	w(t	w(t	PROPN
ejpam-4706	386	15	(	(	PUNCT
ejpam-4706	386	16	0	0	NUM
ejpam-4706	386	17	,	,	PUNCT
ejpam-4706	386	18	a2	a2	NOUN
ejpam-4706	386	19	−a1	−a1	VERB
ejpam-4706	386	20	)	)	PUNCT
ejpam-4706	386	21	)	)	PUNCT
ejpam-4706	386	22	]	]	PUNCT
ejpam-4706	387	1	2×2	2×2	NOUN
ejpam-4706	387	2	,	,	PUNCT
ejpam-4706	387	3	s32	s32	NOUN
ejpam-4706	387	4	=	=	PUNCT
ejpam-4706	387	5	[	[	PUNCT
ejpam-4706	387	6	w(t	w(t	PROPN
ejpam-4706	387	7	(	(	PUNCT
ejpam-4706	387	8	0,−i	0,−i	PROPN
ejpam-4706	387	9	)	)	PUNCT
ejpam-4706	387	10	)	)	PUNCT
ejpam-4706	387	11	w(t	w(t	PROPN
ejpam-4706	387	12	(	(	PUNCT
ejpam-4706	387	13	0,−i	0,−i	PROPN
ejpam-4706	387	14	)	)	PUNCT
ejpam-4706	387	15	)	)	PUNCT
ejpam-4706	387	16	·	·	PUNCT
ejpam-4706	387	17	·	·	PUNCT
ejpam-4706	387	18	·	·	PUNCT
ejpam-4706	387	19	w(t	w(t	PROPN
ejpam-4706	387	20	(	(	PUNCT
ejpam-4706	387	21	i,−i	i,−i	NOUN
ejpam-4706	387	22	)	)	PUNCT
ejpam-4706	387	23	)	)	PUNCT
ejpam-4706	388	1	w(t	w(t	PROPN
ejpam-4706	388	2	(	(	PUNCT
ejpam-4706	388	3	0,−i	0,−i	PROPN
ejpam-4706	388	4	)	)	PUNCT
ejpam-4706	388	5	)	)	PUNCT
ejpam-4706	388	6	w(t	w(t	PROPN
ejpam-4706	388	7	(	(	PUNCT
ejpam-4706	388	8	0	0	NUM
ejpam-4706	388	9	,	,	PUNCT
ejpam-4706	388	10	0	0	NUM
ejpam-4706	388	11	)	)	PUNCT
ejpam-4706	388	12	)	)	PUNCT
ejpam-4706	389	1	w(t	w(t	PROPN
ejpam-4706	389	2	(	(	PUNCT
ejpam-4706	389	3	0	0	NUM
ejpam-4706	389	4	,	,	PUNCT
ejpam-4706	389	5	0	0	NUM
ejpam-4706	389	6	)	)	PUNCT
ejpam-4706	389	7	)	)	PUNCT
ejpam-4706	389	8	·	·	PUNCT
ejpam-4706	389	9	·	·	PUNCT
ejpam-4706	389	10	·	·	PUNCT
ejpam-4706	389	11	w(t	w(t	X
ejpam-4706	389	12	(	(	PUNCT
ejpam-4706	389	13	0	0	NUM
ejpam-4706	389	14	,	,	PUNCT
ejpam-4706	389	15	0	0	NUM
ejpam-4706	389	16	)	)	PUNCT
ejpam-4706	389	17	)	)	PUNCT
ejpam-4706	389	18	w(t	w(t	PROPN
ejpam-4706	389	19	(	(	PUNCT
ejpam-4706	389	20	i	i	NOUN
ejpam-4706	389	21	,	,	PUNCT
ejpam-4706	389	22	0	0	NUM
ejpam-4706	389	23	)	)	PUNCT
ejpam-4706	389	24	)	)	PUNCT
ejpam-4706	389	25	]	]	PUNCT
ejpam-4706	390	1	2×(mn−4	2×(mn−4	NUM
ejpam-4706	390	2	)	)	PUNCT
ejpam-4706	390	3	,	,	PUNCT
ejpam-4706	390	4	and	and	CCONJ
ejpam-4706	390	5	s33	s33	NUM
ejpam-4706	390	6	=	=	PUNCT
ejpam-4706	390	7	[	[	PUNCT
ejpam-4706	390	8	w	w	PROPN
ejpam-4706	390	9	(	(	PUNCT
ejpam-4706	390	10	t	t	PROPN
ejpam-4706	390	11	(	(	PUNCT
ejpam-4706	390	12	−i	−i	PROPN
ejpam-4706	390	13	,	,	PUNCT
ejpam-4706	390	14	0	0	NUM
ejpam-4706	390	15	)	)	PUNCT
ejpam-4706	390	16	)	)	PUNCT
ejpam-4706	391	1	w	w	X
ejpam-4706	391	2	(	(	PUNCT
ejpam-4706	391	3	t	t	PROPN
ejpam-4706	391	4	(	(	PUNCT
ejpam-4706	391	5	0,−i	0,−i	PROPN
ejpam-4706	391	6	)	)	PUNCT
ejpam-4706	391	7	)	)	PUNCT
ejpam-4706	392	1	w	w	PROPN
ejpam-4706	392	2	(	(	PUNCT
ejpam-4706	392	3	t	t	PROPN
ejpam-4706	392	4	(	(	PUNCT
ejpam-4706	392	5	−i	−i	PROPN
ejpam-4706	392	6	,	,	PUNCT
ejpam-4706	392	7	0	0	NUM
ejpam-4706	392	8	)	)	PUNCT
ejpam-4706	392	9	)	)	PUNCT
ejpam-4706	393	1	w	w	X
ejpam-4706	393	2	(	(	PUNCT
ejpam-4706	393	3	0	0	NUM
ejpam-4706	393	4	)	)	PUNCT
ejpam-4706	393	5	]	]	PUNCT
ejpam-4706	393	6	2×2	2×2	NOUN
ejpam-4706	393	7	.	.	PUNCT
ejpam-4706	394	1	we	we	PRON
ejpam-4706	394	2	achieve	achieve	VERB
ejpam-4706	394	3	our	our	PRON
ejpam-4706	394	4	goal	goal	NOUN
ejpam-4706	394	5	by	by	ADP
ejpam-4706	394	6	applying	apply	VERB
ejpam-4706	394	7	lemma	lemma	PROPN
ejpam-4706	394	8	4	4	NUM
ejpam-4706	394	9	on	on	ADP
ejpam-4706	394	10	the	the	DET
ejpam-4706	394	11	matrix	matrix	NOUN
ejpam-4706	394	12	s.	s.	PROPN
ejpam-4706	395	1	so	so	ADV
ejpam-4706	395	2	,	,	PUNCT
ejpam-4706	395	3	we	we	PRON
ejpam-4706	395	4	need	need	VERB
ejpam-4706	395	5	to	to	PART
ejpam-4706	395	6	estimate	estimate	VERB
ejpam-4706	395	7	w(s11	w(s11	NOUN
ejpam-4706	395	8	)	)	PUNCT
ejpam-4706	395	9	,	,	PUNCT
ejpam-4706	395	10	w(s22	w(s22	NOUN
ejpam-4706	395	11	)	)	PUNCT
ejpam-4706	395	12	,	,	PUNCT
ejpam-4706	395	13	w(s33	w(s33	ADJ
ejpam-4706	395	14	)	)	PUNCT
ejpam-4706	395	15	,	,	PUNCT
ejpam-4706	395	16	∥s12∥	∥s12∥	PROPN
ejpam-4706	395	17	,	,	PUNCT
ejpam-4706	395	18	∥s13∥	∥s13∥	NUM
ejpam-4706	395	19	,	,	PUNCT
ejpam-4706	395	20	∥s21∥∥s31∥	∥s21∥∥s31∥	PROPN
ejpam-4706	395	21	,	,	PUNCT
ejpam-4706	395	22	∥s23∥	∥s23∥	PUNCT
ejpam-4706	395	23	and	and	CCONJ
ejpam-4706	395	24	∥s32∥.	∥s32∥.	NOUN
ejpam-4706	395	25	since	since	SCONJ
ejpam-4706	395	26	s11	s11	PROPN
ejpam-4706	395	27	is	be	AUX
ejpam-4706	395	28	hermitian	hermitian	ADJ
ejpam-4706	395	29	,	,	PUNCT
ejpam-4706	395	30	applying	apply	VERB
ejpam-4706	395	31	lemma	lemma	PROPN
ejpam-4706	395	32	3	3	NUM
ejpam-4706	395	33	to	to	PART
ejpam-4706	395	34	get	get	VERB
ejpam-4706	395	35	w(s11	w(s11	NOUN
ejpam-4706	395	36	)	)	PUNCT
ejpam-4706	396	1	=	=	SYM
ejpam-4706	396	2	r(s11	r(s11	NOUN
ejpam-4706	396	3	)	)	PUNCT
ejpam-4706	397	1	=	=	SYM
ejpam-4706	397	2	ξ	ξ	NOUN
ejpam-4706	397	3	,	,	PUNCT
ejpam-4706	397	4	where	where	SCONJ
ejpam-4706	397	5	ξ	ξ	X
ejpam-4706	397	6	=	=	SYM
ejpam-4706	397	7	1	1	NUM
ejpam-4706	397	8	2	2	NUM
ejpam-4706	397	9	(	(	PUNCT
ejpam-4706	397	10	w(bm	w(bm	PROPN
ejpam-4706	397	11	−am	−am	PROPN
ejpam-4706	397	12	+	+	X
ejpam-4706	397	13	i	i	NOUN
ejpam-4706	397	14	)	)	PUNCT
ejpam-4706	398	1	+	+	CCONJ
ejpam-4706	398	2	w(am	w(am	PROPN
ejpam-4706	398	3	−am−1	−am−1	NUM
ejpam-4706	398	4	)	)	PUNCT
ejpam-4706	398	5	)	)	PUNCT
ejpam-4706	399	1	+	+	CCONJ
ejpam-4706	399	2	1	1	NUM
ejpam-4706	399	3	2	2	NUM
ejpam-4706	399	4	√	√	NUM
ejpam-4706	399	5	(	(	PUNCT
ejpam-4706	399	6	w	w	PROPN
ejpam-4706	399	7	(	(	PUNCT
ejpam-4706	399	8	bm	bm	PROPN
ejpam-4706	399	9	−am	−am	PROPN
ejpam-4706	399	10	+	+	PROPN
ejpam-4706	399	11	i)−	i)−	PROPN
ejpam-4706	399	12	w	w	PROPN
ejpam-4706	399	13	(	(	PUNCT
ejpam-4706	399	14	am	be	AUX
ejpam-4706	399	15	−am−1	−am−1	NUM
ejpam-4706	399	16	)	)	PUNCT
ejpam-4706	399	17	)	)	PUNCT
ejpam-4706	399	18	2	2	NUM
ejpam-4706	400	1	+	+	CCONJ
ejpam-4706	400	2	4w2	4w2	NUM
ejpam-4706	400	3	(	(	PUNCT
ejpam-4706	400	4	t	t	PROPN
ejpam-4706	400	5	(	(	PUNCT
ejpam-4706	400	6	bm−1	bm−1	PROPN
ejpam-4706	400	7	−bm	−bm	NOUN
ejpam-4706	401	1	+	+	NOUN
ejpam-4706	401	2	am	be	AUX
ejpam-4706	401	3	−am−1	−am−1	NUM
ejpam-4706	401	4	,	,	PUNCT
ejpam-4706	401	5	i	i	PRON
ejpam-4706	401	6	−am	−am	PROPN
ejpam-4706	401	7	)	)	PUNCT
ejpam-4706	401	8	)	)	PUNCT
ejpam-4706	401	9	.	.	PUNCT
ejpam-4706	402	1	a.	a.	PROPN
ejpam-4706	402	2	burqan	burqan	PROPN
ejpam-4706	402	3	et	et	PROPN
ejpam-4706	402	4	al	al	PROPN
ejpam-4706	402	5	.	.	PUNCT
ejpam-4706	402	6	/	/	SYM
ejpam-4706	402	7	eur	eur	PROPN
ejpam-4706	402	8	.	.	PUNCT
ejpam-4706	403	1	j.	j.	PROPN
ejpam-4706	403	2	pure	pure	PROPN
ejpam-4706	403	3	appl	appl	PROPN
ejpam-4706	403	4	.	.	PROPN
ejpam-4706	403	5	math	math	PROPN
ejpam-4706	403	6	,	,	PUNCT
ejpam-4706	403	7	16	16	NUM
ejpam-4706	403	8	(	(	PUNCT
ejpam-4706	403	9	2	2	NUM
ejpam-4706	403	10	)	)	PUNCT
ejpam-4706	403	11	(	(	PUNCT
ejpam-4706	403	12	2023	2023	NUM
ejpam-4706	403	13	)	)	PUNCT
ejpam-4706	403	14	,	,	PUNCT
ejpam-4706	403	15	806	806	NUM
ejpam-4706	403	16	-	-	SYM
ejpam-4706	403	17	818	818	NUM
ejpam-4706	403	18	815	815	NUM
ejpam-4706	403	19	using	use	VERB
ejpam-4706	403	20	the	the	DET
ejpam-4706	403	21	fact	fact	NOUN
ejpam-4706	403	22	that	that	SCONJ
ejpam-4706	403	23	w	w	INTJ
ejpam-4706	403	24	(	(	PUNCT
ejpam-4706	403	25	[	[	PUNCT
ejpam-4706	403	26	0	0	NUM
ejpam-4706	403	27	a	a	DET
ejpam-4706	403	28	0	0	NUM
ejpam-4706	403	29	0	0	NUM
ejpam-4706	403	30	]	]	PUNCT
ejpam-4706	403	31	)	)	PUNCT
ejpam-4706	404	1	=	=	SYM
ejpam-4706	404	2	w	w	X
ejpam-4706	404	3	(	(	PUNCT
ejpam-4706	404	4	[	[	PUNCT
ejpam-4706	404	5	0	0	NUM
ejpam-4706	404	6	0	0	NUM
ejpam-4706	404	7	a	a	DET
ejpam-4706	404	8	0	0	NUM
ejpam-4706	404	9	]	]	PUNCT
ejpam-4706	404	10	)	)	PUNCT
ejpam-4706	404	11	=	=	PRON
ejpam-4706	404	12	∥a∥	∥a∥	VERB
ejpam-4706	404	13	2	2	NUM
ejpam-4706	404	14	for	for	ADP
ejpam-4706	404	15	every	every	DET
ejpam-4706	404	16	matrix	matrix	NOUN
ejpam-4706	404	17	a	a	DET
ejpam-4706	404	18	∈	∈	PROPN
ejpam-4706	404	19	mn	mn	PROPN
ejpam-4706	404	20	(	(	PUNCT
ejpam-4706	404	21	c	c	NOUN
ejpam-4706	404	22	)	)	PUNCT
ejpam-4706	404	23	,	,	PUNCT
ejpam-4706	404	24	the	the	DET
ejpam-4706	404	25	matrix	matrix	NOUN
ejpam-4706	404	26	s22	s22	NOUN
ejpam-4706	404	27	can	can	AUX
ejpam-4706	404	28	be	be	AUX
ejpam-4706	404	29	written	write	VERB
ejpam-4706	404	30	as	as	ADP
ejpam-4706	404	31	s22	s22	NOUN
ejpam-4706	404	32	=	=	SYM
ejpam-4706	404	33			NOUN
ejpam-4706	404	34	0	0	NUM
ejpam-4706	404	35	0	0	NUM
ejpam-4706	404	36	1	1	NUM
ejpam-4706	404	37	2	2	NUM
ejpam-4706	404	38	0	0	NUM
ejpam-4706	404	39	.	.	PUNCT
ejpam-4706	404	40	.	.	PUNCT
ejpam-4706	405	1	.	.	PUNCT
ejpam-4706	406	1	0	0	NUM
ejpam-4706	407	1	0	0	NUM
ejpam-4706	407	2	0	0	NUM
ejpam-4706	407	3	0	0	NUM
ejpam-4706	407	4	0	0	NUM
ejpam-4706	407	5	1	1	NUM
ejpam-4706	407	6	2	2	NUM
ejpam-4706	407	7	.	.	PUNCT
ejpam-4706	407	8	.	.	PUNCT
ejpam-4706	407	9	.	.	PUNCT
ejpam-4706	408	1	0	0	NUM
ejpam-4706	408	2	0	0	NUM
ejpam-4706	409	1	1	1	NUM
ejpam-4706	409	2	2	2	NUM
ejpam-4706	409	3	0	0	NUM
ejpam-4706	409	4	0	0	NUM
ejpam-4706	409	5	0	0	NUM
ejpam-4706	409	6	.	.	PUNCT
ejpam-4706	409	7	.	.	PUNCT
ejpam-4706	410	1	.	.	PUNCT
ejpam-4706	411	1	0	0	NUM
ejpam-4706	412	1	0	0	NUM
ejpam-4706	412	2	0	0	NUM
ejpam-4706	412	3	1	1	NUM
ejpam-4706	412	4	2	2	NUM
ejpam-4706	412	5	0	0	NUM
ejpam-4706	412	6	0	0	NUM
ejpam-4706	412	7	.	.	PUNCT
ejpam-4706	412	8	.	.	PUNCT
ejpam-4706	412	9	.	.	PUNCT
ejpam-4706	413	1	1	1	NUM
ejpam-4706	413	2	2	2	NUM
ejpam-4706	413	3	0	0	NUM
ejpam-4706	413	4	0	0	NUM
ejpam-4706	413	5	0	0	NUM
ejpam-4706	413	6	1	1	NUM
ejpam-4706	413	7	2	2	NUM
ejpam-4706	413	8	0	0	NUM
ejpam-4706	413	9	.	.	PUNCT
ejpam-4706	413	10	.	.	PUNCT
ejpam-4706	413	11	.	.	PUNCT
ejpam-4706	414	1	0	0	NUM
ejpam-4706	414	2	1	1	NUM
ejpam-4706	414	3	2	2	NUM
ejpam-4706	414	4	...	...	PUNCT
ejpam-4706	414	5	...	...	PUNCT
ejpam-4706	414	6	...	...	PUNCT
ejpam-4706	414	7	.	.	PUNCT
ejpam-4706	414	8	.	.	PUNCT
ejpam-4706	414	9	.	.	PUNCT
ejpam-4706	414	10	.	.	PUNCT
ejpam-4706	414	11	.	.	PUNCT
ejpam-4706	414	12	.	.	PUNCT
ejpam-4706	415	1	0	0	NUM
ejpam-4706	416	1	0	0	NUM
ejpam-4706	416	2	0	0	NUM
ejpam-4706	416	3	0	0	NUM
ejpam-4706	416	4	·	·	PUNCT
ejpam-4706	416	5	·	·	PUNCT
ejpam-4706	416	6	·	·	PUNCT
ejpam-4706	416	7	0	0	NUM
ejpam-4706	416	8	1	1	NUM
ejpam-4706	416	9	2	2	NUM
ejpam-4706	416	10	0	0	NUM
ejpam-4706	416	11	0	0	NUM
ejpam-4706	416	12			NUM
ejpam-4706	416	13	and	and	CCONJ
ejpam-4706	416	14	s33	s33	NUM
ejpam-4706	416	15	=	=	PUNCT
ejpam-4706	416	16	[	[	PUNCT
ejpam-4706	416	17	1	1	NUM
ejpam-4706	416	18	2	2	NUM
ejpam-4706	416	19	1	1	NUM
ejpam-4706	416	20	2	2	NUM
ejpam-4706	416	21	1	1	NUM
ejpam-4706	416	22	2	2	NUM
ejpam-4706	416	23	0	0	NUM
ejpam-4706	416	24	]	]	PUNCT
ejpam-4706	416	25	.	.	PUNCT
ejpam-4706	417	1	so	so	ADV
ejpam-4706	417	2	,	,	PUNCT
ejpam-4706	417	3	s22	s22	NOUN
ejpam-4706	417	4	=	=	SYM
ejpam-4706	417	5	2	2	NUM
ejpam-4706	417	6	(	(	PUNCT
ejpam-4706	417	7	a2	a2	PROPN
ejpam-4706	417	8	−	−	PROPN
ejpam-4706	417	9	diag	diag	NOUN
ejpam-4706	417	10	(	(	PUNCT
ejpam-4706	417	11	1	1	NUM
ejpam-4706	417	12	4	4	NUM
ejpam-4706	417	13	,	,	PUNCT
ejpam-4706	417	14	1	1	NUM
ejpam-4706	417	15	2	2	NUM
ejpam-4706	417	16	,	,	PUNCT
ejpam-4706	417	17	.	.	PUNCT
ejpam-4706	417	18	.	.	PUNCT
ejpam-4706	417	19	.	.	PUNCT
ejpam-4706	418	1	,	,	PUNCT
ejpam-4706	418	2	1	1	NUM
ejpam-4706	418	3	2	2	NUM
ejpam-4706	418	4	,	,	PUNCT
ejpam-4706	418	5	1	1	NUM
ejpam-4706	418	6	4	4	NUM
ejpam-4706	418	7	)	)	PUNCT
ejpam-4706	418	8	)	)	PUNCT
ejpam-4706	418	9	where	where	SCONJ
ejpam-4706	418	10	a	a	DET
ejpam-4706	418	11	=	=	NOUN
ejpam-4706	418	12			NOUN
ejpam-4706	418	13	0	0	NUM
ejpam-4706	418	14	1	1	NUM
ejpam-4706	418	15	2	2	NUM
ejpam-4706	418	16	0	0	NUM
ejpam-4706	418	17	.	.	PUNCT
ejpam-4706	418	18	.	.	PUNCT
ejpam-4706	419	1	.	.	PUNCT
ejpam-4706	420	1	0	0	NUM
ejpam-4706	420	2	1	1	NUM
ejpam-4706	420	3	2	2	NUM
ejpam-4706	420	4	0	0	NUM
ejpam-4706	420	5	1	1	NUM
ejpam-4706	420	6	2	2	NUM
ejpam-4706	420	7	.	.	PUNCT
ejpam-4706	420	8	.	.	PUNCT
ejpam-4706	420	9	.	.	PUNCT
ejpam-4706	421	1	0	0	NUM
ejpam-4706	421	2	0	0	NUM
ejpam-4706	422	1	1	1	NUM
ejpam-4706	422	2	2	2	NUM
ejpam-4706	422	3	0	0	NUM
ejpam-4706	422	4	.	.	PUNCT
ejpam-4706	422	5	.	.	PUNCT
ejpam-4706	422	6	.	.	PUNCT
ejpam-4706	423	1	0	0	NUM
ejpam-4706	424	1	...	...	PUNCT
ejpam-4706	424	2	0	0	NUM
ejpam-4706	424	3	...	...	PUNCT
ejpam-4706	424	4	.	.	PUNCT
ejpam-4706	424	5	.	.	PUNCT
ejpam-4706	425	1	.	.	PUNCT
ejpam-4706	426	1	1	1	NUM
ejpam-4706	426	2	2	2	NUM
ejpam-4706	426	3	0	0	NUM
ejpam-4706	426	4	0	0	NUM
ejpam-4706	426	5	.	.	PUNCT
ejpam-4706	426	6	.	.	PUNCT
ejpam-4706	426	7	.	.	PUNCT
ejpam-4706	427	1	1	1	NUM
ejpam-4706	427	2	2	2	NUM
ejpam-4706	427	3	0	0	NUM
ejpam-4706	427	4			NOUN
ejpam-4706	427	5	.	.	PUNCT
ejpam-4706	428	1	now	now	ADV
ejpam-4706	428	2	,	,	PUNCT
ejpam-4706	428	3	w(s22	w(s22	NOUN
ejpam-4706	428	4	)	)	PUNCT
ejpam-4706	428	5	≤	≤	NUM
ejpam-4706	428	6	2	2	NUM
ejpam-4706	428	7	(	(	PUNCT
ejpam-4706	428	8	w(a2	w(a2	NOUN
ejpam-4706	428	9	)	)	PUNCT
ejpam-4706	429	1	+	+	CCONJ
ejpam-4706	429	2	w(diag	w(diag	NOUN
ejpam-4706	429	3	(	(	PUNCT
ejpam-4706	429	4	1	1	NUM
ejpam-4706	429	5	4	4	NUM
ejpam-4706	429	6	,	,	PUNCT
ejpam-4706	429	7	1	1	NUM
ejpam-4706	429	8	2	2	NUM
ejpam-4706	429	9	,	,	PUNCT
ejpam-4706	429	10	.	.	PUNCT
ejpam-4706	429	11	.	.	PUNCT
ejpam-4706	429	12	.	.	PUNCT
ejpam-4706	430	1	,	,	PUNCT
ejpam-4706	430	2	1	1	NUM
ejpam-4706	430	3	2	2	NUM
ejpam-4706	430	4	,	,	PUNCT
ejpam-4706	430	5	1	1	NUM
ejpam-4706	430	6	4	4	NUM
ejpam-4706	430	7	)	)	PUNCT
ejpam-4706	430	8	)	)	PUNCT
ejpam-4706	430	9	.	.	PUNCT
ejpam-4706	431	1	given	give	VERB
ejpam-4706	431	2	that	that	SCONJ
ejpam-4706	431	3	a	a	PRON
ejpam-4706	431	4	is	be	AUX
ejpam-4706	431	5	normal	normal	ADJ
ejpam-4706	431	6	,	,	PUNCT
ejpam-4706	431	7	thus	thus	ADV
ejpam-4706	431	8	w(a2	w(a2	ADJ
ejpam-4706	431	9	)	)	PUNCT
ejpam-4706	432	1	=	=	SYM
ejpam-4706	432	2	w2(a	w2(a	PROPN
ejpam-4706	432	3	)	)	PUNCT
ejpam-4706	432	4	.	.	PUNCT
ejpam-4706	433	1	then	then	ADV
ejpam-4706	433	2	applying	apply	VERB
ejpam-4706	433	3	lemma	lemma	PROPN
ejpam-4706	433	4	2	2	NUM
ejpam-4706	433	5	,	,	PUNCT
ejpam-4706	433	6	to	to	PART
ejpam-4706	433	7	get	get	VERB
ejpam-4706	433	8	w	w	ADP
ejpam-4706	433	9	(	(	PUNCT
ejpam-4706	433	10	s22	s22	NOUN
ejpam-4706	433	11	)	)	PUNCT
ejpam-4706	433	12	≤	≤	NUM
ejpam-4706	433	13	2	2	NUM
ejpam-4706	433	14	cos2	cos2	NOUN
ejpam-4706	433	15	(	(	PUNCT
ejpam-4706	433	16	π	π	PROPN
ejpam-4706	433	17	mn−	mn−	PROPN
ejpam-4706	433	18	3	3	NUM
ejpam-4706	433	19	)	)	PUNCT
ejpam-4706	434	1	+	+	CCONJ
ejpam-4706	434	2	1	1	X
ejpam-4706	434	3	.	.	PUNCT
ejpam-4706	434	4	also	also	ADV
ejpam-4706	434	5	,	,	PUNCT
ejpam-4706	434	6	we	we	PRON
ejpam-4706	434	7	have	have	VERB
ejpam-4706	434	8	w(s33	w(s33	NOUN
ejpam-4706	434	9	)	)	PUNCT
ejpam-4706	435	1	=	=	SYM
ejpam-4706	435	2	r	r	NOUN
ejpam-4706	435	3	(	(	PUNCT
ejpam-4706	435	4	s33	s33	PROPN
ejpam-4706	435	5	)	)	PUNCT
ejpam-4706	435	6	=	=	SYM
ejpam-4706	435	7	2	2	NUM
ejpam-4706	435	8	+	+	CCONJ
ejpam-4706	435	9	√	√	NUM
ejpam-4706	435	10	5	5	NUM
ejpam-4706	435	11	4	4	NUM
ejpam-4706	435	12	.	.	PUNCT
ejpam-4706	436	1	since	since	SCONJ
ejpam-4706	436	2	s12	s12	PROPN
ejpam-4706	436	3	can	can	AUX
ejpam-4706	436	4	be	be	AUX
ejpam-4706	436	5	written	write	VERB
ejpam-4706	436	6	as	as	ADP
ejpam-4706	436	7	s12	s12	NOUN
ejpam-4706	436	8	=	=	PUNCT
ejpam-4706	436	9	[	[	PUNCT
ejpam-4706	436	10	w	w	PROPN
ejpam-4706	436	11	(	(	PUNCT
ejpam-4706	436	12	t	t	PROPN
ejpam-4706	436	13	(	(	PUNCT
ejpam-4706	436	14	bm−2	bm−2	PROPN
ejpam-4706	436	15	−bm−1	−bm−1	NOUN
ejpam-4706	436	16	+	+	PROPN
ejpam-4706	436	17	am−1	am−1	PROPN
ejpam-4706	436	18	−am−2	−am−2	PRON
ejpam-4706	436	19	,	,	PUNCT
ejpam-4706	436	20	i	i	NOUN
ejpam-4706	436	21	)	)	PUNCT
ejpam-4706	436	22	)	)	PUNCT
ejpam-4706	436	23	∥bm−3−bm−2+am−2−am−3∥	∥bm−3−bm−2+am−2−am−3∥	VERB
ejpam-4706	436	24	2	2	NUM
ejpam-4706	436	25	.	.	PUNCT
ejpam-4706	436	26	.	.	PUNCT
ejpam-4706	436	27	.	.	PUNCT
ejpam-4706	436	28	.	.	PUNCT
ejpam-4706	437	1	.	.	PUNCT
ejpam-4706	438	1	.	.	PUNCT
ejpam-4706	439	1	∥b3−b4+a4−a3∥	∥b3−b4+a4−a3∥	ADJ
ejpam-4706	439	2	2	2	NUM
ejpam-4706	440	1	∥am−1−am−2∥	∥am−1−am−2∥	NUM
ejpam-4706	440	2	2	2	NUM
ejpam-4706	440	3	w(t	w(t	PROPN
ejpam-4706	440	4	(	(	PUNCT
ejpam-4706	440	5	am−2	am−2	PROPN
ejpam-4706	440	6	−am−3	−am−3	PROPN
ejpam-4706	440	7	,	,	PUNCT
ejpam-4706	440	8	i	i	NOUN
ejpam-4706	440	9	)	)	PUNCT
ejpam-4706	440	10	)	)	PUNCT
ejpam-4706	441	1	∥am−3−am−4∥	∥am−3−am−4∥	PROPN
ejpam-4706	441	2	2	2	NUM
ejpam-4706	441	3	.	.	PUNCT
ejpam-4706	441	4	.	.	PUNCT
ejpam-4706	441	5	.	.	PUNCT
ejpam-4706	442	1	∥a4−a3∥	∥a4−a3∥	PROPN
ejpam-4706	442	2	2	2	NUM
ejpam-4706	442	3	]	]	PUNCT
ejpam-4706	442	4	.	.	PUNCT
ejpam-4706	443	1	and	and	CCONJ
ejpam-4706	443	2	s∗	s∗	PROPN
ejpam-4706	443	3	12	12	NUM
ejpam-4706	443	4	=	=	SYM
ejpam-4706	443	5	st	st	PROPN
ejpam-4706	443	6	12	12	NUM
ejpam-4706	443	7	,	,	PUNCT
ejpam-4706	443	8	we	we	PRON
ejpam-4706	443	9	have	have	VERB
ejpam-4706	443	10	s12s	s12	NOUN
ejpam-4706	443	11	∗	∗	NOUN
ejpam-4706	443	12	12	12	NUM
ejpam-4706	443	13	=	=	SYM
ejpam-4706	443	14	[	[	PUNCT
ejpam-4706	443	15	α	α	X
ejpam-4706	443	16	β	β	X
ejpam-4706	443	17	β	β	X
ejpam-4706	443	18	η	η	PROPN
ejpam-4706	443	19	]	]	PUNCT
ejpam-4706	443	20	,	,	PUNCT
ejpam-4706	443	21	where	where	SCONJ
ejpam-4706	443	22	α	α	PROPN
ejpam-4706	443	23	=	=	PROPN
ejpam-4706	443	24	w2	w2	PROPN
ejpam-4706	443	25	(	(	PUNCT
ejpam-4706	443	26	t	t	PROPN
ejpam-4706	443	27	(	(	PUNCT
ejpam-4706	443	28	bm−2	bm−2	PROPN
ejpam-4706	443	29	−bm−1	−bm−1	NOUN
ejpam-4706	443	30	+	+	PROPN
ejpam-4706	443	31	am−1	am−1	PROPN
ejpam-4706	443	32	−am−2	−am−2	PRON
ejpam-4706	443	33	,	,	PUNCT
ejpam-4706	443	34	i	i	NOUN
ejpam-4706	443	35	)	)	PUNCT
ejpam-4706	443	36	)	)	PUNCT
ejpam-4706	444	1	+	+	CCONJ
ejpam-4706	444	2	1	1	NUM
ejpam-4706	444	3	4	4	NUM
ejpam-4706	444	4	m∑	m∑	NOUN
ejpam-4706	444	5	j=6	j=6	VERB
ejpam-4706	444	6	∥bj−3	∥bj−3	NUM
ejpam-4706	444	7	−bj−2	−bj−2	X
ejpam-4706	444	8	+	+	ADJ
ejpam-4706	444	9	aj−2	aj−2	PROPN
ejpam-4706	444	10	−aj−3∥2	−aj−3∥2	PROPN
ejpam-4706	444	11	,	,	PUNCT
ejpam-4706	444	12	a.	a.	PROPN
ejpam-4706	444	13	burqan	burqan	PROPN
ejpam-4706	444	14	et	et	PROPN
ejpam-4706	444	15	al	al	PROPN
ejpam-4706	444	16	.	.	PUNCT
ejpam-4706	444	17	/	/	SYM
ejpam-4706	444	18	eur	eur	PROPN
ejpam-4706	444	19	.	.	PUNCT
ejpam-4706	445	1	j.	j.	PROPN
ejpam-4706	445	2	pure	pure	PROPN
ejpam-4706	445	3	appl	appl	PROPN
ejpam-4706	445	4	.	.	PROPN
ejpam-4706	445	5	math	math	PROPN
ejpam-4706	445	6	,	,	PUNCT
ejpam-4706	445	7	16	16	NUM
ejpam-4706	445	8	(	(	PUNCT
ejpam-4706	445	9	2	2	NUM
ejpam-4706	445	10	)	)	PUNCT
ejpam-4706	445	11	(	(	PUNCT
ejpam-4706	445	12	2023	2023	NUM
ejpam-4706	445	13	)	)	PUNCT
ejpam-4706	445	14	,	,	PUNCT
ejpam-4706	445	15	806	806	NUM
ejpam-4706	445	16	-	-	SYM
ejpam-4706	445	17	818	818	NUM
ejpam-4706	445	18	816	816	NUM
ejpam-4706	445	19	η	η	NOUN
ejpam-4706	445	20	=	=	SYM
ejpam-4706	445	21	1	1	NUM
ejpam-4706	445	22	4	4	NUM
ejpam-4706	445	23	∥am−1	∥am−1	NOUN
ejpam-4706	445	24	−am−2∥2	−am−2∥2	ADP
ejpam-4706	445	25	+	+	CCONJ
ejpam-4706	445	26	w2(t	w2(t	PROPN
ejpam-4706	445	27	(	(	PUNCT
ejpam-4706	445	28	am−2	am−2	PROPN
ejpam-4706	445	29	−am−3	−am−3	PROPN
ejpam-4706	445	30	,	,	PUNCT
ejpam-4706	445	31	i	i	NOUN
ejpam-4706	445	32	)	)	PUNCT
ejpam-4706	445	33	)	)	PUNCT
ejpam-4706	446	1	+	+	CCONJ
ejpam-4706	446	2	1	1	NUM
ejpam-4706	446	3	4	4	NUM
ejpam-4706	446	4	m∑	m∑	NOUN
ejpam-4706	446	5	j=7	j=7	ADJ
ejpam-4706	446	6	∥aj−3	∥aj−3	NOUN
ejpam-4706	446	7	−aj−4∥2	−aj−4∥2	NOUN
ejpam-4706	446	8	,	,	PUNCT
ejpam-4706	446	9	and	and	CCONJ
ejpam-4706	446	10	β	β	X
ejpam-4706	446	11	=	=	SYM
ejpam-4706	446	12	1	1	NUM
ejpam-4706	446	13	2	2	NUM
ejpam-4706	446	14	w	w	NOUN
ejpam-4706	446	15	(	(	PUNCT
ejpam-4706	446	16	t	t	PROPN
ejpam-4706	446	17	(	(	PUNCT
ejpam-4706	446	18	bm−2	bm−2	PROPN
ejpam-4706	446	19	−bm−1	−bm−1	NOUN
ejpam-4706	446	20	+	+	PROPN
ejpam-4706	446	21	am−1	am−1	PROPN
ejpam-4706	446	22	−am−2	−am−2	PRON
ejpam-4706	446	23	,	,	PUNCT
ejpam-4706	446	24	i	i	NOUN
ejpam-4706	446	25	)	)	PUNCT
ejpam-4706	446	26	)	)	PUNCT
ejpam-4706	447	1	∥am−1	∥am−1	PROPN
ejpam-4706	447	2	−am−2∥	−am−2∥	NOUN
ejpam-4706	447	3	+	+	CCONJ
ejpam-4706	447	4	1	1	NUM
ejpam-4706	447	5	2	2	NUM
ejpam-4706	447	6	∥bm−3	∥bm−3	NOUN
ejpam-4706	447	7	−bm−2	−bm−2	ADP
ejpam-4706	447	8	+	+	ADJ
ejpam-4706	447	9	am−2	am−2	PROPN
ejpam-4706	447	10	−am−3∥w(t	−am−3∥w(t	PROPN
ejpam-4706	447	11	(	(	PUNCT
ejpam-4706	447	12	am−2	am−2	PROPN
ejpam-4706	447	13	−am−3	−am−3	PROPN
ejpam-4706	447	14	,	,	PUNCT
ejpam-4706	447	15	i	i	NOUN
ejpam-4706	447	16	)	)	PUNCT
ejpam-4706	447	17	)	)	PUNCT
ejpam-4706	448	1	+	+	CCONJ
ejpam-4706	448	2	1	1	NUM
ejpam-4706	448	3	4	4	NUM
ejpam-4706	448	4	m∑	m∑	NOUN
ejpam-4706	448	5	j=7	j=7	PROPN
ejpam-4706	448	6	∥bj−4	∥bj−4	NOUN
ejpam-4706	448	7	−bj−3	−bj−3	X
ejpam-4706	449	1	+	+	SCONJ
ejpam-4706	449	2	aj−3	aj−3	PROPN
ejpam-4706	449	3	−aj−4∥∥aj−3	−aj−4∥∥aj−3	VERB
ejpam-4706	449	4	−aj−4∥.	−aj−4∥.	NUM
ejpam-4706	449	5	applying	apply	VERB
ejpam-4706	449	6	lemma	lemma	PROPN
ejpam-4706	449	7	3	3	NUM
ejpam-4706	449	8	,	,	PUNCT
ejpam-4706	449	9	to	to	PART
ejpam-4706	449	10	get	get	VERB
ejpam-4706	449	11	∥s12∥2	∥s12∥2	ADJ
ejpam-4706	449	12	=	=	SYM
ejpam-4706	449	13	∥s12s	∥s12s	PROPN
ejpam-4706	449	14	∗	∗	NOUN
ejpam-4706	449	15	12∥	12∥	NUM
ejpam-4706	450	1	=	=	SYM
ejpam-4706	450	2	r	r	NOUN
ejpam-4706	450	3	(	(	PUNCT
ejpam-4706	450	4	s12s	s12s	NOUN
ejpam-4706	450	5	∗	∗	PROPN
ejpam-4706	450	6	12	12	NUM
ejpam-4706	450	7	)	)	PUNCT
ejpam-4706	450	8	=	=	SYM
ejpam-4706	450	9	1	1	NUM
ejpam-4706	450	10	2	2	NUM
ejpam-4706	450	11	(	(	PUNCT
ejpam-4706	450	12	α+	α+	X
ejpam-4706	450	13	η	η	PROPN
ejpam-4706	450	14	+	+	NOUN
ejpam-4706	450	15	√	√	PROPN
ejpam-4706	450	16	(	(	PUNCT
ejpam-4706	450	17	a−	a−	PROPN
ejpam-4706	450	18	η)2	η)2	NOUN
ejpam-4706	450	19	+	+	CCONJ
ejpam-4706	450	20	4β2	4β2	NUM
ejpam-4706	450	21	)	)	PUNCT
ejpam-4706	450	22	.	.	PUNCT
ejpam-4706	451	1	since	since	SCONJ
ejpam-4706	451	2	s12	s12	PROPN
ejpam-4706	451	3	=	=	SYM
ejpam-4706	451	4	st	st	PROPN
ejpam-4706	451	5	21	21	NUM
ejpam-4706	451	6	,	,	PUNCT
ejpam-4706	451	7	we	we	PRON
ejpam-4706	451	8	have	have	VERB
ejpam-4706	451	9	∥s21∥2	∥s21∥2	NOUN
ejpam-4706	451	10	=	=	SYM
ejpam-4706	451	11	1	1	NUM
ejpam-4706	451	12	2	2	NUM
ejpam-4706	451	13	(	(	PUNCT
ejpam-4706	451	14	α+	α+	X
ejpam-4706	451	15	η	η	PROPN
ejpam-4706	451	16	+	+	NOUN
ejpam-4706	451	17	√	√	PROPN
ejpam-4706	451	18	(	(	PUNCT
ejpam-4706	451	19	a−	a−	PROPN
ejpam-4706	451	20	η)2	η)2	NOUN
ejpam-4706	451	21	+	+	CCONJ
ejpam-4706	451	22	4β2	4β2	NUM
ejpam-4706	451	23	)	)	PUNCT
ejpam-4706	451	24	.	.	PUNCT
ejpam-4706	452	1	now	now	ADV
ejpam-4706	452	2	,	,	PUNCT
ejpam-4706	452	3	we	we	PRON
ejpam-4706	452	4	need	need	VERB
ejpam-4706	452	5	to	to	PART
ejpam-4706	452	6	find	find	VERB
ejpam-4706	452	7	the	the	DET
ejpam-4706	452	8	numerical	numerical	ADJ
ejpam-4706	452	9	radius	radius	PROPN
ejpam-4706	452	10	of	of	ADP
ejpam-4706	452	11	s13	s13	PROPN
ejpam-4706	452	12	,	,	PUNCT
ejpam-4706	452	13	s31	s31	NOUN
ejpam-4706	452	14	.	.	PUNCT
ejpam-4706	453	1	s13	s13	PROPN
ejpam-4706	453	2	=	=	PUNCT
ejpam-4706	454	1	[	[	PUNCT
ejpam-4706	454	2	∥b2−b3+a3−a2∥	∥b2−b3+a3−a2∥	NUM
ejpam-4706	454	3	2	2	NUM
ejpam-4706	454	4	∥b1−b2+a2−a1∥	∥b1−b2+a2−a1∥	NUM
ejpam-4706	454	5	2	2	NUM
ejpam-4706	454	6	∥a3−a2−i∥	∥a3−a2−i∥	NOUN
ejpam-4706	454	7	2	2	NUM
ejpam-4706	454	8	∥a2−a1∥	∥a2−a1∥	SYM
ejpam-4706	454	9	2	2	NUM
ejpam-4706	454	10	]	]	PUNCT
ejpam-4706	454	11	,	,	PUNCT
ejpam-4706	454	12	s13	s13	NOUN
ejpam-4706	454	13	=	=	PUNCT
ejpam-4706	454	14	[	[	PUNCT
ejpam-4706	454	15	∥b2−b3+a3−a2∥	∥b2−b3+a3−a2∥	NUM
ejpam-4706	454	16	2	2	NUM
ejpam-4706	454	17	∥a3−a2−i∥	∥a3−a2−i∥	NOUN
ejpam-4706	454	18	2	2	NUM
ejpam-4706	454	19	∥b1−b2+a2−a1∥	∥b1−b2+a2−a1∥	NUM
ejpam-4706	454	20	2	2	NUM
ejpam-4706	454	21	∥a2−a1∥	∥a2−a1∥	NUM
ejpam-4706	454	22	2	2	NUM
ejpam-4706	454	23	]	]	PUNCT
ejpam-4706	454	24	,	,	PUNCT
ejpam-4706	454	25	by	by	ADP
ejpam-4706	454	26	lemma	lemma	PROPN
ejpam-4706	454	27	1	1	NUM
ejpam-4706	454	28	,	,	PUNCT
ejpam-4706	454	29	we	we	PRON
ejpam-4706	454	30	have	have	VERB
ejpam-4706	454	31	τ	τ	X
ejpam-4706	454	32	=	=	SYM
ejpam-4706	454	33	∥s31∥	∥s31∥	PROPN
ejpam-4706	455	1	=	=	SYM
ejpam-4706	456	1	∥s13∥	∥s13∥	PROPN
ejpam-4706	456	2	,	,	PUNCT
ejpam-4706	456	3	where	where	SCONJ
ejpam-4706	456	4	τ	τ	PROPN
ejpam-4706	456	5	=	=	SYM
ejpam-4706	456	6	1	1	NUM
ejpam-4706	456	7	2	2	NUM
ejpam-4706	456	8	(	(	PUNCT
ejpam-4706	456	9	∥b2	∥b2	VERB
ejpam-4706	456	10	−b3	−b3	PROPN
ejpam-4706	456	11	+	+	NOUN
ejpam-4706	456	12	a3	a3	NOUN
ejpam-4706	456	13	−a2∥2	−a2∥2	VERB
ejpam-4706	456	14	4	4	NUM
ejpam-4706	456	15	+	+	CCONJ
ejpam-4706	456	16	∥a3	∥a3	X
ejpam-4706	456	17	−a2	−a2	NOUN
ejpam-4706	456	18	−	−	PROPN
ejpam-4706	456	19	i∥2	i∥2	NOUN
ejpam-4706	456	20	4	4	NUM
ejpam-4706	456	21	−	−	NOUN
ejpam-4706	456	22	∥b1	∥b1	ADJ
ejpam-4706	456	23	−b2	−b2	PROPN
ejpam-4706	456	24	+	+	PROPN
ejpam-4706	456	25	a2	a2	PROPN
ejpam-4706	456	26	−a1∥2	−a1∥2	ADJ
ejpam-4706	456	27	4	4	NUM
ejpam-4706	456	28	−	−	NOUN
ejpam-4706	456	29	∥a2	∥a2	VERB
ejpam-4706	456	30	−a1∥2	−a1∥2	ADJ
ejpam-4706	456	31	4	4	NUM
ejpam-4706	456	32	)	)	PUNCT
ejpam-4706	456	33	√√√√	√√√√	ADP
ejpam-4706	456	34	(	(	PUNCT
ejpam-4706	456	35	∥b2−b3+a3−a2∥2	∥b2−b3+a3−a2∥2	X
ejpam-4706	456	36	4	4	NUM
ejpam-4706	456	37	+	+	NUM
ejpam-4706	456	38	∥a3−a2−i∥2	∥a3−a2−i∥2	NOUN
ejpam-4706	456	39	4	4	NUM
ejpam-4706	456	40	−	−	NOUN
ejpam-4706	456	41	∥b1−b2+a2−a1∥2	∥b1−b2+a2−a1∥2	PROPN
ejpam-4706	456	42	4	4	NUM
ejpam-4706	456	43	−	−	NOUN
ejpam-4706	456	44	∥a2−a1∥2	∥a2−a1∥2	PROPN
ejpam-4706	456	45	4	4	NUM
ejpam-4706	456	46	)	)	SYM
ejpam-4706	456	47	2	2	NUM
ejpam-4706	456	48	+1	+1	NOUN
ejpam-4706	456	49	4	4	NUM
ejpam-4706	456	50	(	(	PUNCT
ejpam-4706	456	51	∥b2	∥b2	VERB
ejpam-4706	456	52	−b3	−b3	PROPN
ejpam-4706	456	53	+	+	NOUN
ejpam-4706	456	54	a3	a3	NOUN
ejpam-4706	456	55	−a2∥∥b1	−a2∥∥b1	NOUN
ejpam-4706	456	56	−b2	−b2	PROPN
ejpam-4706	456	57	+	+	NOUN
ejpam-4706	456	58	a2	a2	PROPN
ejpam-4706	456	59	−a1∥+	−a1∥+	NOUN
ejpam-4706	456	60	∥a3	∥a3	X
ejpam-4706	457	1	−a2	−a2	NOUN
ejpam-4706	458	1	−	−	PROPN
ejpam-4706	458	2	i∥∥a2	i∥∥a2	PROPN
ejpam-4706	458	3	−a1∥)2	−a1∥)2	NOUN
ejpam-4706	458	4	to	to	PART
ejpam-4706	458	5	find	find	VERB
ejpam-4706	458	6	the	the	DET
ejpam-4706	458	7	numerical	numerical	ADJ
ejpam-4706	458	8	radius	radius	NOUN
ejpam-4706	458	9	of	of	ADP
ejpam-4706	458	10	s32	s32	PROPN
ejpam-4706	458	11	,	,	PUNCT
ejpam-4706	458	12	we	we	PRON
ejpam-4706	458	13	have	have	VERB
ejpam-4706	458	14	∥s32∥2	∥s32∥2	NOUN
ejpam-4706	458	15	=	=	PUNCT
ejpam-4706	458	16	∥s32s	∥s32s	NUM
ejpam-4706	458	17	∗	∗	NOUN
ejpam-4706	458	18	32∥	32∥	NUM
ejpam-4706	458	19	=	=	SYM
ejpam-4706	458	20	∥∥∥∥mn	∥∥∥∥mn	PROPN
ejpam-4706	459	1	4	4	NUM
ejpam-4706	459	2	−	−	NOUN
ejpam-4706	459	3	1	1	NUM
ejpam-4706	459	4	1	1	NUM
ejpam-4706	459	5	4	4	NUM
ejpam-4706	459	6	1	1	NUM
ejpam-4706	459	7	4	4	NUM
ejpam-4706	459	8	1	1	NUM
ejpam-4706	459	9	4	4	NUM
ejpam-4706	459	10	∥∥∥∥	∥∥∥∥	NUM
ejpam-4706	459	11	.	.	PUNCT
ejpam-4706	460	1	so	so	ADV
ejpam-4706	460	2	,	,	PUNCT
ejpam-4706	460	3	µ	µ	X
ejpam-4706	460	4	=	=	SYM
ejpam-4706	460	5	∥s23∥2	∥s23∥2	PROPN
ejpam-4706	460	6	=	=	PUNCT
ejpam-4706	460	7	∥s32s	∥s32s	NUM
ejpam-4706	460	8	∗	∗	NOUN
ejpam-4706	460	9	32∥	32∥	NUM
ejpam-4706	460	10	=	=	SYM
ejpam-4706	460	11	r(s32s	r(s32s	NOUN
ejpam-4706	460	12	∗	∗	NOUN
ejpam-4706	460	13	32	32	NUM
ejpam-4706	460	14	)	)	PUNCT
ejpam-4706	460	15	=	=	SYM
ejpam-4706	460	16	1	1	NUM
ejpam-4706	460	17	2	2	NUM
ejpam-4706	460	18	mn−	mn−	NOUN
ejpam-4706	460	19	3	3	NUM
ejpam-4706	460	20	4	4	NUM
ejpam-4706	460	21	+	+	CCONJ
ejpam-4706	460	22	√	√	PROPN
ejpam-4706	460	23	(	(	PUNCT
ejpam-4706	460	24	m−	m−	PROPN
ejpam-4706	460	25	5	5	NUM
ejpam-4706	460	26	4	4	NUM
ejpam-4706	460	27	)	)	SYM
ejpam-4706	460	28	2	2	NUM
ejpam-4706	460	29	+	+	CCONJ
ejpam-4706	460	30	1	1	NUM
ejpam-4706	460	31	4	4	NUM
ejpam-4706	460	32			PROPN
ejpam-4706	460	33	.	.	PUNCT
ejpam-4706	461	1	references	reference	NOUN
ejpam-4706	461	2	817	817	NUM
ejpam-4706	461	3	finally	finally	ADV
ejpam-4706	461	4	,	,	PUNCT
ejpam-4706	461	5	applying	apply	VERB
ejpam-4706	461	6	lemma	lemma	PROPN
ejpam-4706	461	7	4	4	NUM
ejpam-4706	461	8	to	to	PART
ejpam-4706	461	9	get	get	VERB
ejpam-4706	461	10	w	w	PROPN
ejpam-4706	461	11	(	(	PUNCT
ejpam-4706	461	12	h	h	NOUN
ejpam-4706	461	13	)	)	PUNCT
ejpam-4706	461	14	≤	≤	NOUN
ejpam-4706	462	1	w	w	ADP
ejpam-4706	462	2	(	(	PUNCT
ejpam-4706	462	3	s	s	NOUN
ejpam-4706	462	4	)	)	PUNCT
ejpam-4706	462	5	≤	≤	NUM
ejpam-4706	462	6	1	1	NUM
ejpam-4706	462	7	2	2	NUM
ejpam-4706	462	8	(	(	PUNCT
ejpam-4706	462	9	w	w	PROPN
ejpam-4706	462	10	(	(	PUNCT
ejpam-4706	462	11	s11	s11	PROPN
ejpam-4706	462	12	)	)	PUNCT
ejpam-4706	463	1	+	+	NUM
ejpam-4706	463	2	w	w	PROPN
ejpam-4706	463	3	(	(	PUNCT
ejpam-4706	463	4	s22	s22	NOUN
ejpam-4706	463	5	)	)	PUNCT
ejpam-4706	464	1	+	+	PROPN
ejpam-4706	464	2	w	w	PROPN
ejpam-4706	464	3	(	(	PUNCT
ejpam-4706	464	4	s33	s33	PROPN
ejpam-4706	464	5	)	)	PUNCT
ejpam-4706	465	1	+	+	CCONJ
ejpam-4706	465	2	√	√	PROPN
ejpam-4706	465	3	w2(s11)+}|s12∥2	w2(s11)+}|s12∥2	PROPN
ejpam-4706	465	4	+	+	CCONJ
ejpam-4706	465	5	∥s13∥2	∥s13∥2	NOUN
ejpam-4706	465	6	+	+	CCONJ
ejpam-4706	465	7	√	√	PROPN
ejpam-4706	465	8	w2(s22)+}∥s21∥2	w2(s22)+}∥s21∥2	PROPN
ejpam-4706	465	9	+	+	X
ejpam-4706	465	10	∥s23∥2	∥s23∥2	X
ejpam-4706	466	1	+	+	PROPN
ejpam-4706	466	2	+	+	ADJ
ejpam-4706	466	3	√	√	ADJ
ejpam-4706	466	4	w2(s33)+}∥s31∥2	w2(s33)+}∥s31∥2	ADV
ejpam-4706	466	5	+	+	CCONJ
ejpam-4706	466	6	∥s32∥2	∥s32∥2	NOUN
ejpam-4706	466	7	thus	thus	ADV
ejpam-4706	466	8	,	,	PUNCT
ejpam-4706	466	9	w(h	w(h	PROPN
ejpam-4706	466	10	)	)	PUNCT
ejpam-4706	466	11	≤	≤	NUM
ejpam-4706	466	12	1	1	NUM
ejpam-4706	466	13	2	2	NUM
ejpam-4706	466	14	ξ	ξ	NUM
ejpam-4706	466	15	+	+	CCONJ
ejpam-4706	466	16	2	2	NUM
ejpam-4706	466	17	cos2	cos2	NOUN
ejpam-4706	466	18	(	(	PUNCT
ejpam-4706	466	19	π	π	PROPN
ejpam-4706	466	20	mn−	mn−	PROPN
ejpam-4706	466	21	3	3	NUM
ejpam-4706	466	22	)	)	PUNCT
ejpam-4706	467	1	+	+	CCONJ
ejpam-4706	467	2	1	1	NUM
ejpam-4706	467	3	+	+	CCONJ
ejpam-4706	467	4	√	√	NOUN
ejpam-4706	467	5	ξ2	ξ2	NOUN
ejpam-4706	467	6	+	+	CCONJ
ejpam-4706	467	7	(	(	PUNCT
ejpam-4706	467	8	1	1	NUM
ejpam-4706	467	9	2	2	NUM
ejpam-4706	467	10	(	(	PUNCT
ejpam-4706	467	11	α+	α+	X
ejpam-4706	467	12	η	η	PROPN
ejpam-4706	467	13	+	+	NOUN
ejpam-4706	467	14	√	√	PROPN
ejpam-4706	467	15	(	(	PUNCT
ejpam-4706	467	16	α−	α−	ADP
ejpam-4706	467	17	η)2	η)2	NOUN
ejpam-4706	467	18	+	+	CCONJ
ejpam-4706	467	19	4β2	4β2	NUM
ejpam-4706	467	20	)	)	PUNCT
ejpam-4706	467	21	)	)	PUNCT
ejpam-4706	468	1	2	2	NUM
ejpam-4706	469	1	+	+	X
ejpam-4706	469	2	τ2	τ2	VERB
ejpam-4706	469	3	+	+	CCONJ
ejpam-4706	469	4	2	2	NUM
ejpam-4706	469	5	+	+	CCONJ
ejpam-4706	469	6	√	√	NUM
ejpam-4706	469	7	5	5	NUM
ejpam-4706	469	8	4	4	NUM
ejpam-4706	469	9	+	+	NUM
ejpam-4706	469	10	√	√	PROPN
ejpam-4706	469	11	(	(	PUNCT
ejpam-4706	469	12	2	2	NUM
ejpam-4706	469	13	cos2	cos2	NOUN
ejpam-4706	469	14	(	(	PUNCT
ejpam-4706	469	15	π	π	PROPN
ejpam-4706	469	16	mn−	mn−	PROPN
ejpam-4706	469	17	3	3	NUM
ejpam-4706	469	18	)	)	PUNCT
ejpam-4706	470	1	+	+	CCONJ
ejpam-4706	470	2	1	1	NUM
ejpam-4706	470	3	)	)	SYM
ejpam-4706	470	4	2	2	NUM
ejpam-4706	471	1	+	+	CCONJ
ejpam-4706	471	2	(	(	PUNCT
ejpam-4706	471	3	1	1	NUM
ejpam-4706	471	4	2	2	NUM
ejpam-4706	471	5	(	(	PUNCT
ejpam-4706	471	6	α+	α+	X
ejpam-4706	471	7	η	η	PROPN
ejpam-4706	471	8	+	+	NOUN
ejpam-4706	471	9	√	√	PROPN
ejpam-4706	471	10	(	(	PUNCT
ejpam-4706	471	11	α−	α−	ADP
ejpam-4706	471	12	η)2	η)2	NOUN
ejpam-4706	471	13	+	+	CCONJ
ejpam-4706	471	14	4β2	4β2	NUM
ejpam-4706	471	15	)	)	PUNCT
ejpam-4706	471	16	)	)	PUNCT
ejpam-4706	472	1	2	2	NUM
ejpam-4706	472	2	+	+	SYM
ejpam-4706	472	3	µ	µ	X
ejpam-4706	472	4	+	+	NUM
ejpam-4706	472	5	√√√√(2	√√√√(2	PROPN
ejpam-4706	472	6	+	+	CCONJ
ejpam-4706	472	7	√	√	NUM
ejpam-4706	472	8	5	5	NUM
ejpam-4706	472	9	4	4	NUM
ejpam-4706	472	10	)	)	SYM
ejpam-4706	472	11	2	2	NUM
ejpam-4706	472	12	+	+	CCONJ
ejpam-4706	472	13	τ2	τ2	NOUN
ejpam-4706	472	14	+	+	CCONJ
ejpam-4706	472	15	µ.	µ.	ADJ
ejpam-4706	472	16	conclusion	conclusion	NOUN
ejpam-4706	472	17	we	we	PRON
ejpam-4706	472	18	have	have	AUX
ejpam-4706	472	19	established	establish	VERB
ejpam-4706	472	20	new	new	ADJ
ejpam-4706	472	21	effective	effective	ADJ
ejpam-4706	472	22	bounds	bound	NOUN
ejpam-4706	472	23	for	for	ADP
ejpam-4706	472	24	the	the	DET
ejpam-4706	472	25	eigenvalues	eigenvalue	NOUN
ejpam-4706	472	26	of	of	ADP
ejpam-4706	472	27	matrix	matrix	NOUN
ejpam-4706	472	28	polynomials	polynomial	NOUN
ejpam-4706	472	29	by	by	ADP
ejpam-4706	472	30	employing	employ	VERB
ejpam-4706	472	31	the	the	DET
ejpam-4706	472	32	similarity	similarity	NOUN
ejpam-4706	472	33	of	of	ADP
ejpam-4706	472	34	matrices	matrix	NOUN
ejpam-4706	472	35	and	and	CCONJ
ejpam-4706	472	36	matrix	matrix	NOUN
ejpam-4706	472	37	inequalities	inequality	NOUN
ejpam-4706	472	38	including	include	VERB
ejpam-4706	472	39	the	the	DET
ejpam-4706	472	40	numerical	numerical	ADJ
ejpam-4706	472	41	radius	radius	NOUN
ejpam-4706	472	42	,	,	PUNCT
ejpam-4706	472	43	spectral	spectral	ADJ
ejpam-4706	472	44	radius	radius	NOUN
ejpam-4706	472	45	and	and	CCONJ
ejpam-4706	472	46	matrix	matrix	NOUN
ejpam-4706	472	47	norms	norm	NOUN
ejpam-4706	472	48	.	.	PUNCT
ejpam-4706	473	1	it	it	PRON
ejpam-4706	473	2	is	be	AUX
ejpam-4706	473	3	worth	worth	ADJ
ejpam-4706	473	4	noting	note	VERB
ejpam-4706	473	5	that	that	SCONJ
ejpam-4706	473	6	our	our	PRON
ejpam-4706	473	7	results	result	NOUN
ejpam-4706	473	8	can	can	AUX
ejpam-4706	473	9	be	be	AUX
ejpam-4706	473	10	used	use	VERB
ejpam-4706	473	11	in	in	ADP
ejpam-4706	473	12	many	many	ADJ
ejpam-4706	473	13	applications	application	NOUN
ejpam-4706	473	14	in	in	ADP
ejpam-4706	473	15	geometry	geometry	NOUN
ejpam-4706	473	16	and	and	CCONJ
ejpam-4706	473	17	matrix	matrix	NOUN
ejpam-4706	473	18	analysis	analysis	NOUN
ejpam-4706	473	19	.	.	PUNCT
ejpam-4706	474	1	acknowledgements	acknowledgement	NOUN
ejpam-4706	474	2	the	the	DET
ejpam-4706	474	3	authors	author	NOUN
ejpam-4706	474	4	express	express	VERB
ejpam-4706	474	5	their	their	PRON
ejpam-4706	474	6	gratitude	gratitude	NOUN
ejpam-4706	474	7	to	to	ADP
ejpam-4706	474	8	the	the	DET
ejpam-4706	474	9	dear	dear	ADJ
ejpam-4706	474	10	referees	referee	NOUN
ejpam-4706	474	11	,	,	PUNCT
ejpam-4706	474	12	who	who	PRON
ejpam-4706	474	13	wish	wish	VERB
ejpam-4706	474	14	to	to	PART
ejpam-4706	474	15	remain	remain	VERB
ejpam-4706	474	16	anonymous	anonymous	ADJ
ejpam-4706	474	17	,	,	PUNCT
ejpam-4706	474	18	and	and	CCONJ
ejpam-4706	474	19	the	the	DET
ejpam-4706	474	20	editor	editor	NOUN
ejpam-4706	474	21	for	for	ADP
ejpam-4706	474	22	their	their	PRON
ejpam-4706	474	23	helpful	helpful	ADJ
ejpam-4706	474	24	suggestions	suggestion	NOUN
ejpam-4706	474	25	,	,	PUNCT
ejpam-4706	474	26	which	which	PRON
ejpam-4706	474	27	improved	improve	VERB
ejpam-4706	474	28	the	the	DET
ejpam-4706	474	29	final	final	ADJ
ejpam-4706	474	30	version	version	NOUN
ejpam-4706	474	31	of	of	ADP
ejpam-4706	474	32	this	this	DET
ejpam-4706	474	33	paper	paper	NOUN
ejpam-4706	474	34	.	.	PUNCT
ejpam-4706	475	1	conflicts	conflict	NOUN
ejpam-4706	475	2	of	of	ADP
ejpam-4706	475	3	interest	interest	NOUN
ejpam-4706	475	4	the	the	DET
ejpam-4706	475	5	authors	author	NOUN
ejpam-4706	475	6	declare	declare	VERB
ejpam-4706	475	7	no	no	DET
ejpam-4706	475	8	conflict	conflict	NOUN
ejpam-4706	475	9	of	of	ADP
ejpam-4706	475	10	interest	interest	NOUN
ejpam-4706	475	11	.	.	PUNCT
ejpam-4706	476	1	references	reference	NOUN
ejpam-4706	476	2	[	[	X
ejpam-4706	476	3	1	1	X
ejpam-4706	476	4	]	]	PUNCT
ejpam-4706	476	5	a	a	DET
ejpam-4706	476	6	abu	abu	PROPN
ejpam-4706	476	7	-	-	PUNCT
ejpam-4706	476	8	omar	omar	PROPN
ejpam-4706	476	9	and	and	CCONJ
ejpam-4706	476	10	f	f	PROPN
ejpam-4706	476	11	kittaneh	kittaneh	PROPN
ejpam-4706	476	12	.	.	PUNCT
ejpam-4706	477	1	numerical	numerical	PROPN
ejpam-4706	477	2	radius	radius	PROPN
ejpam-4706	477	3	inequalities	inequality	NOUN
ejpam-4706	477	4	for	for	ADP
ejpam-4706	477	5	n×	n×	PROPN
ejpam-4706	477	6	n	n	PRON
ejpam-4706	477	7	operator	operator	NOUN
ejpam-4706	477	8	matrices	matrix	NOUN
ejpam-4706	477	9	.	.	PUNCT
ejpam-4706	478	1	linear	linear	ADJ
ejpam-4706	478	2	algebra	algebra	NOUN
ejpam-4706	478	3	and	and	CCONJ
ejpam-4706	478	4	its	its	PRON
ejpam-4706	478	5	applications	application	NOUN
ejpam-4706	478	6	,	,	PUNCT
ejpam-4706	478	7	468:18–26	468:18–26	NUM
ejpam-4706	478	8	,	,	PUNCT
ejpam-4706	478	9	2015	2015	NUM
ejpam-4706	478	10	.	.	PUNCT
ejpam-4706	479	1	[	[	X
ejpam-4706	479	2	2	2	X
ejpam-4706	479	3	]	]	PUNCT
ejpam-4706	479	4	a	a	DET
ejpam-4706	479	5	burqan	burqan	NOUN
ejpam-4706	479	6	a	a	DET
ejpam-4706	479	7	alsawaftah	alsawaftah	NOUN
ejpam-4706	479	8	and	and	CCONJ
ejpam-4706	479	9	z	z	PROPN
ejpam-4706	479	10	al	al	PROPN
ejpam-4706	479	11	-	-	PUNCT
ejpam-4706	479	12	zhour	zhour	PROPN
ejpam-4706	479	13	.	.	PUNCT
ejpam-4706	480	1	new	new	ADJ
ejpam-4706	480	2	efficient	efficient	ADJ
ejpam-4706	480	3	and	and	CCONJ
ejpam-4706	480	4	accurate	accurate	ADJ
ejpam-4706	480	5	bounds	bound	NOUN
ejpam-4706	480	6	for	for	ADP
ejpam-4706	480	7	zeros	zero	NOUN
ejpam-4706	480	8	of	of	ADP
ejpam-4706	480	9	a	a	DET
ejpam-4706	480	10	polynomial	polynomial	NOUN
ejpam-4706	480	11	based	base	VERB
ejpam-4706	480	12	on	on	ADP
ejpam-4706	480	13	similarity	similarity	NOUN
ejpam-4706	480	14	of	of	ADP
ejpam-4706	480	15	companion	companion	NOUN
ejpam-4706	480	16	complex	complex	ADJ
ejpam-4706	480	17	matrices	matrix	NOUN
ejpam-4706	480	18	.	.	PUNCT
ejpam-4706	481	1	filomat	filomat	NOUN
ejpam-4706	481	2	,	,	PUNCT
ejpam-4706	481	3	37(9):2961–2968	37(9):2961–2968	NUM
ejpam-4706	481	4	,	,	PUNCT
ejpam-4706	481	5	2023	2023	NUM
ejpam-4706	481	6	.	.	PUNCT
ejpam-4706	482	1	references	reference	NOUN
ejpam-4706	482	2	818	818	NUM
ejpam-4706	482	3	[	[	X
ejpam-4706	482	4	3	3	NUM
ejpam-4706	482	5	]	]	PUNCT
ejpam-4706	482	6	t	t	NOUN
ejpam-4706	482	7	h	h	PROPN
ejpam-4706	482	8	b	b	PROPN
ejpam-4706	482	9	du	du	PROPN
ejpam-4706	482	10	c	c	PROPN
ejpam-4706	482	11	t	t	PROPN
ejpam-4706	482	12	le	le	X
ejpam-4706	482	13	and	and	CCONJ
ejpam-4706	482	14	t	t	PROPN
ejpam-4706	482	15	d	d	X
ejpam-4706	482	16	nguyen	nguyen	NOUN
ejpam-4706	482	17	.	.	PUNCT
ejpam-4706	483	1	on	on	ADP
ejpam-4706	483	2	the	the	DET
ejpam-4706	483	3	location	location	NOUN
ejpam-4706	483	4	of	of	ADP
ejpam-4706	483	5	eigenvalues	eigenvalue	NOUN
ejpam-4706	483	6	of	of	ADP
ejpam-4706	483	7	matrix	matrix	NOUN
ejpam-4706	483	8	polynomials	polynomial	NOUN
ejpam-4706	483	9	.	.	PUNCT
ejpam-4706	484	1	oper	oper	NOUN
ejpam-4706	484	2	.	.	PUNCT
ejpam-4706	484	3	matrices	matrix	NOUN
ejpam-4706	484	4	,	,	PUNCT
ejpam-4706	484	5	13:937–954	13:937–954	PROPN
ejpam-4706	484	6	,	,	PUNCT
ejpam-4706	484	7	2019	2019	NUM
ejpam-4706	484	8	.	.	PUNCT
ejpam-4706	485	1	[	[	X
ejpam-4706	485	2	4	4	X
ejpam-4706	485	3	]	]	PUNCT
ejpam-4706	485	4	h	h	NOUN
ejpam-4706	485	5	guelfen	guelfen	PROPN
ejpam-4706	485	6	and	and	CCONJ
ejpam-4706	485	7	f	f	PROPN
ejpam-4706	485	8	kittaneh	kittaneh	PROPN
ejpam-4706	485	9	.	.	PUNCT
ejpam-4706	486	1	on	on	ADP
ejpam-4706	486	2	numerical	numerical	ADJ
ejpam-4706	486	3	radius	radius	PROPN
ejpam-4706	486	4	inequalities	inequality	NOUN
ejpam-4706	486	5	for	for	ADP
ejpam-4706	486	6	operator	operator	NOUN
ejpam-4706	486	7	matrices	matrix	NOUN
ejpam-4706	486	8	.	.	PUNCT
ejpam-4706	487	1	numerical	numerical	ADJ
ejpam-4706	487	2	functional	functional	ADJ
ejpam-4706	487	3	analysis	analysis	NOUN
ejpam-4706	487	4	and	and	CCONJ
ejpam-4706	487	5	optimization	optimization	NOUN
ejpam-4706	487	6	,	,	PUNCT
ejpam-4706	487	7	40(11):1231–1241	40(11):1231–1241	NUM
ejpam-4706	487	8	,	,	PUNCT
ejpam-4706	487	9	2019	2019	NUM
ejpam-4706	487	10	.	.	PUNCT
ejpam-4706	488	1	[	[	X
ejpam-4706	488	2	5	5	NUM
ejpam-4706	488	3	]	]	PUNCT
ejpam-4706	488	4	n	n	PRON
ejpam-4706	488	5	j	j	PROPN
ejpam-4706	488	6	higham	higham	PROPN
ejpam-4706	488	7	and	and	CCONJ
ejpam-4706	488	8	f	f	PROPN
ejpam-4706	488	9	tisseur	tisseur	PROPN
ejpam-4706	488	10	.	.	PUNCT
ejpam-4706	489	1	bounds	bound	VERB
ejpam-4706	489	2	for	for	ADP
ejpam-4706	489	3	eigenvalues	eigenvalue	NOUN
ejpam-4706	489	4	of	of	ADP
ejpam-4706	489	5	matrix	matrix	NOUN
ejpam-4706	489	6	polynomials	polynomial	NOUN
ejpam-4706	489	7	.	.	PUNCT
ejpam-4706	490	1	linear	linear	ADJ
ejpam-4706	490	2	algebra	algebra	PROPN
ejpam-4706	490	3	appl	appl	NOUN
ejpam-4706	490	4	.	.	PROPN
ejpam-4706	490	5	,	,	PUNCT
ejpam-4706	490	6	258:5–22	258:5–22	NUM
ejpam-4706	490	7	,	,	PUNCT
ejpam-4706	490	8	2003	2003	NUM
ejpam-4706	490	9	.	.	PUNCT
ejpam-4706	491	1	[	[	X
ejpam-4706	491	2	6	6	NUM
ejpam-4706	491	3	]	]	X
ejpam-4706	491	4	r	r	NOUN
ejpam-4706	491	5	a	a	DET
ejpam-4706	491	6	horn	horn	NOUN
ejpam-4706	491	7	.	.	PUNCT
ejpam-4706	492	1	and	and	CCONJ
ejpam-4706	492	2	c	c	NOUN
ejpam-4706	492	3	r	r	PROPN
ejpam-4706	492	4	johnson	johnson	PROPN
ejpam-4706	492	5	.	.	PROPN
ejpam-4706	492	6	matrix	matrix	NOUN
ejpam-4706	492	7	analysis	analysis	NOUN
ejpam-4706	492	8	.	.	PUNCT
ejpam-4706	493	1	cambridge	cambridge	PROPN
ejpam-4706	493	2	university	university	PROPN
ejpam-4706	493	3	press	press	NOUN
ejpam-4706	493	4	,	,	PUNCT
ejpam-4706	493	5	2012	2012	NUM
ejpam-4706	493	6	.	.	PUNCT
ejpam-4706	494	1	[	[	X
ejpam-4706	494	2	7	7	X
ejpam-4706	494	3	]	]	X
ejpam-4706	494	4	a	a	DET
ejpam-4706	494	5	jaradat	jaradat	PROPN
ejpam-4706	494	6	and	and	CCONJ
ejpam-4706	494	7	f	f	PROPN
ejpam-4706	494	8	kittaneh	kittaneh	PROPN
ejpam-4706	494	9	.	.	PUNCT
ejpam-4706	494	10	bounds	bound	VERB
ejpam-4706	494	11	for	for	ADP
ejpam-4706	494	12	the	the	DET
ejpam-4706	494	13	eigenvalues	eigenvalue	NOUN
ejpam-4706	494	14	of	of	ADP
ejpam-4706	494	15	monic	monic	ADJ
ejpam-4706	494	16	matrix	matrix	NOUN
ejpam-4706	494	17	polynomials	polynomial	NOUN
ejpam-4706	494	18	from	from	ADP
ejpam-4706	494	19	numerical	numerical	ADJ
ejpam-4706	494	20	radius	radius	PROPN
ejpam-4706	494	21	inequalities	inequality	NOUN
ejpam-4706	494	22	.	.	PUNCT
ejpam-4706	495	1	advances	advance	NOUN
ejpam-4706	495	2	in	in	ADP
ejpam-4706	495	3	operator	operator	NOUN
ejpam-4706	495	4	theory	theory	NOUN
ejpam-4706	495	5	,	,	PUNCT
ejpam-4706	495	6	5(3):734–743	5(3):734–743	NUM
ejpam-4706	495	7	,	,	PUNCT
ejpam-4706	495	8	2020	2020	NUM
ejpam-4706	495	9	.	.	PUNCT
ejpam-4706	496	1	[	[	X
ejpam-4706	496	2	8	8	NUM
ejpam-4706	496	3	]	]	PUNCT
ejpam-4706	496	4	a	a	DET
ejpam-4706	496	5	melman	melman	NOUN
ejpam-4706	496	6	.	.	PUNCT
ejpam-4706	497	1	polynomial	polynomial	PROPN
ejpam-4706	497	2	eigenvalue	eigenvalue	PROPN
ejpam-4706	497	3	bounds	bound	NOUN
ejpam-4706	497	4	from	from	ADP
ejpam-4706	497	5	companion	companion	NOUN
ejpam-4706	497	6	matrix	matrix	NOUN
ejpam-4706	497	7	polynomials	polynomial	NOUN
ejpam-4706	497	8	.	.	PUNCT
ejpam-4706	498	1	linear	linear	PROPN
ejpam-4706	498	2	multilinear	multilinear	PROPN
ejpam-4706	498	3	algebra	algebra	PROPN
ejpam-4706	498	4	,	,	PUNCT
ejpam-4706	498	5	67:598–612	67:598–612	NUM
ejpam-4706	498	6	,	,	PUNCT
ejpam-4706	498	7	2019	2019	NUM
ejpam-4706	498	8	.	.	PUNCT
ejpam-4706	499	1	[	[	X
ejpam-4706	499	2	9	9	NUM
ejpam-4706	499	3	]	]	SYM
ejpam-4706	499	4	l	l	NOUN
ejpam-4706	499	5	qiao	qiao	PROPN
ejpam-4706	499	6	d	d	PROPN
ejpam-4706	499	7	xu	xu	PROPN
ejpam-4706	499	8	and	and	CCONJ
ejpam-4706	499	9	w	w	PROPN
ejpam-4706	499	10	qiu	qiu	PROPN
ejpam-4706	499	11	.	.	PUNCT
ejpam-4706	500	1	the	the	DET
ejpam-4706	500	2	formally	formally	ADV
ejpam-4706	500	3	second	second	ADJ
ejpam-4706	500	4	-	-	PUNCT
ejpam-4706	500	5	order	order	NOUN
ejpam-4706	500	6	bdf	bdf	NOUN
ejpam-4706	500	7	adi	adi	PROPN
ejpam-4706	500	8	difference	difference	NOUN
ejpam-4706	500	9	/	/	SYM
ejpam-4706	500	10	compact	compact	ADJ
ejpam-4706	500	11	difference	difference	NOUN
ejpam-4706	500	12	scheme	scheme	NOUN
ejpam-4706	500	13	for	for	ADP
ejpam-4706	500	14	the	the	DET
ejpam-4706	500	15	nonlocal	nonlocal	ADJ
ejpam-4706	500	16	evolution	evolution	NOUN
ejpam-4706	500	17	problem	problem	NOUN
ejpam-4706	500	18	in	in	ADP
ejpam-4706	500	19	three	three	NUM
ejpam-4706	500	20	-	-	PUNCT
ejpam-4706	500	21	dimensional	dimensional	ADJ
ejpam-4706	500	22	space	space	NOUN
ejpam-4706	500	23	.	.	PUNCT
ejpam-4706	501	1	applied	apply	VERB
ejpam-4706	501	2	numerical	numerical	ADJ
ejpam-4706	501	3	mathematics	mathematic	NOUN
ejpam-4706	501	4	,	,	PUNCT
ejpam-4706	501	5	172:359–381	172:359–381	NUM
ejpam-4706	501	6	,	,	PUNCT
ejpam-4706	501	7	2022	2022	NUM
ejpam-4706	501	8	.	.	PUNCT