id	sid	tid	token	lemma	pos
ejpam-5844	1	1	european	european	PROPN
ejpam-5844	1	2	journal	journal	PROPN
ejpam-5844	1	3	of	of	ADP
ejpam-5844	1	4	pure	pure	ADJ
ejpam-5844	1	5	and	and	CCONJ
ejpam-5844	1	6	applied	applied	ADJ
ejpam-5844	1	7	mathematics	mathematic	NOUN
ejpam-5844	1	8	2025	2025	NUM
ejpam-5844	1	9	,	,	PUNCT
ejpam-5844	1	10	vol	vol	NOUN
ejpam-5844	1	11	.	.	PROPN
ejpam-5844	1	12	18	18	NUM
ejpam-5844	1	13	,	,	PUNCT
ejpam-5844	1	14	issue	issue	NOUN
ejpam-5844	1	15	2	2	NUM
ejpam-5844	1	16	,	,	PUNCT
ejpam-5844	1	17	article	article	NOUN
ejpam-5844	1	18	number	number	NOUN
ejpam-5844	1	19	5844	5844	NUM
ejpam-5844	1	20	issn	issn	PROPN
ejpam-5844	1	21	1307	1307	NUM
ejpam-5844	1	22	-	-	SYM
ejpam-5844	1	23	5543	5543	NUM
ejpam-5844	1	24	–	–	PUNCT
ejpam-5844	1	25	ejpam.com	ejpam.com	X
ejpam-5844	1	26	published	publish	VERB
ejpam-5844	1	27	by	by	ADP
ejpam-5844	1	28	new	new	PROPN
ejpam-5844	1	29	york	york	PROPN
ejpam-5844	1	30	business	business	PROPN
ejpam-5844	1	31	global	global	ADJ
ejpam-5844	1	32	singular	singular	PROPN
ejpam-5844	1	33	value	value	NOUN
ejpam-5844	1	34	inequalities	inequality	NOUN
ejpam-5844	1	35	for	for	ADP
ejpam-5844	1	36	matrix	matrix	NOUN
ejpam-5844	1	37	sums	sum	NOUN
ejpam-5844	1	38	and	and	CCONJ
ejpam-5844	1	39	products	product	NOUN
ejpam-5844	1	40	ahmad	ahmad	PROPN
ejpam-5844	1	41	al	al	PROPN
ejpam-5844	1	42	-	-	PUNCT
ejpam-5844	1	43	natoor1,∗	natoor1,∗	NOUN
ejpam-5844	1	44	,	,	PUNCT
ejpam-5844	1	45	rawan	rawan	PROPN
ejpam-5844	1	46	al	al	PROPN
ejpam-5844	1	47	-	-	PUNCT
ejpam-5844	1	48	smadi2	smadi2	PROPN
ejpam-5844	1	49	,	,	PUNCT
ejpam-5844	1	50	aliaa	aliaa	ADJ
ejpam-5844	1	51	burqan2	burqan2	PROPN
ejpam-5844	1	52	1	1	NUM
ejpam-5844	1	53	department	department	NOUN
ejpam-5844	1	54	of	of	ADP
ejpam-5844	1	55	mathematics	mathematic	NOUN
ejpam-5844	1	56	,	,	PUNCT
ejpam-5844	1	57	faculty	faculty	NOUN
ejpam-5844	1	58	of	of	ADP
ejpam-5844	1	59	sciences	science	NOUN
ejpam-5844	1	60	,	,	PUNCT
ejpam-5844	1	61	isra	isra	PROPN
ejpam-5844	1	62	university	university	PROPN
ejpam-5844	1	63	,	,	PUNCT
ejpam-5844	1	64	amman	amman	NOUN
ejpam-5844	1	65	11622	11622	NUM
ejpam-5844	1	66	,	,	PUNCT
ejpam-5844	1	67	jordan	jordan	PROPN
ejpam-5844	1	68	2	2	NUM
ejpam-5844	1	69	department	department	NOUN
ejpam-5844	1	70	of	of	ADP
ejpam-5844	1	71	mathematics	mathematic	NOUN
ejpam-5844	1	72	,	,	PUNCT
ejpam-5844	1	73	faculty	faculty	NOUN
ejpam-5844	1	74	of	of	ADP
ejpam-5844	1	75	science	science	NOUN
ejpam-5844	1	76	,	,	PUNCT
ejpam-5844	1	77	zarqa	zarqa	PROPN
ejpam-5844	1	78	university	university	PROPN
ejpam-5844	1	79	,	,	PUNCT
ejpam-5844	1	80	zarqa	zarqa	PROPN
ejpam-5844	1	81	13110	13110	NUM
ejpam-5844	1	82	,	,	PUNCT
ejpam-5844	1	83	jordan	jordan	PROPN
ejpam-5844	1	84	abstract	abstract	PROPN
ejpam-5844	1	85	.	.	PUNCT
ejpam-5844	2	1	in	in	ADP
ejpam-5844	2	2	this	this	DET
ejpam-5844	2	3	paper	paper	NOUN
ejpam-5844	2	4	,	,	PUNCT
ejpam-5844	2	5	we	we	PRON
ejpam-5844	2	6	discuss	discuss	VERB
ejpam-5844	2	7	some	some	DET
ejpam-5844	2	8	inequalities	inequality	NOUN
ejpam-5844	2	9	involving	involve	VERB
ejpam-5844	2	10	singular	singular	ADJ
ejpam-5844	2	11	values	value	NOUN
ejpam-5844	2	12	for	for	ADP
ejpam-5844	2	13	matrix	matrix	NOUN
ejpam-5844	2	14	sums	sum	NOUN
ejpam-5844	2	15	and	and	CCONJ
ejpam-5844	2	16	products	product	NOUN
ejpam-5844	2	17	.	.	PUNCT
ejpam-5844	3	1	in	in	ADP
ejpam-5844	3	2	some	some	PRON
ejpam-5844	3	3	of	of	ADP
ejpam-5844	3	4	our	our	PRON
ejpam-5844	3	5	results	result	NOUN
ejpam-5844	3	6	,	,	PUNCT
ejpam-5844	3	7	we	we	PRON
ejpam-5844	3	8	prove	prove	VERB
ejpam-5844	3	9	inequalities	inequality	NOUN
ejpam-5844	3	10	for	for	ADP
ejpam-5844	3	11	functions	function	NOUN
ejpam-5844	3	12	of	of	ADP
ejpam-5844	3	13	matrices	matrix	NOUN
ejpam-5844	3	14	and	and	CCONJ
ejpam-5844	3	15	this	this	PRON
ejpam-5844	3	16	enables	enable	VERB
ejpam-5844	3	17	us	we	PRON
ejpam-5844	3	18	to	to	PART
ejpam-5844	3	19	give	give	VERB
ejpam-5844	3	20	a	a	DET
ejpam-5844	3	21	generalization	generalization	NOUN
ejpam-5844	3	22	of	of	ADP
ejpam-5844	3	23	known	know	VERB
ejpam-5844	3	24	recent	recent	ADJ
ejpam-5844	3	25	result	result	NOUN
ejpam-5844	3	26	.	.	PUNCT
ejpam-5844	4	1	2020	2020	NUM
ejpam-5844	4	2	mathematics	mathematic	NOUN
ejpam-5844	4	3	subject	subject	NOUN
ejpam-5844	4	4	classifications	classification	NOUN
ejpam-5844	4	5	:	:	PUNCT
ejpam-5844	4	6	15a18	15a18	NUM
ejpam-5844	4	7	,	,	PUNCT
ejpam-5844	4	8	15a60	15a60	NUM
ejpam-5844	4	9	15a42	15a42	NUM
ejpam-5844	4	10	,	,	PUNCT
ejpam-5844	4	11	15a16	15a16	NUM
ejpam-5844	4	12	key	key	ADJ
ejpam-5844	4	13	words	word	NOUN
ejpam-5844	4	14	and	and	CCONJ
ejpam-5844	4	15	phrases	phrase	NOUN
ejpam-5844	4	16	:	:	PUNCT
ejpam-5844	4	17	positive	positive	ADJ
ejpam-5844	4	18	semidefinite	semidefinite	NOUN
ejpam-5844	4	19	matrix	matrix	NOUN
ejpam-5844	4	20	,	,	PUNCT
ejpam-5844	4	21	singular	singular	NOUN
ejpam-5844	4	22	value	value	NOUN
ejpam-5844	4	23	,	,	PUNCT
ejpam-5844	4	24	spectral	spectral	ADJ
ejpam-5844	4	25	norm	norm	NOUN
ejpam-5844	4	26	,	,	PUNCT
ejpam-5844	4	27	inequality	inequality	NOUN
ejpam-5844	4	28	1	1	NUM
ejpam-5844	4	29	.	.	PUNCT
ejpam-5844	5	1	introduction	introduction	NOUN
ejpam-5844	5	2	in	in	ADP
ejpam-5844	5	3	this	this	DET
ejpam-5844	5	4	paper	paper	NOUN
ejpam-5844	5	5	,	,	PUNCT
ejpam-5844	5	6	the	the	DET
ejpam-5844	5	7	symbol	symbol	NOUN
ejpam-5844	5	8	mn(c	mn(c	VERB
ejpam-5844	5	9	)	)	PUNCT
ejpam-5844	5	10	denote	denote	VERB
ejpam-5844	5	11	the	the	DET
ejpam-5844	5	12	space	space	NOUN
ejpam-5844	5	13	of	of	ADP
ejpam-5844	5	14	n	n	NUM
ejpam-5844	5	15	×	×	NOUN
ejpam-5844	5	16	n	n	CCONJ
ejpam-5844	5	17	complex	complex	ADJ
ejpam-5844	5	18	matrices	matrix	NOUN
ejpam-5844	5	19	.	.	PUNCT
ejpam-5844	6	1	the	the	DET
ejpam-5844	6	2	numbers	number	NOUN
ejpam-5844	6	3	s1(a	s1(a	ADP
ejpam-5844	6	4	)	)	PUNCT
ejpam-5844	6	5	≥	≥	NUM
ejpam-5844	6	6	,	,	PUNCT
ejpam-5844	6	7	...	...	PUNCT
ejpam-5844	6	8	,	,	PUNCT
ejpam-5844	6	9	≥	≥	NOUN
ejpam-5844	6	10	sn(a	sn(a	X
ejpam-5844	6	11	)	)	PUNCT
ejpam-5844	6	12	≥	≥	X
ejpam-5844	6	13	0	0	NUM
ejpam-5844	6	14	are	be	AUX
ejpam-5844	6	15	called	call	VERB
ejpam-5844	6	16	the	the	DET
ejpam-5844	6	17	singular	singular	ADJ
ejpam-5844	6	18	values	value	NOUN
ejpam-5844	6	19	of	of	ADP
ejpam-5844	6	20	a	a	DET
ejpam-5844	6	21	∈	∈	NOUN
ejpam-5844	6	22	mn(c	mn(c	X
ejpam-5844	6	23	)	)	PUNCT
ejpam-5844	6	24	which	which	PRON
ejpam-5844	6	25	are	be	AUX
ejpam-5844	6	26	the	the	DET
ejpam-5844	6	27	eigenvalues	eigenvalue	NOUN
ejpam-5844	6	28	of	of	ADP
ejpam-5844	6	29	|a|	|a|	NOUN
ejpam-5844	6	30	=	=	SYM
ejpam-5844	6	31	(	(	PUNCT
ejpam-5844	6	32	a∗a)1/2	a∗a)1/2	PROPN
ejpam-5844	6	33	arranged	arrange	VERB
ejpam-5844	6	34	in	in	ADP
ejpam-5844	6	35	decreasing	decrease	VERB
ejpam-5844	6	36	order	order	NOUN
ejpam-5844	6	37	and	and	CCONJ
ejpam-5844	6	38	counted	count	VERB
ejpam-5844	6	39	according	accord	VERB
ejpam-5844	6	40	to	to	ADP
ejpam-5844	6	41	multiplicity	multiplicity	NOUN
ejpam-5844	6	42	.	.	PUNCT
ejpam-5844	7	1	the	the	DET
ejpam-5844	7	2	spectral	spectral	ADJ
ejpam-5844	7	3	norm	norm	NOUN
ejpam-5844	7	4	of	of	ADP
ejpam-5844	7	5	a	a	DET
ejpam-5844	7	6	∈	∈	PROPN
ejpam-5844	7	7	mn	mn	PROPN
ejpam-5844	7	8	(	(	PUNCT
ejpam-5844	7	9	c	c	NOUN
ejpam-5844	7	10	)	)	PUNCT
ejpam-5844	7	11	,	,	PUNCT
ejpam-5844	7	12	denoted	denote	VERB
ejpam-5844	7	13	by	by	ADP
ejpam-5844	7	14	∥a∥	∥a∥	NOUN
ejpam-5844	7	15	,	,	PUNCT
ejpam-5844	7	16	can	can	AUX
ejpam-5844	7	17	be	be	AUX
ejpam-5844	7	18	expressed	express	VERB
ejpam-5844	7	19	as	as	ADP
ejpam-5844	7	20	the	the	DET
ejpam-5844	7	21	largest	large	ADJ
ejpam-5844	7	22	singular	singular	ADJ
ejpam-5844	7	23	value	value	NOUN
ejpam-5844	7	24	of	of	ADP
ejpam-5844	7	25	a	a	PRON
ejpam-5844	7	26	,	,	PUNCT
ejpam-5844	7	27	i.e	i.e	PROPN
ejpam-5844	7	28	,	,	PUNCT
ejpam-5844	7	29	∥a∥	∥a∥	ADJ
ejpam-5844	7	30	=	=	SYM
ejpam-5844	7	31	s1	s1	NOUN
ejpam-5844	7	32	.	.	PUNCT
ejpam-5844	8	1	it	it	PRON
ejpam-5844	8	2	is	be	AUX
ejpam-5844	8	3	known	know	VERB
ejpam-5844	8	4	(	(	PUNCT
ejpam-5844	8	5	see	see	VERB
ejpam-5844	8	6	[	[	X
ejpam-5844	8	7	1	1	X
ejpam-5844	8	8	]	]	PUNCT
ejpam-5844	8	9	or	or	CCONJ
ejpam-5844	8	10	[	[	X
ejpam-5844	8	11	2	2	NUM
ejpam-5844	8	12	]	]	PUNCT
ejpam-5844	8	13	)	)	PUNCT
ejpam-5844	8	14	that	that	SCONJ
ejpam-5844	8	15	if	if	SCONJ
ejpam-5844	8	16	x	x	SYM
ejpam-5844	8	17	∈	∈	PROPN
ejpam-5844	8	18	mm	mm	PROPN
ejpam-5844	8	19	and	and	CCONJ
ejpam-5844	8	20	y	y	PROPN
ejpam-5844	8	21	∈	∈	PROPN
ejpam-5844	8	22	mn	mn	PROPN
ejpam-5844	8	23	are	be	AUX
ejpam-5844	8	24	such	such	ADJ
ejpam-5844	8	25	that	that	SCONJ
ejpam-5844	8	26	[	[	PUNCT
ejpam-5844	8	27	x	x	X
ejpam-5844	8	28	z	z	X
ejpam-5844	8	29	z∗	z∗	PROPN
ejpam-5844	8	30	y	y	PROPN
ejpam-5844	8	31	]	]	PUNCT
ejpam-5844	8	32	≥	≥	PROPN
ejpam-5844	8	33	0	0	NUM
ejpam-5844	8	34	,	,	PUNCT
ejpam-5844	8	35	then	then	ADV
ejpam-5844	8	36	sj	sj	INTJ
ejpam-5844	8	37	(	(	PUNCT
ejpam-5844	8	38	z	z	NOUN
ejpam-5844	8	39	)	)	PUNCT
ejpam-5844	8	40	≤	≤	NOUN
ejpam-5844	8	41	1	1	NUM
ejpam-5844	8	42	2	2	NUM
ejpam-5844	8	43	sj	sj	NOUN
ejpam-5844	8	44	(	(	PUNCT
ejpam-5844	8	45	[	[	PUNCT
ejpam-5844	8	46	x	x	X
ejpam-5844	8	47	z	z	X
ejpam-5844	8	48	z∗	z∗	PROPN
ejpam-5844	8	49	y	y	PROPN
ejpam-5844	8	50	]	]	PUNCT
ejpam-5844	8	51	)	)	PUNCT
ejpam-5844	8	52	(	(	PUNCT
ejpam-5844	8	53	1	1	X
ejpam-5844	8	54	)	)	PUNCT
ejpam-5844	8	55	for	for	ADP
ejpam-5844	8	56	j	j	PROPN
ejpam-5844	8	57	=	=	SYM
ejpam-5844	8	58	1	1	NUM
ejpam-5844	8	59	,	,	PUNCT
ejpam-5844	8	60	2	2	NUM
ejpam-5844	8	61	,	,	PUNCT
ejpam-5844	8	62	...	...	PUNCT
ejpam-5844	8	63	,	,	PUNCT
ejpam-5844	8	64	r	r	NOUN
ejpam-5844	8	65	,	,	PUNCT
ejpam-5844	8	66	where	where	SCONJ
ejpam-5844	8	67	r	r	NOUN
ejpam-5844	8	68	=	=	SYM
ejpam-5844	8	69	min(n	min(n	PROPN
ejpam-5844	8	70	,	,	PUNCT
ejpam-5844	8	71	m	m	NOUN
ejpam-5844	8	72	)	)	PUNCT
ejpam-5844	8	73	.	.	PUNCT
ejpam-5844	9	1	if	if	SCONJ
ejpam-5844	9	2	a	a	PRON
ejpam-5844	9	3	and	and	CCONJ
ejpam-5844	9	4	b	b	NOUN
ejpam-5844	9	5	are	be	AUX
ejpam-5844	9	6	positive	positive	ADJ
ejpam-5844	9	7	semidefinite	semidefinite	NOUN
ejpam-5844	9	8	matrices	matrix	NOUN
ejpam-5844	9	9	,	,	PUNCT
ejpam-5844	9	10	then	then	ADV
ejpam-5844	9	11	by	by	ADP
ejpam-5844	9	12	letting	let	VERB
ejpam-5844	9	13	z	z	PROPN
ejpam-5844	9	14	=	=	SYM
ejpam-5844	9	15	ab	ab	PROPN
ejpam-5844	9	16	,	,	PUNCT
ejpam-5844	9	17	x	x	SYM
ejpam-5844	9	18	=	=	SYM
ejpam-5844	9	19	a2	a2	PROPN
ejpam-5844	9	20	,	,	PUNCT
ejpam-5844	9	21	and	and	CCONJ
ejpam-5844	9	22	y	y	PROPN
ejpam-5844	9	23	=	=	PUNCT
ejpam-5844	9	24	b2	b2	PROPN
ejpam-5844	9	25	in	in	ADP
ejpam-5844	9	26	inequality	inequality	NOUN
ejpam-5844	9	27	(	(	PUNCT
ejpam-5844	9	28	1	1	NUM
ejpam-5844	9	29	)	)	PUNCT
ejpam-5844	9	30	,	,	PUNCT
ejpam-5844	9	31	we	we	PRON
ejpam-5844	9	32	have	have	VERB
ejpam-5844	9	33	sj	sj	INTJ
ejpam-5844	9	34	(	(	PUNCT
ejpam-5844	9	35	ab	ab	NOUN
ejpam-5844	9	36	)	)	PUNCT
ejpam-5844	9	37	≤	≤	NOUN
ejpam-5844	9	38	1	1	NUM
ejpam-5844	9	39	2	2	NUM
ejpam-5844	9	40	sj	sj	NOUN
ejpam-5844	9	41	(	(	PUNCT
ejpam-5844	9	42	[	[	PUNCT
ejpam-5844	9	43	a2	a2	PROPN
ejpam-5844	9	44	ab	ab	PROPN
ejpam-5844	9	45	ba	ba	PROPN
ejpam-5844	9	46	b2	b2	PROPN
ejpam-5844	9	47	]	]	PUNCT
ejpam-5844	9	48	)	)	PUNCT
ejpam-5844	9	49	.	.	PUNCT
ejpam-5844	10	1	(	(	PUNCT
ejpam-5844	10	2	2	2	X
ejpam-5844	10	3	)	)	PUNCT
ejpam-5844	10	4	among	among	ADP
ejpam-5844	10	5	other	other	ADJ
ejpam-5844	10	6	results	result	NOUN
ejpam-5844	10	7	in	in	ADP
ejpam-5844	10	8	this	this	DET
ejpam-5844	10	9	paper	paper	NOUN
ejpam-5844	10	10	,	,	PUNCT
ejpam-5844	10	11	we	we	PRON
ejpam-5844	10	12	give	give	VERB
ejpam-5844	10	13	a	a	DET
ejpam-5844	10	14	general	general	ADJ
ejpam-5844	10	15	version	version	NOUN
ejpam-5844	10	16	of	of	ADP
ejpam-5844	10	17	inequality	inequality	NOUN
ejpam-5844	10	18	(	(	PUNCT
ejpam-5844	10	19	2	2	NUM
ejpam-5844	10	20	)	)	PUNCT
ejpam-5844	10	21	.	.	PUNCT
ejpam-5844	11	1	for	for	ADP
ejpam-5844	11	2	more	more	ADJ
ejpam-5844	11	3	singular	singular	ADJ
ejpam-5844	11	4	value	value	NOUN
ejpam-5844	11	5	and	and	CCONJ
ejpam-5844	11	6	norm	norm	NOUN
ejpam-5844	11	7	inequalities	inequality	NOUN
ejpam-5844	11	8	for	for	ADP
ejpam-5844	11	9	matrices	matrix	NOUN
ejpam-5844	11	10	,	,	PUNCT
ejpam-5844	11	11	we	we	PRON
ejpam-5844	11	12	refer	refer	VERB
ejpam-5844	11	13	the	the	DET
ejpam-5844	11	14	reader	reader	NOUN
ejpam-5844	11	15	to	to	ADP
ejpam-5844	11	16	[	[	X
ejpam-5844	11	17	3	3	NUM
ejpam-5844	11	18	]	]	PUNCT
ejpam-5844	11	19	,	,	PUNCT
ejpam-5844	11	20	[	[	X
ejpam-5844	11	21	4	4	NUM
ejpam-5844	11	22	]	]	PUNCT
ejpam-5844	11	23	,	,	PUNCT
ejpam-5844	11	24	[	[	X
ejpam-5844	11	25	5	5	NUM
ejpam-5844	11	26	]	]	PUNCT
ejpam-5844	11	27	,	,	PUNCT
ejpam-5844	11	28	[	[	X
ejpam-5844	11	29	6	6	NUM
ejpam-5844	11	30	]	]	PUNCT
ejpam-5844	11	31	,	,	PUNCT
ejpam-5844	11	32	and	and	CCONJ
ejpam-5844	11	33	[	[	X
ejpam-5844	11	34	7	7	NUM
ejpam-5844	11	35	]	]	PUNCT
ejpam-5844	11	36	.	.	PUNCT
ejpam-5844	12	1	∗corresponding	∗corresponde	VERB
ejpam-5844	12	2	author	author	NOUN
ejpam-5844	12	3	.	.	PUNCT
ejpam-5844	13	1	doi	doi	NOUN
ejpam-5844	13	2	:	:	PUNCT
ejpam-5844	13	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5844	https://doi.org/10.29020/nybg.ejpam.v18i2.5844	NOUN
ejpam-5844	13	4	email	email	NOUN
ejpam-5844	13	5	addresses	address	NOUN
ejpam-5844	13	6	:	:	PUNCT
ejpam-5844	13	7	ahmad.alnatoor@iu.edu.jo	ahmad.alnatoor@iu.edu.jo	NOUN
ejpam-5844	13	8	(	(	PUNCT
ejpam-5844	13	9	a.	a.	NOUN
ejpam-5844	13	10	al	al	PROPN
ejpam-5844	13	11	-	-	PUNCT
ejpam-5844	13	12	natoor	natoor	NOUN
ejpam-5844	13	13	)	)	PUNCT
ejpam-5844	13	14	,	,	PUNCT
ejpam-5844	13	15	rawansmadi2@gmail.com	rawansmadi2@gmail.com	X
ejpam-5844	13	16	(	(	PUNCT
ejpam-5844	13	17	r.	r.	PROPN
ejpam-5844	13	18	al	al	PROPN
ejpam-5844	13	19	-	-	PUNCT
ejpam-5844	13	20	smadi	smadi	NOUN
ejpam-5844	13	21	)	)	PUNCT
ejpam-5844	13	22	,	,	PUNCT
ejpam-5844	13	23	aliaaburqan@zu.edu.jo	aliaaburqan@zu.edu.jo	PROPN
ejpam-5844	13	24	(	(	PUNCT
ejpam-5844	13	25	a.	a.	NOUN
ejpam-5844	13	26	burqan	burqan	PROPN
ejpam-5844	13	27	)	)	PUNCT
ejpam-5844	13	28	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5844	14	1	1	1	NUM
ejpam-5844	14	2	copyright	copyright	NOUN
ejpam-5844	14	3	:	:	PUNCT
ejpam-5844	14	4	©	©	PROPN
ejpam-5844	14	5	2025	2025	NUM
ejpam-5844	14	6	the	the	DET
ejpam-5844	14	7	author(s	author(s	NOUN
ejpam-5844	14	8	)	)	PUNCT
ejpam-5844	14	9	.	.	PUNCT
ejpam-5844	15	1	(	(	PUNCT
ejpam-5844	15	2	cc	cc	NOUN
ejpam-5844	15	3	by	by	ADP
ejpam-5844	15	4	-	-	PUNCT
ejpam-5844	15	5	nc	nc	PROPN
ejpam-5844	15	6	4.0	4.0	NUM
ejpam-5844	15	7	)	)	PUNCT
ejpam-5844	15	8	a.	a.	NOUN
ejpam-5844	15	9	al	al	PROPN
ejpam-5844	15	10	-	-	PUNCT
ejpam-5844	15	11	natoor	natoor	NOUN
ejpam-5844	15	12	,	,	PUNCT
ejpam-5844	15	13	r.	r.	PROPN
ejpam-5844	15	14	al	al	PROPN
ejpam-5844	15	15	-	-	PUNCT
ejpam-5844	15	16	smadi	smadi	PROPN
ejpam-5844	15	17	,	,	PUNCT
ejpam-5844	15	18	a.	a.	NOUN
ejpam-5844	15	19	burqan	burqan	PROPN
ejpam-5844	15	20	/	/	SYM
ejpam-5844	15	21	eur	eur	PROPN
ejpam-5844	15	22	.	.	PUNCT
ejpam-5844	16	1	j.	j.	PROPN
ejpam-5844	16	2	pure	pure	PROPN
ejpam-5844	16	3	appl	appl	PROPN
ejpam-5844	16	4	.	.	PROPN
ejpam-5844	16	5	math	math	PROPN
ejpam-5844	16	6	,	,	PUNCT
ejpam-5844	16	7	18	18	NUM
ejpam-5844	16	8	(	(	PUNCT
ejpam-5844	16	9	2	2	NUM
ejpam-5844	16	10	)	)	PUNCT
ejpam-5844	16	11	(	(	PUNCT
ejpam-5844	16	12	2025	2025	NUM
ejpam-5844	16	13	)	)	PUNCT
ejpam-5844	16	14	,	,	PUNCT
ejpam-5844	16	15	5844	5844	NUM
ejpam-5844	16	16	2	2	NUM
ejpam-5844	16	17	of	of	ADP
ejpam-5844	16	18	10	10	NUM
ejpam-5844	16	19	2	2	NUM
ejpam-5844	16	20	.	.	PUNCT
ejpam-5844	16	21	main	main	ADJ
ejpam-5844	16	22	results	result	NOUN
ejpam-5844	16	23	to	to	PART
ejpam-5844	16	24	start	start	VERB
ejpam-5844	16	25	our	our	PRON
ejpam-5844	16	26	analysis	analysis	NOUN
ejpam-5844	16	27	,	,	PUNCT
ejpam-5844	16	28	we	we	PRON
ejpam-5844	16	29	need	need	VERB
ejpam-5844	16	30	the	the	DET
ejpam-5844	16	31	fact	fact	NOUN
ejpam-5844	16	32	that	that	SCONJ
ejpam-5844	16	33	if	if	SCONJ
ejpam-5844	16	34	a	a	DET
ejpam-5844	16	35	,	,	PUNCT
ejpam-5844	16	36	b	b	NOUN
ejpam-5844	16	37	∈	∈	PROPN
ejpam-5844	16	38	mn(c	mn(c	X
ejpam-5844	16	39	)	)	PUNCT
ejpam-5844	16	40	,	,	PUNCT
ejpam-5844	16	41	then	then	ADV
ejpam-5844	16	42	sj(a	sj(a	NUM
ejpam-5844	16	43	)	)	PUNCT
ejpam-5844	16	44	≤	≤	NOUN
ejpam-5844	16	45	sj(b	sj(b	NOUN
ejpam-5844	16	46	)	)	PUNCT
ejpam-5844	16	47	iff	iff	NOUN
ejpam-5844	16	48	sj(a⊕a	sj(a⊕a	NOUN
ejpam-5844	16	49	)	)	PUNCT
ejpam-5844	16	50	≤	≤	NOUN
ejpam-5844	16	51	sj(b	sj(b	PUNCT
ejpam-5844	16	52	⊕b	⊕b	NOUN
ejpam-5844	16	53	)	)	PUNCT
ejpam-5844	16	54	(	(	PUNCT
ejpam-5844	16	55	3	3	X
ejpam-5844	16	56	)	)	PUNCT
ejpam-5844	16	57	for	for	ADP
ejpam-5844	16	58	j	j	PROPN
ejpam-5844	16	59	=	=	SYM
ejpam-5844	16	60	1	1	NUM
ejpam-5844	16	61	,	,	PUNCT
ejpam-5844	16	62	...	...	PUNCT
ejpam-5844	16	63	,	,	PUNCT
ejpam-5844	16	64	2n	2n	X
ejpam-5844	16	65	.	.	PUNCT
ejpam-5844	17	1	lemma	lemma	PROPN
ejpam-5844	17	2	1	1	X
ejpam-5844	17	3	.	.	PUNCT
ejpam-5844	18	1	let	let	VERB
ejpam-5844	18	2	a	a	DET
ejpam-5844	18	3	,	,	PUNCT
ejpam-5844	18	4	b	b	NOUN
ejpam-5844	18	5	,	,	PUNCT
ejpam-5844	18	6	y	y	PROPN
ejpam-5844	18	7	∈	∈	PROPN
ejpam-5844	18	8	mn	mn	PROPN
ejpam-5844	18	9	(	(	PUNCT
ejpam-5844	18	10	c	c	X
ejpam-5844	18	11	)	)	PUNCT
ejpam-5844	18	12	be	be	AUX
ejpam-5844	18	13	such	such	ADJ
ejpam-5844	18	14	that	that	SCONJ
ejpam-5844	18	15	a	a	PRON
ejpam-5844	18	16	and	and	CCONJ
ejpam-5844	18	17	b	b	NOUN
ejpam-5844	18	18	are	be	AUX
ejpam-5844	18	19	positive	positive	ADJ
ejpam-5844	18	20	semidefinite	semidefinite	NOUN
ejpam-5844	18	21	.	.	PUNCT
ejpam-5844	19	1	then	then	ADV
ejpam-5844	19	2	for	for	ADP
ejpam-5844	19	3	j	j	PROPN
ejpam-5844	19	4	=	=	SYM
ejpam-5844	19	5	1	1	NUM
ejpam-5844	19	6	,	,	PUNCT
ejpam-5844	19	7	...	...	PUNCT
ejpam-5844	19	8	,	,	PUNCT
ejpam-5844	19	9	2n	2n	NUM
ejpam-5844	19	10	,	,	PUNCT
ejpam-5844	19	11	we	we	PRON
ejpam-5844	19	12	have	have	VERB
ejpam-5844	19	13	sj	sj	INTJ
ejpam-5844	19	14	(	(	PUNCT
ejpam-5844	19	15	(	(	PUNCT
ejpam-5844	19	16	ay	ay	INTJ
ejpam-5844	19	17	−	−	PROPN
ejpam-5844	19	18	y	y	PROPN
ejpam-5844	19	19	b)⊕	b)⊕	PROPN
ejpam-5844	19	20	0	0	NUM
ejpam-5844	19	21	)	)	PUNCT
ejpam-5844	20	1	≤	≤	NUM
ejpam-5844	20	2	max	max	NOUN
ejpam-5844	20	3	(	(	PUNCT
ejpam-5844	20	4	∥a∥	∥a∥	NOUN
ejpam-5844	20	5	,	,	PUNCT
ejpam-5844	20	6	∥b∥	∥b∥	NUM
ejpam-5844	20	7	)	)	PUNCT
ejpam-5844	20	8	sj	sj	INTJ
ejpam-5844	20	9	(	(	PUNCT
ejpam-5844	20	10	y	y	PROPN
ejpam-5844	20	11	⊕	⊕	PROPN
ejpam-5844	20	12	y	y	PROPN
ejpam-5844	20	13	)	)	PUNCT
ejpam-5844	20	14	.	.	PUNCT
ejpam-5844	21	1	in	in	ADP
ejpam-5844	21	2	particular	particular	ADJ
ejpam-5844	21	3	,	,	PUNCT
ejpam-5844	21	4	if	if	SCONJ
ejpam-5844	21	5	b	b	X
ejpam-5844	21	6	=	=	SYM
ejpam-5844	21	7	a	a	NOUN
ejpam-5844	21	8	,	,	PUNCT
ejpam-5844	21	9	then	then	ADV
ejpam-5844	21	10	sj	sj	INTJ
ejpam-5844	21	11	(	(	PUNCT
ejpam-5844	21	12	(	(	PUNCT
ejpam-5844	21	13	ay	ay	INTJ
ejpam-5844	21	14	−	−	PROPN
ejpam-5844	21	15	y	y	PROPN
ejpam-5844	21	16	a)⊕	a)⊕	NOUN
ejpam-5844	21	17	0	0	NUM
ejpam-5844	21	18	)	)	PUNCT
ejpam-5844	21	19	≤	≤	NOUN
ejpam-5844	21	20	∥a∥	∥a∥	NOUN
ejpam-5844	21	21	sj	sj	INTJ
ejpam-5844	21	22	(	(	PUNCT
ejpam-5844	21	23	y	y	PROPN
ejpam-5844	21	24	⊕	⊕	PROPN
ejpam-5844	21	25	y	y	PROPN
ejpam-5844	21	26	)	)	PUNCT
ejpam-5844	21	27	.	.	PUNCT
ejpam-5844	22	1	theorem	theorem	NOUN
ejpam-5844	22	2	1	1	NUM
ejpam-5844	22	3	.	.	PUNCT
ejpam-5844	23	1	let	let	VERB
ejpam-5844	23	2	a	a	DET
ejpam-5844	23	3	,	,	PUNCT
ejpam-5844	23	4	b	b	PROPN
ejpam-5844	23	5	∈	∈	PROPN
ejpam-5844	23	6	mn	mn	PROPN
ejpam-5844	23	7	(	(	PUNCT
ejpam-5844	23	8	c	c	AUX
ejpam-5844	23	9	)	)	PUNCT
ejpam-5844	23	10	be	be	AUX
ejpam-5844	23	11	positive	positive	ADJ
ejpam-5844	23	12	semidefinite	semidefinite	NOUN
ejpam-5844	23	13	and	and	CCONJ
ejpam-5844	23	14	let	let	VERB
ejpam-5844	23	15	g(t	g(t	PROPN
ejpam-5844	23	16	)	)	PUNCT
ejpam-5844	23	17	,	,	PUNCT
ejpam-5844	23	18	h(t	h(t	PROPN
ejpam-5844	23	19	)	)	PUNCT
ejpam-5844	24	1	be	be	AUX
ejpam-5844	24	2	real	real	ADJ
ejpam-5844	24	3	polynomials	polynomial	NOUN
ejpam-5844	24	4	.	.	PUNCT
ejpam-5844	25	1	then	then	ADV
ejpam-5844	25	2	for	for	ADP
ejpam-5844	25	3	j	j	PROPN
ejpam-5844	25	4	=	=	SYM
ejpam-5844	25	5	1	1	NUM
ejpam-5844	25	6	,	,	PUNCT
ejpam-5844	25	7	...	...	PUNCT
ejpam-5844	25	8	,	,	PUNCT
ejpam-5844	25	9	2n	2n	NUM
ejpam-5844	25	10	,	,	PUNCT
ejpam-5844	25	11	we	we	PRON
ejpam-5844	25	12	have	have	VERB
ejpam-5844	25	13	sj	sj	INTJ
ejpam-5844	25	14	(	(	PUNCT
ejpam-5844	25	15	(	(	PUNCT
ejpam-5844	25	16	abh	abh	PROPN
ejpam-5844	25	17	(	(	PUNCT
ejpam-5844	25	18	b	b	NOUN
ejpam-5844	25	19	)	)	PUNCT
ejpam-5844	26	1	+	+	CCONJ
ejpam-5844	26	2	g	g	PROPN
ejpam-5844	26	3	(	(	PUNCT
ejpam-5844	26	4	a)ab)⊕	a)ab)⊕	PROPN
ejpam-5844	26	5	0	0	NUM
ejpam-5844	26	6	)	)	PUNCT
ejpam-5844	26	7	≤	≤	PUNCT
ejpam-5844	27	1	∥∥a2	∥∥a2	PROPN
ejpam-5844	27	2	+	+	NOUN
ejpam-5844	27	3	b2	b2	NOUN
ejpam-5844	27	4	∥∥	∥∥	X
ejpam-5844	27	5	sj	sj	INTJ
ejpam-5844	27	6	(	(	PUNCT
ejpam-5844	27	7	g	g	PROPN
ejpam-5844	27	8	(	(	PUNCT
ejpam-5844	27	9	a)⊕	a)⊕	INTJ
ejpam-5844	27	10	h	h	NOUN
ejpam-5844	27	11	(	(	PUNCT
ejpam-5844	27	12	b	b	NOUN
ejpam-5844	27	13	)	)	PUNCT
ejpam-5844	27	14	)	)	PUNCT
ejpam-5844	27	15	.	.	PUNCT
ejpam-5844	28	1	proof	proof	NOUN
ejpam-5844	28	2	.	.	PUNCT
ejpam-5844	29	1	let	let	VERB
ejpam-5844	29	2	q1	q1	PROPN
ejpam-5844	29	3	=	=	PUNCT
ejpam-5844	30	1	[	[	PUNCT
ejpam-5844	30	2	a	a	DET
ejpam-5844	30	3	0	0	NUM
ejpam-5844	30	4	b	b	NOUN
ejpam-5844	30	5	0	0	NUM
ejpam-5844	30	6	]	]	PUNCT
ejpam-5844	30	7	[	[	PUNCT
ejpam-5844	30	8	a	a	DET
ejpam-5844	30	9	b	b	NOUN
ejpam-5844	30	10	0	0	NUM
ejpam-5844	30	11	0	0	NUM
ejpam-5844	30	12	]	]	PUNCT
ejpam-5844	31	1	[	[	PUNCT
ejpam-5844	31	2	g	g	NOUN
ejpam-5844	31	3	(	(	PUNCT
ejpam-5844	31	4	a	a	NOUN
ejpam-5844	31	5	)	)	PUNCT
ejpam-5844	31	6	0	0	NUM
ejpam-5844	31	7	0	0	NUM
ejpam-5844	31	8	h	h	NOUN
ejpam-5844	31	9	(	(	PUNCT
ejpam-5844	31	10	b	b	NOUN
ejpam-5844	31	11	)	)	PUNCT
ejpam-5844	31	12	]	]	PUNCT
ejpam-5844	32	1	=	=	PUNCT
ejpam-5844	32	2	[	[	PUNCT
ejpam-5844	32	3	a2	a2	PROPN
ejpam-5844	32	4	g	g	PROPN
ejpam-5844	32	5	(	(	PUNCT
ejpam-5844	32	6	a	a	PRON
ejpam-5844	32	7	)	)	PUNCT
ejpam-5844	32	8	abh(b	abh(b	PROPN
ejpam-5844	32	9	)	)	PUNCT
ejpam-5844	32	10	bag	bag	NOUN
ejpam-5844	32	11	(	(	PUNCT
ejpam-5844	32	12	a	a	NOUN
ejpam-5844	32	13	)	)	PUNCT
ejpam-5844	32	14	b2h	b2h	PROPN
ejpam-5844	32	15	(	(	PUNCT
ejpam-5844	32	16	b	b	NOUN
ejpam-5844	32	17	)	)	PUNCT
ejpam-5844	32	18	]	]	PUNCT
ejpam-5844	32	19	,	,	PUNCT
ejpam-5844	32	20	and	and	CCONJ
ejpam-5844	32	21	q2	q2	NOUN
ejpam-5844	32	22	=	=	PUNCT
ejpam-5844	33	1	[	[	PUNCT
ejpam-5844	33	2	g	g	PROPN
ejpam-5844	33	3	(	(	PUNCT
ejpam-5844	33	4	a	a	NOUN
ejpam-5844	33	5	)	)	PUNCT
ejpam-5844	33	6	0	0	NUM
ejpam-5844	33	7	0	0	NUM
ejpam-5844	33	8	h	h	NOUN
ejpam-5844	33	9	(	(	PUNCT
ejpam-5844	33	10	b	b	NOUN
ejpam-5844	33	11	)	)	PUNCT
ejpam-5844	33	12	]	]	PUNCT
ejpam-5844	34	1	[	[	PUNCT
ejpam-5844	34	2	a	a	DET
ejpam-5844	34	3	0	0	NUM
ejpam-5844	34	4	−b	−b	NOUN
ejpam-5844	34	5	0	0	NUM
ejpam-5844	34	6	]	]	PUNCT
ejpam-5844	35	1	[	[	PUNCT
ejpam-5844	35	2	a	a	DET
ejpam-5844	35	3	−b	−b	NOUN
ejpam-5844	35	4	0	0	NUM
ejpam-5844	35	5	0	0	NUM
ejpam-5844	35	6	]	]	PUNCT
ejpam-5844	36	1	=	=	PUNCT
ejpam-5844	36	2	[	[	PUNCT
ejpam-5844	36	3	g	g	PROPN
ejpam-5844	36	4	(	(	PUNCT
ejpam-5844	36	5	a)a2	a)a2	PROPN
ejpam-5844	36	6	−g	−g	NOUN
ejpam-5844	36	7	(	(	PUNCT
ejpam-5844	36	8	a)ab	a)ab	PROPN
ejpam-5844	36	9	−h	−h	VERB
ejpam-5844	36	10	(	(	PUNCT
ejpam-5844	36	11	b)ba	b)ba	PROPN
ejpam-5844	36	12	h	h	NOUN
ejpam-5844	36	13	(	(	PUNCT
ejpam-5844	36	14	b)b2	b)b2	PROPN
ejpam-5844	36	15	]	]	PUNCT
ejpam-5844	36	16	.	.	PUNCT
ejpam-5844	37	1	so	so	ADV
ejpam-5844	37	2	,	,	PUNCT
ejpam-5844	37	3	q1	q1	PROPN
ejpam-5844	37	4	−	−	PROPN
ejpam-5844	37	5	q2	q2	NOUN
ejpam-5844	37	6	=	=	PUNCT
ejpam-5844	37	7	[	[	PUNCT
ejpam-5844	37	8	a2	a2	PROPN
ejpam-5844	37	9	g	g	PROPN
ejpam-5844	37	10	(	(	PUNCT
ejpam-5844	37	11	a)−	a)−	PROPN
ejpam-5844	37	12	g	g	PROPN
ejpam-5844	37	13	(	(	PUNCT
ejpam-5844	37	14	a)a2	a)a2	PROPN
ejpam-5844	37	15	abh(b	abh(b	PROPN
ejpam-5844	37	16	)	)	PUNCT
ejpam-5844	38	1	+	+	CCONJ
ejpam-5844	38	2	g	g	NOUN
ejpam-5844	38	3	(	(	PUNCT
ejpam-5844	38	4	a)ab	a)ab	PROPN
ejpam-5844	38	5	bag	bag	NOUN
ejpam-5844	38	6	(	(	PUNCT
ejpam-5844	38	7	a	a	NOUN
ejpam-5844	38	8	)	)	PUNCT
ejpam-5844	38	9	+	+	NUM
ejpam-5844	38	10	h	h	NOUN
ejpam-5844	38	11	(	(	PUNCT
ejpam-5844	38	12	b)ba	b)ba	PROPN
ejpam-5844	38	13	b2h	b2h	PROPN
ejpam-5844	38	14	(	(	PUNCT
ejpam-5844	38	15	b)−	b)−	PROPN
ejpam-5844	38	16	h	h	NOUN
ejpam-5844	38	17	(	(	PUNCT
ejpam-5844	38	18	b)b2	b)b2	PROPN
ejpam-5844	38	19	]	]	PUNCT
ejpam-5844	38	20	=	=	PUNCT
ejpam-5844	39	1	[	[	PUNCT
ejpam-5844	39	2	0	0	NUM
ejpam-5844	39	3	q	q	NOUN
ejpam-5844	39	4	q∗	q∗	NOUN
ejpam-5844	39	5	0	0	NUM
ejpam-5844	39	6	]	]	PUNCT
ejpam-5844	39	7	,	,	PUNCT
ejpam-5844	39	8	where	where	SCONJ
ejpam-5844	39	9	q	q	NOUN
ejpam-5844	39	10	=	=	SYM
ejpam-5844	39	11	abh(b	abh(b	PROPN
ejpam-5844	39	12	)	)	PUNCT
ejpam-5844	40	1	+	+	CCONJ
ejpam-5844	40	2	g	g	PROPN
ejpam-5844	40	3	(	(	PUNCT
ejpam-5844	40	4	a)ab	a)ab	PROPN
ejpam-5844	40	5	.	.	PUNCT
ejpam-5844	41	1	now	now	ADV
ejpam-5844	41	2	,	,	PUNCT
ejpam-5844	41	3	sj	sj	INTJ
ejpam-5844	41	4	(	(	PUNCT
ejpam-5844	41	5	(	(	PUNCT
ejpam-5844	41	6	abh(b	abh(b	NOUN
ejpam-5844	41	7	)	)	PUNCT
ejpam-5844	41	8	+	+	CCONJ
ejpam-5844	41	9	g	g	PROPN
ejpam-5844	41	10	(	(	PUNCT
ejpam-5844	41	11	a)ab)⊕	a)ab)⊕	PROPN
ejpam-5844	41	12	(	(	PUNCT
ejpam-5844	41	13	abh(b	abh(b	PROPN
ejpam-5844	41	14	)	)	PUNCT
ejpam-5844	41	15	+	+	CCONJ
ejpam-5844	41	16	g	g	PROPN
ejpam-5844	41	17	(	(	PUNCT
ejpam-5844	41	18	a)ab	a)ab	PROPN
ejpam-5844	41	19	)	)	PUNCT
ejpam-5844	41	20	)	)	PUNCT
ejpam-5844	42	1	=	=	PUNCT
ejpam-5844	42	2	sj((abh(b	sj((abh(b	X
ejpam-5844	42	3	)	)	PUNCT
ejpam-5844	43	1	+	+	CCONJ
ejpam-5844	43	2	g	g	PROPN
ejpam-5844	43	3	(	(	PUNCT
ejpam-5844	43	4	a)ab)⊕	a)ab)⊕	PROPN
ejpam-5844	43	5	(	(	PUNCT
ejpam-5844	43	6	bag	bag	NOUN
ejpam-5844	43	7	(	(	PUNCT
ejpam-5844	43	8	a	a	NOUN
ejpam-5844	43	9	)	)	PUNCT
ejpam-5844	43	10	+	+	NUM
ejpam-5844	43	11	h	h	NOUN
ejpam-5844	43	12	(	(	PUNCT
ejpam-5844	43	13	b)ba	b)ba	PROPN
ejpam-5844	43	14	)	)	PUNCT
ejpam-5844	43	15	)	)	PUNCT
ejpam-5844	44	1	=	=	PUNCT
ejpam-5844	44	2	sj	sj	INTJ
ejpam-5844	44	3	(	(	PUNCT
ejpam-5844	44	4	q⊕q∗	q⊕q∗	PROPN
ejpam-5844	44	5	)	)	PUNCT
ejpam-5844	44	6	=	=	PUNCT
ejpam-5844	44	7	sj	sj	INTJ
ejpam-5844	44	8	(	(	PUNCT
ejpam-5844	44	9	[	[	PUNCT
ejpam-5844	44	10	0	0	NUM
ejpam-5844	44	11	q	q	NOUN
ejpam-5844	44	12	q∗	q∗	NOUN
ejpam-5844	44	13	0	0	NUM
ejpam-5844	44	14	]	]	PUNCT
ejpam-5844	44	15	)	)	PUNCT
ejpam-5844	45	1	=	=	SYM
ejpam-5844	45	2	sj	sj	INTJ
ejpam-5844	45	3	(	(	PUNCT
ejpam-5844	45	4	q1	q1	PROPN
ejpam-5844	45	5	−q2	−q2	PROPN
ejpam-5844	45	6	)	)	PUNCT
ejpam-5844	45	7	.	.	PUNCT
ejpam-5844	46	1	(	(	PUNCT
ejpam-5844	46	2	4	4	X
ejpam-5844	46	3	)	)	PUNCT
ejpam-5844	46	4	using	use	VERB
ejpam-5844	46	5	lemma	lemma	PROPN
ejpam-5844	46	6	1	1	NUM
ejpam-5844	46	7	and	and	CCONJ
ejpam-5844	46	8	the	the	DET
ejpam-5844	46	9	fact	fact	NOUN
ejpam-5844	46	10	that	that	SCONJ
ejpam-5844	46	11	[	[	PUNCT
ejpam-5844	46	12	a2	a2	PROPN
ejpam-5844	46	13	ab	ab	PROPN
ejpam-5844	46	14	ba	ba	PROPN
ejpam-5844	46	15	b2	b2	PROPN
ejpam-5844	46	16	]	]	PUNCT
ejpam-5844	46	17	and	and	CCONJ
ejpam-5844	46	18	[	[	PUNCT
ejpam-5844	46	19	a2	a2	PROPN
ejpam-5844	46	20	−ab	−ab	NUM
ejpam-5844	46	21	−ba	−ba	PROPN
ejpam-5844	46	22	b2	b2	PROPN
ejpam-5844	46	23	]	]	PUNCT
ejpam-5844	46	24	are	be	AUX
ejpam-5844	46	25	unitarily	unitarily	ADV
ejpam-5844	46	26	equivalent	equivalent	ADJ
ejpam-5844	46	27	via	via	ADP
ejpam-5844	46	28	u=	u=	PROPN
ejpam-5844	46	29	[	[	PUNCT
ejpam-5844	46	30	i	i	NOUN
ejpam-5844	46	31	0	0	NUM
ejpam-5844	46	32	0	0	NUM
ejpam-5844	47	1	−i	−i	NOUN
ejpam-5844	47	2	]	]	PUNCT
ejpam-5844	47	3	yield	yield	VERB
ejpam-5844	47	4	that	that	SCONJ
ejpam-5844	47	5	a.	a.	PROPN
ejpam-5844	47	6	al	al	PROPN
ejpam-5844	47	7	-	-	PUNCT
ejpam-5844	47	8	natoor	natoor	NOUN
ejpam-5844	47	9	,	,	PUNCT
ejpam-5844	47	10	r.	r.	PROPN
ejpam-5844	47	11	al	al	PROPN
ejpam-5844	47	12	-	-	PUNCT
ejpam-5844	47	13	smadi	smadi	PROPN
ejpam-5844	47	14	,	,	PUNCT
ejpam-5844	47	15	a.	a.	NOUN
ejpam-5844	47	16	burqan	burqan	PROPN
ejpam-5844	47	17	/	/	SYM
ejpam-5844	47	18	eur	eur	PROPN
ejpam-5844	47	19	.	.	PUNCT
ejpam-5844	48	1	j.	j.	PROPN
ejpam-5844	48	2	pure	pure	PROPN
ejpam-5844	48	3	appl	appl	PROPN
ejpam-5844	48	4	.	.	PROPN
ejpam-5844	48	5	math	math	PROPN
ejpam-5844	48	6	,	,	PUNCT
ejpam-5844	48	7	18	18	NUM
ejpam-5844	48	8	(	(	PUNCT
ejpam-5844	48	9	2	2	NUM
ejpam-5844	48	10	)	)	PUNCT
ejpam-5844	48	11	(	(	PUNCT
ejpam-5844	48	12	2025	2025	NUM
ejpam-5844	48	13	)	)	PUNCT
ejpam-5844	48	14	,	,	PUNCT
ejpam-5844	48	15	5844	5844	NUM
ejpam-5844	48	16	3	3	NUM
ejpam-5844	48	17	of	of	ADP
ejpam-5844	48	18	10	10	NUM
ejpam-5844	48	19	sj	sj	NOUN
ejpam-5844	48	20	(	(	PUNCT
ejpam-5844	48	21	(	(	PUNCT
ejpam-5844	48	22	q1	q1	PROPN
ejpam-5844	48	23	−q2)⊕	−q2)⊕	NOUN
ejpam-5844	48	24	0	0	NUM
ejpam-5844	48	25	)	)	PUNCT
ejpam-5844	49	1	=	=	PRON
ejpam-5844	49	2	sj	sj	ADP
ejpam-5844	49	3			PROPN
ejpam-5844	49	4	[	[	PUNCT
ejpam-5844	49	5	a	a	DET
ejpam-5844	49	6	0	0	NUM
ejpam-5844	49	7	b	b	NOUN
ejpam-5844	49	8	0	0	NUM
ejpam-5844	49	9	]	]	PUNCT
ejpam-5844	49	10	[	[	PUNCT
ejpam-5844	49	11	a	a	DET
ejpam-5844	49	12	b	b	NOUN
ejpam-5844	49	13	0	0	NUM
ejpam-5844	49	14	0	0	NUM
ejpam-5844	49	15	]	]	PUNCT
ejpam-5844	50	1	[	[	PUNCT
ejpam-5844	50	2	g	g	NOUN
ejpam-5844	50	3	(	(	PUNCT
ejpam-5844	50	4	a	a	NOUN
ejpam-5844	50	5	)	)	PUNCT
ejpam-5844	50	6	0	0	NUM
ejpam-5844	50	7	0	0	NUM
ejpam-5844	50	8	h	h	NOUN
ejpam-5844	50	9	(	(	PUNCT
ejpam-5844	50	10	b	b	NOUN
ejpam-5844	50	11	)	)	PUNCT
ejpam-5844	50	12	]	]	PUNCT
ejpam-5844	50	13	−	−	PROPN
ejpam-5844	50	14	[	[	PUNCT
ejpam-5844	50	15	g	g	PROPN
ejpam-5844	50	16	(	(	PUNCT
ejpam-5844	50	17	a	a	NOUN
ejpam-5844	50	18	)	)	PUNCT
ejpam-5844	50	19	0	0	NUM
ejpam-5844	50	20	0	0	NUM
ejpam-5844	50	21	h	h	NOUN
ejpam-5844	50	22	(	(	PUNCT
ejpam-5844	50	23	b	b	NOUN
ejpam-5844	50	24	)	)	PUNCT
ejpam-5844	50	25	]	]	PUNCT
ejpam-5844	51	1	[	[	PUNCT
ejpam-5844	51	2	a	a	DET
ejpam-5844	51	3	0	0	NUM
ejpam-5844	51	4	−b	−b	NOUN
ejpam-5844	51	5	0	0	NUM
ejpam-5844	51	6	]	]	PUNCT
ejpam-5844	52	1	[	[	PUNCT
ejpam-5844	52	2	a	a	DET
ejpam-5844	52	3	−b	−b	NOUN
ejpam-5844	52	4	0	0	NUM
ejpam-5844	52	5	0	0	NUM
ejpam-5844	52	6	]	]	PUNCT
ejpam-5844	52	7			NOUN
ejpam-5844	52	8	=	=	PUNCT
ejpam-5844	52	9	sj	sj	PROPN
ejpam-5844	52	10			PROPN
ejpam-5844	52	11			PROPN
ejpam-5844	52	12	[	[	PUNCT
ejpam-5844	52	13	a2	a2	PROPN
ejpam-5844	52	14	ab	ab	PROPN
ejpam-5844	52	15	ba	ba	PROPN
ejpam-5844	52	16	b2	b2	PROPN
ejpam-5844	52	17	]	]	PUNCT
ejpam-5844	52	18	[	[	PUNCT
ejpam-5844	52	19	g	g	NOUN
ejpam-5844	52	20	(	(	PUNCT
ejpam-5844	52	21	a	a	NOUN
ejpam-5844	52	22	)	)	PUNCT
ejpam-5844	52	23	0	0	NUM
ejpam-5844	52	24	0	0	NUM
ejpam-5844	52	25	h	h	NOUN
ejpam-5844	52	26	(	(	PUNCT
ejpam-5844	52	27	b	b	NOUN
ejpam-5844	52	28	)	)	PUNCT
ejpam-5844	52	29	]	]	PUNCT
ejpam-5844	52	30	−	−	PROPN
ejpam-5844	53	1	[	[	PUNCT
ejpam-5844	53	2	g	g	PROPN
ejpam-5844	53	3	(	(	PUNCT
ejpam-5844	53	4	a	a	NOUN
ejpam-5844	53	5	)	)	PUNCT
ejpam-5844	53	6	0	0	NUM
ejpam-5844	53	7	0	0	NUM
ejpam-5844	53	8	h	h	NOUN
ejpam-5844	53	9	(	(	PUNCT
ejpam-5844	53	10	b	b	NOUN
ejpam-5844	53	11	)	)	PUNCT
ejpam-5844	53	12	]	]	PUNCT
ejpam-5844	53	13	[	[	PUNCT
ejpam-5844	53	14	a2	a2	PROPN
ejpam-5844	53	15	−ab	−ab	NUM
ejpam-5844	53	16	−ba	−ba	PROPN
ejpam-5844	53	17	b2	b2	PROPN
ejpam-5844	53	18	]	]	PUNCT
ejpam-5844	53	19	⊕	⊕	X
ejpam-5844	53	20	0	0	NUM
ejpam-5844	53	21			NOUN
ejpam-5844	53	22	≤	≤	ADJ
ejpam-5844	53	23	max	max	PROPN
ejpam-5844	53	24	(	(	PUNCT
ejpam-5844	53	25	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5844	53	26	[	[	PUNCT
ejpam-5844	53	27	a2	a2	PROPN
ejpam-5844	53	28	ab	ab	PROPN
ejpam-5844	53	29	ba	ba	PROPN
ejpam-5844	53	30	b2	b2	PROPN
ejpam-5844	53	31	]	]	PUNCT
ejpam-5844	53	32	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	53	33	,	,	PUNCT
ejpam-5844	53	34	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5844	53	35	[	[	PUNCT
ejpam-5844	53	36	a2	a2	PROPN
ejpam-5844	53	37	−ab	−ab	PROPN
ejpam-5844	53	38	−ba	−ba	PROPN
ejpam-5844	53	39	b2	b2	NOUN
ejpam-5844	53	40	]	]	PUNCT
ejpam-5844	53	41	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	53	42	)	)	PUNCT
ejpam-5844	53	43	×sj	×sj	NOUN
ejpam-5844	53	44	(	(	PUNCT
ejpam-5844	53	45	[	[	PUNCT
ejpam-5844	53	46	g	g	NOUN
ejpam-5844	53	47	(	(	PUNCT
ejpam-5844	53	48	a	a	NOUN
ejpam-5844	53	49	)	)	PUNCT
ejpam-5844	53	50	0	0	NUM
ejpam-5844	53	51	0	0	NUM
ejpam-5844	53	52	h	h	NOUN
ejpam-5844	53	53	(	(	PUNCT
ejpam-5844	53	54	b	b	NOUN
ejpam-5844	53	55	)	)	PUNCT
ejpam-5844	53	56	]	]	PUNCT
ejpam-5844	54	1	⊕	⊕	PROPN
ejpam-5844	54	2	[	[	PUNCT
ejpam-5844	54	3	g	g	PROPN
ejpam-5844	54	4	(	(	PUNCT
ejpam-5844	54	5	a	a	NOUN
ejpam-5844	54	6	)	)	PUNCT
ejpam-5844	54	7	0	0	NUM
ejpam-5844	54	8	0	0	NUM
ejpam-5844	54	9	h	h	NOUN
ejpam-5844	54	10	(	(	PUNCT
ejpam-5844	54	11	b	b	NOUN
ejpam-5844	54	12	)	)	PUNCT
ejpam-5844	54	13	]	]	PUNCT
ejpam-5844	54	14	)	)	PUNCT
ejpam-5844	54	15	=	=	SYM
ejpam-5844	54	16	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5844	54	17	[	[	PUNCT
ejpam-5844	54	18	a2	a2	PROPN
ejpam-5844	54	19	ab	ab	PROPN
ejpam-5844	54	20	ba	ba	PROPN
ejpam-5844	54	21	b2	b2	PROPN
ejpam-5844	54	22	]	]	PUNCT
ejpam-5844	54	23	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	54	24	sj	sj	INTJ
ejpam-5844	54	25	(	(	PUNCT
ejpam-5844	54	26	[	[	PUNCT
ejpam-5844	54	27	g	g	NOUN
ejpam-5844	54	28	(	(	PUNCT
ejpam-5844	54	29	a	a	NOUN
ejpam-5844	54	30	)	)	PUNCT
ejpam-5844	54	31	0	0	NUM
ejpam-5844	54	32	0	0	NUM
ejpam-5844	54	33	h	h	NOUN
ejpam-5844	54	34	(	(	PUNCT
ejpam-5844	54	35	b	b	NOUN
ejpam-5844	54	36	)	)	PUNCT
ejpam-5844	54	37	]	]	PUNCT
ejpam-5844	55	1	⊕	⊕	PROPN
ejpam-5844	55	2	[	[	PUNCT
ejpam-5844	55	3	g	g	PROPN
ejpam-5844	55	4	(	(	PUNCT
ejpam-5844	55	5	a	a	NOUN
ejpam-5844	55	6	)	)	PUNCT
ejpam-5844	55	7	0	0	NUM
ejpam-5844	55	8	0	0	NUM
ejpam-5844	55	9	h	h	NOUN
ejpam-5844	55	10	(	(	PUNCT
ejpam-5844	55	11	b	b	NOUN
ejpam-5844	55	12	)	)	PUNCT
ejpam-5844	55	13	]	]	PUNCT
ejpam-5844	55	14	)	)	PUNCT
ejpam-5844	55	15	=	=	SYM
ejpam-5844	55	16	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5844	55	17	[	[	PUNCT
ejpam-5844	55	18	a2	a2	PROPN
ejpam-5844	55	19	ab	ab	PROPN
ejpam-5844	55	20	ba	ba	PROPN
ejpam-5844	55	21	b2	b2	PROPN
ejpam-5844	55	22	]	]	PUNCT
ejpam-5844	55	23	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	55	24	sj	sj	INTJ
ejpam-5844	55	25	(	(	PUNCT
ejpam-5844	55	26	(	(	PUNCT
ejpam-5844	55	27	g	g	NOUN
ejpam-5844	55	28	(	(	PUNCT
ejpam-5844	55	29	a)⊕	a)⊕	INTJ
ejpam-5844	55	30	h	h	NOUN
ejpam-5844	55	31	(	(	PUNCT
ejpam-5844	55	32	b))⊕	b))⊕	PROPN
ejpam-5844	55	33	(	(	PUNCT
ejpam-5844	55	34	g	g	NOUN
ejpam-5844	55	35	(	(	PUNCT
ejpam-5844	55	36	a)⊕	a)⊕	INTJ
ejpam-5844	55	37	h	h	NOUN
ejpam-5844	55	38	(	(	PUNCT
ejpam-5844	55	39	b	b	NOUN
ejpam-5844	55	40	)	)	PUNCT
ejpam-5844	55	41	)	)	PUNCT
ejpam-5844	55	42	)	)	PUNCT
ejpam-5844	55	43	.	.	PUNCT
ejpam-5844	56	1	now	now	ADV
ejpam-5844	56	2	,	,	PUNCT
ejpam-5844	56	3	by	by	ADP
ejpam-5844	56	4	using	use	VERB
ejpam-5844	56	5	the	the	DET
ejpam-5844	56	6	fact	fact	NOUN
ejpam-5844	56	7	that	that	SCONJ
ejpam-5844	56	8	∥t	∥t	ADJ
ejpam-5844	56	9	∗t∥	∗t∥	X
ejpam-5844	56	10	=	=	SYM
ejpam-5844	56	11	∥tt	∥tt	NOUN
ejpam-5844	56	12	∗∥	∗∥	PUNCT
ejpam-5844	56	13	for	for	ADP
ejpam-5844	56	14	any	any	DET
ejpam-5844	56	15	t	t	PROPN
ejpam-5844	56	16	∈	∈	PROPN
ejpam-5844	56	17	mn	mn	PROPN
ejpam-5844	56	18	(	(	PUNCT
ejpam-5844	56	19	c	c	PROPN
ejpam-5844	56	20	)	)	PUNCT
ejpam-5844	56	21	,	,	PUNCT
ejpam-5844	56	22	we	we	PRON
ejpam-5844	56	23	have∥∥∥∥	have∥∥∥∥	VERB
ejpam-5844	56	24	[	[	PUNCT
ejpam-5844	56	25	a2	a2	PROPN
ejpam-5844	56	26	ab	ab	PROPN
ejpam-5844	56	27	ba	ba	PROPN
ejpam-5844	56	28	b2	b2	PROPN
ejpam-5844	56	29	]	]	PUNCT
ejpam-5844	56	30	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5844	56	31	=	=	SYM
ejpam-5844	56	32	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5844	56	33	[	[	PUNCT
ejpam-5844	56	34	a	a	DET
ejpam-5844	56	35	0	0	NUM
ejpam-5844	56	36	b	b	NOUN
ejpam-5844	56	37	0	0	NUM
ejpam-5844	56	38	]	]	PUNCT
ejpam-5844	57	1	[	[	PUNCT
ejpam-5844	57	2	a	a	DET
ejpam-5844	57	3	b	b	NOUN
ejpam-5844	57	4	0	0	NUM
ejpam-5844	57	5	0	0	NUM
ejpam-5844	57	6	]	]	SYM
ejpam-5844	57	7	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	57	8	=	=	SYM
ejpam-5844	57	9	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5844	57	10	[	[	PUNCT
ejpam-5844	57	11	a	a	DET
ejpam-5844	57	12	b	b	NOUN
ejpam-5844	57	13	0	0	NUM
ejpam-5844	57	14	0	0	NUM
ejpam-5844	57	15	]	]	PUNCT
ejpam-5844	57	16	[	[	PUNCT
ejpam-5844	57	17	a	a	PRON
ejpam-5844	57	18	0	0	NUM
ejpam-5844	57	19	b	b	NOUN
ejpam-5844	57	20	0	0	NUM
ejpam-5844	57	21	]	]	SYM
ejpam-5844	57	22	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	57	23	=	=	SYM
ejpam-5844	57	24	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5844	57	25	[	[	SYM
ejpam-5844	57	26	a2	a2	NOUN
ejpam-5844	57	27	+	+	NOUN
ejpam-5844	57	28	b2	b2	NOUN
ejpam-5844	57	29	0	0	NUM
ejpam-5844	57	30	0	0	NUM
ejpam-5844	57	31	0	0	NUM
ejpam-5844	57	32	]	]	SYM
ejpam-5844	57	33	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	57	34	=	=	SYM
ejpam-5844	58	1	∥∥a2	∥∥a2	PROPN
ejpam-5844	58	2	+	+	ADJ
ejpam-5844	58	3	b2	b2	NOUN
ejpam-5844	58	4	∥∥	∥∥	X
ejpam-5844	58	5	.	.	PUNCT
ejpam-5844	59	1	so	so	ADV
ejpam-5844	59	2	,	,	PUNCT
ejpam-5844	59	3	sj	sj	INTJ
ejpam-5844	59	4	(	(	PUNCT
ejpam-5844	59	5	(	(	PUNCT
ejpam-5844	59	6	abh(b	abh(b	NOUN
ejpam-5844	59	7	)	)	PUNCT
ejpam-5844	60	1	+	+	CCONJ
ejpam-5844	60	2	g	g	PROPN
ejpam-5844	60	3	(	(	PUNCT
ejpam-5844	60	4	a)ab)⊕	a)ab)⊕	PROPN
ejpam-5844	60	5	(	(	PUNCT
ejpam-5844	60	6	abh(b	abh(b	PROPN
ejpam-5844	60	7	)	)	PUNCT
ejpam-5844	61	1	+	+	CCONJ
ejpam-5844	61	2	g	g	PROPN
ejpam-5844	61	3	(	(	PUNCT
ejpam-5844	61	4	a)ab)⊕	a)ab)⊕	PROPN
ejpam-5844	61	5	0	0	NUM
ejpam-5844	61	6	)	)	PUNCT
ejpam-5844	61	7	≤	≤	PUNCT
ejpam-5844	62	1	∥∥a2	∥∥a2	PROPN
ejpam-5844	62	2	+	+	NOUN
ejpam-5844	62	3	b2	b2	NOUN
ejpam-5844	62	4	∥∥	∥∥	X
ejpam-5844	62	5	sj	sj	INTJ
ejpam-5844	62	6	(	(	PUNCT
ejpam-5844	62	7	(	(	PUNCT
ejpam-5844	62	8	g	g	NOUN
ejpam-5844	62	9	(	(	PUNCT
ejpam-5844	62	10	a)⊕	a)⊕	INTJ
ejpam-5844	62	11	h	h	NOUN
ejpam-5844	62	12	(	(	PUNCT
ejpam-5844	62	13	b))⊕	b))⊕	PROPN
ejpam-5844	62	14	(	(	PUNCT
ejpam-5844	62	15	g	g	NOUN
ejpam-5844	62	16	(	(	PUNCT
ejpam-5844	62	17	a)⊕	a)⊕	INTJ
ejpam-5844	62	18	h	h	NOUN
ejpam-5844	62	19	(	(	PUNCT
ejpam-5844	62	20	b	b	NOUN
ejpam-5844	62	21	)	)	PUNCT
ejpam-5844	62	22	)	)	PUNCT
ejpam-5844	62	23	)	)	PUNCT
ejpam-5844	62	24	.	.	PUNCT
ejpam-5844	63	1	(	(	PUNCT
ejpam-5844	63	2	5	5	X
ejpam-5844	63	3	)	)	PUNCT
ejpam-5844	63	4	now	now	ADV
ejpam-5844	63	5	,	,	PUNCT
ejpam-5844	63	6	the	the	DET
ejpam-5844	63	7	desired	desire	VERB
ejpam-5844	63	8	result	result	NOUN
ejpam-5844	63	9	follows	follow	VERB
ejpam-5844	63	10	by	by	ADP
ejpam-5844	63	11	inequalities	inequality	NOUN
ejpam-5844	63	12	(	(	PUNCT
ejpam-5844	63	13	3	3	NUM
ejpam-5844	63	14	)	)	PUNCT
ejpam-5844	63	15	,	,	PUNCT
ejpam-5844	63	16	(	(	PUNCT
ejpam-5844	63	17	4	4	NUM
ejpam-5844	63	18	)	)	PUNCT
ejpam-5844	63	19	,	,	PUNCT
ejpam-5844	63	20	and	and	CCONJ
ejpam-5844	63	21	(	(	PUNCT
ejpam-5844	63	22	5	5	NUM
ejpam-5844	63	23	)	)	PUNCT
ejpam-5844	63	24	.	.	PUNCT
ejpam-5844	64	1	lemma	lemma	PROPN
ejpam-5844	64	2	2	2	NUM
ejpam-5844	64	3	.	.	PUNCT
ejpam-5844	65	1	[	[	X
ejpam-5844	65	2	8]let	8]let	NOUN
ejpam-5844	65	3	a	a	DET
ejpam-5844	65	4	,	,	PUNCT
ejpam-5844	65	5	b	b	NOUN
ejpam-5844	65	6	,	,	PUNCT
ejpam-5844	65	7	y	y	PROPN
ejpam-5844	65	8	∈	∈	PROPN
ejpam-5844	65	9	mn	mn	PROPN
ejpam-5844	65	10	(	(	PUNCT
ejpam-5844	65	11	c	c	X
ejpam-5844	65	12	)	)	PUNCT
ejpam-5844	65	13	be	be	AUX
ejpam-5844	65	14	such	such	ADJ
ejpam-5844	65	15	that	that	SCONJ
ejpam-5844	65	16	a	a	PRON
ejpam-5844	65	17	and	and	CCONJ
ejpam-5844	65	18	b	b	NOUN
ejpam-5844	65	19	are	be	AUX
ejpam-5844	65	20	positive	positive	ADJ
ejpam-5844	65	21	semidefinite	semidefinite	NOUN
ejpam-5844	65	22	.	.	PUNCT
ejpam-5844	66	1	then	then	ADV
ejpam-5844	66	2	for	for	ADP
ejpam-5844	66	3	j	j	PROPN
ejpam-5844	66	4	=	=	SYM
ejpam-5844	66	5	1	1	NUM
ejpam-5844	66	6	,	,	PUNCT
ejpam-5844	66	7	...	...	PUNCT
ejpam-5844	66	8	,	,	PUNCT
ejpam-5844	66	9	2n	2n	NUM
ejpam-5844	66	10	,	,	PUNCT
ejpam-5844	66	11	we	we	PRON
ejpam-5844	66	12	have	have	VERB
ejpam-5844	66	13	sj	sj	INTJ
ejpam-5844	66	14	(	(	PUNCT
ejpam-5844	66	15	(	(	PUNCT
ejpam-5844	66	16	ay	ay	INTJ
ejpam-5844	66	17	−	−	PROPN
ejpam-5844	66	18	y	y	PROPN
ejpam-5844	66	19	b)⊕	b)⊕	ADV
ejpam-5844	66	20	0	0	NUM
ejpam-5844	66	21	)	)	PUNCT
ejpam-5844	66	22	≤	≤	PUNCT
ejpam-5844	67	1	∥y	∥y	ADV
ejpam-5844	67	2	∥	∥	PUNCT
ejpam-5844	67	3	sj	sj	X
ejpam-5844	67	4	(	(	PUNCT
ejpam-5844	67	5	a⊕b	a⊕b	PROPN
ejpam-5844	67	6	)	)	PUNCT
ejpam-5844	67	7	.	.	PUNCT
ejpam-5844	68	1	a.	a.	PROPN
ejpam-5844	68	2	al	al	PROPN
ejpam-5844	68	3	-	-	PUNCT
ejpam-5844	68	4	natoor	natoor	NOUN
ejpam-5844	68	5	,	,	PUNCT
ejpam-5844	68	6	r.	r.	PROPN
ejpam-5844	68	7	al	al	PROPN
ejpam-5844	68	8	-	-	PUNCT
ejpam-5844	68	9	smadi	smadi	PROPN
ejpam-5844	68	10	,	,	PUNCT
ejpam-5844	68	11	a.	a.	NOUN
ejpam-5844	68	12	burqan	burqan	PROPN
ejpam-5844	68	13	/	/	SYM
ejpam-5844	68	14	eur	eur	PROPN
ejpam-5844	68	15	.	.	PUNCT
ejpam-5844	69	1	j.	j.	PROPN
ejpam-5844	69	2	pure	pure	PROPN
ejpam-5844	69	3	appl	appl	PROPN
ejpam-5844	69	4	.	.	PROPN
ejpam-5844	69	5	math	math	PROPN
ejpam-5844	69	6	,	,	PUNCT
ejpam-5844	69	7	18	18	NUM
ejpam-5844	69	8	(	(	PUNCT
ejpam-5844	69	9	2	2	NUM
ejpam-5844	69	10	)	)	PUNCT
ejpam-5844	69	11	(	(	PUNCT
ejpam-5844	69	12	2025	2025	NUM
ejpam-5844	69	13	)	)	PUNCT
ejpam-5844	69	14	,	,	PUNCT
ejpam-5844	69	15	5844	5844	NUM
ejpam-5844	69	16	4	4	NUM
ejpam-5844	69	17	of	of	ADP
ejpam-5844	69	18	10	10	NUM
ejpam-5844	69	19	theorem	theorem	NOUN
ejpam-5844	69	20	2	2	NUM
ejpam-5844	69	21	.	.	PUNCT
ejpam-5844	70	1	let	let	VERB
ejpam-5844	70	2	a	a	DET
ejpam-5844	70	3	,	,	PUNCT
ejpam-5844	70	4	b	b	PROPN
ejpam-5844	70	5	∈	∈	PROPN
ejpam-5844	70	6	mn	mn	PROPN
ejpam-5844	70	7	(	(	PUNCT
ejpam-5844	70	8	c	c	AUX
ejpam-5844	70	9	)	)	PUNCT
ejpam-5844	70	10	be	be	AUX
ejpam-5844	70	11	positive	positive	ADJ
ejpam-5844	70	12	semidefinite	semidefinite	NOUN
ejpam-5844	70	13	and	and	CCONJ
ejpam-5844	70	14	let	let	VERB
ejpam-5844	70	15	g(t	g(t	PROPN
ejpam-5844	70	16	)	)	PUNCT
ejpam-5844	70	17	,	,	PUNCT
ejpam-5844	70	18	h(t	h(t	PROPN
ejpam-5844	70	19	)	)	PUNCT
ejpam-5844	71	1	be	be	AUX
ejpam-5844	71	2	real	real	ADJ
ejpam-5844	71	3	polynomials	polynomial	NOUN
ejpam-5844	71	4	.	.	PUNCT
ejpam-5844	72	1	then	then	ADV
ejpam-5844	72	2	for	for	ADP
ejpam-5844	72	3	j	j	PROPN
ejpam-5844	72	4	=	=	SYM
ejpam-5844	72	5	1	1	NUM
ejpam-5844	72	6	,	,	PUNCT
ejpam-5844	72	7	...	...	PUNCT
ejpam-5844	72	8	,	,	PUNCT
ejpam-5844	72	9	2n	2n	NUM
ejpam-5844	72	10	,	,	PUNCT
ejpam-5844	72	11	we	we	PRON
ejpam-5844	72	12	have	have	VERB
ejpam-5844	72	13	sj	sj	INTJ
ejpam-5844	72	14	(	(	PUNCT
ejpam-5844	72	15	abh(b	abh(b	PROPN
ejpam-5844	72	16	)	)	PUNCT
ejpam-5844	73	1	+	+	CCONJ
ejpam-5844	73	2	g	g	PROPN
ejpam-5844	73	3	(	(	PUNCT
ejpam-5844	73	4	a)ab	a)ab	PROPN
ejpam-5844	73	5	)	)	PUNCT
ejpam-5844	73	6	≤	≤	NUM
ejpam-5844	73	7	max	max	NOUN
ejpam-5844	73	8	(	(	PUNCT
ejpam-5844	73	9	∥g(a)∥	∥g(a)∥	PROPN
ejpam-5844	73	10	,	,	PUNCT
ejpam-5844	73	11	∥h(b)∥	∥h(b)∥	PROPN
ejpam-5844	73	12	)	)	PUNCT
ejpam-5844	74	1	sj	sj	INTJ
ejpam-5844	74	2	(	(	PUNCT
ejpam-5844	74	3	[	[	PUNCT
ejpam-5844	74	4	a2	a2	PROPN
ejpam-5844	74	5	ab	ab	PROPN
ejpam-5844	74	6	ba	ba	PROPN
ejpam-5844	74	7	b2	b2	PROPN
ejpam-5844	74	8	]	]	PUNCT
ejpam-5844	74	9	)	)	PUNCT
ejpam-5844	74	10	.	.	PUNCT
ejpam-5844	75	1	(	(	PUNCT
ejpam-5844	75	2	6	6	X
ejpam-5844	75	3	)	)	PUNCT
ejpam-5844	75	4	proof	proof	NOUN
ejpam-5844	75	5	.	.	PUNCT
ejpam-5844	76	1	let	let	VERB
ejpam-5844	76	2	q1	q1	PROPN
ejpam-5844	76	3	,	,	PUNCT
ejpam-5844	76	4	q2	q2	NOUN
ejpam-5844	76	5	,	,	PUNCT
ejpam-5844	76	6	q	q	X
ejpam-5844	76	7	,	,	PUNCT
ejpam-5844	76	8	and	and	CCONJ
ejpam-5844	76	9	u	u	NOUN
ejpam-5844	76	10	be	be	VERB
ejpam-5844	76	11	as	as	ADP
ejpam-5844	76	12	in	in	ADP
ejpam-5844	76	13	the	the	DET
ejpam-5844	76	14	proof	proof	NOUN
ejpam-5844	76	15	of	of	ADP
ejpam-5844	76	16	theorem	theorem	NOUN
ejpam-5844	76	17	1	1	NUM
ejpam-5844	76	18	.	.	PUNCT
ejpam-5844	76	19	then	then	ADV
ejpam-5844	76	20	by	by	ADP
ejpam-5844	76	21	equation	equation	NOUN
ejpam-5844	76	22	(	(	PUNCT
ejpam-5844	76	23	4	4	NUM
ejpam-5844	76	24	)	)	PUNCT
ejpam-5844	76	25	,	,	PUNCT
ejpam-5844	76	26	we	we	PRON
ejpam-5844	76	27	have	have	VERB
ejpam-5844	76	28	sj	sj	INTJ
ejpam-5844	76	29	(	(	PUNCT
ejpam-5844	76	30	(	(	PUNCT
ejpam-5844	76	31	abh(b	abh(b	NOUN
ejpam-5844	76	32	)	)	PUNCT
ejpam-5844	77	1	+	+	CCONJ
ejpam-5844	77	2	g	g	PROPN
ejpam-5844	77	3	(	(	PUNCT
ejpam-5844	77	4	a)ab)⊕	a)ab)⊕	PROPN
ejpam-5844	77	5	(	(	PUNCT
ejpam-5844	77	6	abh(b	abh(b	PROPN
ejpam-5844	77	7	)	)	PUNCT
ejpam-5844	77	8	+	+	CCONJ
ejpam-5844	77	9	g	g	PROPN
ejpam-5844	77	10	(	(	PUNCT
ejpam-5844	77	11	a)ab	a)ab	PROPN
ejpam-5844	77	12	)	)	PUNCT
ejpam-5844	77	13	)	)	PUNCT
ejpam-5844	78	1	=	=	PUNCT
ejpam-5844	78	2	sj	sj	INTJ
ejpam-5844	78	3	(	(	PUNCT
ejpam-5844	78	4	q1	q1	PROPN
ejpam-5844	78	5	−q2	−q2	PROPN
ejpam-5844	78	6	)	)	PUNCT
ejpam-5844	78	7	≤	≤	NUM
ejpam-5844	78	8	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5844	78	9	[	[	PUNCT
ejpam-5844	78	10	g(a	g(a	PROPN
ejpam-5844	78	11	)	)	PUNCT
ejpam-5844	78	12	0	0	NUM
ejpam-5844	78	13	0	0	NUM
ejpam-5844	78	14	h(b	h(b	PROPN
ejpam-5844	78	15	)	)	PUNCT
ejpam-5844	78	16	]	]	PUNCT
ejpam-5844	78	17	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5844	78	18	sj	sj	INTJ
ejpam-5844	78	19	(	(	PUNCT
ejpam-5844	78	20	[	[	PUNCT
ejpam-5844	78	21	a2	a2	PROPN
ejpam-5844	78	22	ab	ab	PROPN
ejpam-5844	78	23	ba	ba	PROPN
ejpam-5844	78	24	b2	b2	PROPN
ejpam-5844	78	25	]	]	PUNCT
ejpam-5844	78	26	⊕	⊕	PROPN
ejpam-5844	78	27	[	[	PUNCT
ejpam-5844	78	28	a2	a2	PROPN
ejpam-5844	78	29	−ab	−ab	PROPN
ejpam-5844	78	30	−ba	−ba	PROPN
ejpam-5844	78	31	b2	b2	NOUN
ejpam-5844	78	32	]	]	PUNCT
ejpam-5844	78	33	)	)	PUNCT
ejpam-5844	78	34	(	(	PUNCT
ejpam-5844	78	35	by	by	ADP
ejpam-5844	78	36	lemma	lemma	PROPN
ejpam-5844	78	37	2	2	NUM
ejpam-5844	78	38	)	)	PUNCT
ejpam-5844	78	39	=	=	SYM
ejpam-5844	78	40	max	max	PROPN
ejpam-5844	78	41	(	(	PUNCT
ejpam-5844	78	42	∥g(a)∥	∥g(a)∥	PROPN
ejpam-5844	78	43	,	,	PUNCT
ejpam-5844	78	44	∥h(b)∥	∥h(b)∥	PROPN
ejpam-5844	78	45	)	)	PUNCT
ejpam-5844	78	46	sj	sj	INTJ
ejpam-5844	78	47	(	(	PUNCT
ejpam-5844	78	48	[	[	PUNCT
ejpam-5844	78	49	a2	a2	PROPN
ejpam-5844	78	50	ab	ab	PROPN
ejpam-5844	78	51	ba	ba	PROPN
ejpam-5844	78	52	b2	b2	PROPN
ejpam-5844	78	53	]	]	PUNCT
ejpam-5844	79	1	⊕	⊕	PROPN
ejpam-5844	79	2	(	(	PUNCT
ejpam-5844	79	3	u	u	X
ejpam-5844	79	4	[	[	PUNCT
ejpam-5844	79	5	a2	a2	PROPN
ejpam-5844	79	6	−ab	−ab	NUM
ejpam-5844	79	7	−ba	−ba	PROPN
ejpam-5844	79	8	b2	b2	PROPN
ejpam-5844	79	9	]	]	PUNCT
ejpam-5844	79	10	u∗	u∗	ADV
ejpam-5844	79	11	)	)	PUNCT
ejpam-5844	79	12	)	)	PUNCT
ejpam-5844	80	1	=	=	SYM
ejpam-5844	80	2	max	max	PROPN
ejpam-5844	80	3	(	(	PUNCT
ejpam-5844	80	4	∥g(a)∥	∥g(a)∥	PROPN
ejpam-5844	80	5	,	,	PUNCT
ejpam-5844	80	6	∥h(b)∥	∥h(b)∥	PROPN
ejpam-5844	80	7	)	)	PUNCT
ejpam-5844	80	8	sj	sj	INTJ
ejpam-5844	80	9	(	(	PUNCT
ejpam-5844	80	10	[	[	PUNCT
ejpam-5844	80	11	a2	a2	PROPN
ejpam-5844	80	12	ab	ab	PROPN
ejpam-5844	80	13	ba	ba	PROPN
ejpam-5844	80	14	b2	b2	PROPN
ejpam-5844	80	15	]	]	PUNCT
ejpam-5844	80	16	⊕	⊕	PROPN
ejpam-5844	80	17	[	[	PUNCT
ejpam-5844	80	18	a2	a2	PROPN
ejpam-5844	80	19	ab	ab	PROPN
ejpam-5844	80	20	ba	ba	PROPN
ejpam-5844	80	21	b2	b2	PROPN
ejpam-5844	80	22	]	]	PUNCT
ejpam-5844	80	23	)	)	PUNCT
ejpam-5844	80	24	.	.	PUNCT
ejpam-5844	81	1	(	(	PUNCT
ejpam-5844	81	2	7	7	X
ejpam-5844	81	3	)	)	PUNCT
ejpam-5844	81	4	now	now	ADV
ejpam-5844	81	5	,	,	PUNCT
ejpam-5844	81	6	the	the	DET
ejpam-5844	81	7	desired	desire	VERB
ejpam-5844	81	8	result	result	NOUN
ejpam-5844	81	9	follows	follow	VERB
ejpam-5844	81	10	by	by	ADP
ejpam-5844	81	11	inequalities	inequality	NOUN
ejpam-5844	81	12	(	(	PUNCT
ejpam-5844	81	13	3	3	NUM
ejpam-5844	81	14	)	)	PUNCT
ejpam-5844	81	15	and	and	CCONJ
ejpam-5844	81	16	(	(	PUNCT
ejpam-5844	81	17	7	7	NUM
ejpam-5844	81	18	)	)	PUNCT
ejpam-5844	81	19	.	.	PUNCT
ejpam-5844	82	1	inequality	inequality	NOUN
ejpam-5844	82	2	(	(	PUNCT
ejpam-5844	82	3	6	6	NUM
ejpam-5844	82	4	)	)	PUNCT
ejpam-5844	82	5	represents	represent	VERB
ejpam-5844	82	6	a	a	DET
ejpam-5844	82	7	general	general	ADJ
ejpam-5844	82	8	version	version	NOUN
ejpam-5844	82	9	of	of	ADP
ejpam-5844	82	10	inequality	inequality	NOUN
ejpam-5844	82	11	(	(	PUNCT
ejpam-5844	82	12	2	2	NUM
ejpam-5844	82	13	)	)	PUNCT
ejpam-5844	82	14	.	.	PUNCT
ejpam-5844	83	1	in	in	ADP
ejpam-5844	83	2	fact	fact	NOUN
ejpam-5844	83	3	,	,	PUNCT
ejpam-5844	83	4	letting	let	VERB
ejpam-5844	83	5	h(t	h(t	PRON
ejpam-5844	83	6	)	)	PUNCT
ejpam-5844	83	7	=	=	SYM
ejpam-5844	83	8	g(t	g(t	PROPN
ejpam-5844	83	9	)	)	PUNCT
ejpam-5844	83	10	=	=	SYM
ejpam-5844	83	11	1	1	NUM
ejpam-5844	83	12	in	in	ADP
ejpam-5844	83	13	corollary	corollary	ADJ
ejpam-5844	83	14	2	2	NUM
ejpam-5844	83	15	,	,	PUNCT
ejpam-5844	83	16	we	we	PRON
ejpam-5844	83	17	have	have	VERB
ejpam-5844	83	18	sj	sj	INTJ
ejpam-5844	83	19	(	(	PUNCT
ejpam-5844	83	20	ab	ab	NOUN
ejpam-5844	83	21	)	)	PUNCT
ejpam-5844	83	22	≤	≤	NOUN
ejpam-5844	83	23	1	1	NUM
ejpam-5844	83	24	2	2	NUM
ejpam-5844	83	25	sj	sj	NOUN
ejpam-5844	83	26	(	(	PUNCT
ejpam-5844	83	27	[	[	PUNCT
ejpam-5844	83	28	a2	a2	PROPN
ejpam-5844	83	29	ab	ab	PROPN
ejpam-5844	83	30	ba	ba	PROPN
ejpam-5844	83	31	b2	b2	PROPN
ejpam-5844	83	32	]	]	PUNCT
ejpam-5844	83	33	)	)	PUNCT
ejpam-5844	83	34	,	,	PUNCT
ejpam-5844	83	35	which	which	PRON
ejpam-5844	83	36	is	be	AUX
ejpam-5844	83	37	inequality	inequality	NOUN
ejpam-5844	83	38	(	(	PUNCT
ejpam-5844	83	39	2	2	NUM
ejpam-5844	83	40	)	)	PUNCT
ejpam-5844	83	41	.	.	PUNCT
ejpam-5844	84	1	an	an	DET
ejpam-5844	84	2	application	application	NOUN
ejpam-5844	84	3	of	of	ADP
ejpam-5844	84	4	theorem	theorem	ADJ
ejpam-5844	84	5	2	2	NUM
ejpam-5844	84	6	can	can	AUX
ejpam-5844	84	7	be	be	AUX
ejpam-5844	84	8	seen	see	VERB
ejpam-5844	84	9	in	in	ADP
ejpam-5844	84	10	the	the	DET
ejpam-5844	84	11	following	follow	VERB
ejpam-5844	84	12	corollary	corollary	NOUN
ejpam-5844	84	13	,	,	PUNCT
ejpam-5844	84	14	which	which	PRON
ejpam-5844	84	15	depends	depend	VERB
ejpam-5844	84	16	on	on	ADP
ejpam-5844	84	17	the	the	DET
ejpam-5844	84	18	following	follow	VERB
ejpam-5844	84	19	lemma	lemma	PROPN
ejpam-5844	84	20	.	.	PUNCT
ejpam-5844	85	1	lemma	lemma	PROPN
ejpam-5844	85	2	3	3	NUM
ejpam-5844	85	3	.	.	PUNCT
ejpam-5844	86	1	[	[	X
ejpam-5844	86	2	9]let	9]let	NOUN
ejpam-5844	86	3	a	a	X
ejpam-5844	86	4	,	,	PUNCT
ejpam-5844	86	5	b	b	PROPN
ejpam-5844	86	6	∈	∈	PROPN
ejpam-5844	86	7	mn	mn	PROPN
ejpam-5844	86	8	(	(	PUNCT
ejpam-5844	86	9	c	c	NOUN
ejpam-5844	86	10	)	)	PUNCT
ejpam-5844	86	11	.	.	PUNCT
ejpam-5844	87	1	then	then	ADV
ejpam-5844	87	2	for	for	ADP
ejpam-5844	87	3	j	j	PROPN
ejpam-5844	87	4	=	=	SYM
ejpam-5844	87	5	1	1	NUM
ejpam-5844	87	6	,	,	PUNCT
ejpam-5844	87	7	...	...	PUNCT
ejpam-5844	87	8	,	,	PUNCT
ejpam-5844	87	9	2n	2n	NUM
ejpam-5844	87	10	,	,	PUNCT
ejpam-5844	87	11	we	we	PRON
ejpam-5844	87	12	have	have	AUX
ejpam-5844	87	13	sj	sj	INTJ
ejpam-5844	87	14	(	(	PUNCT
ejpam-5844	87	15	(	(	PUNCT
ejpam-5844	87	16	a±b)⊕	a±b)⊕	ADV
ejpam-5844	87	17	0	0	NUM
ejpam-5844	87	18	)	)	PUNCT
ejpam-5844	87	19	≤	≤	NUM
ejpam-5844	87	20	sj	sj	PROPN
ejpam-5844	87	21	(	(	PUNCT
ejpam-5844	87	22	a⊕b	a⊕b	PROPN
ejpam-5844	87	23	)	)	PUNCT
ejpam-5844	88	1	+	+	CCONJ
ejpam-5844	88	2	1	1	NUM
ejpam-5844	88	3	2	2	NUM
ejpam-5844	88	4	∥a±b∥	∥a±b∥	NUM
ejpam-5844	88	5	.	.	PUNCT
ejpam-5844	89	1	corollary	corollary	ADJ
ejpam-5844	89	2	1	1	NUM
ejpam-5844	89	3	.	.	PUNCT
ejpam-5844	90	1	let	let	VERB
ejpam-5844	90	2	a	a	DET
ejpam-5844	90	3	,	,	PUNCT
ejpam-5844	90	4	b	b	NOUN
ejpam-5844	90	5	,	,	PUNCT
ejpam-5844	90	6	y	y	PROPN
ejpam-5844	90	7	∈	∈	PROPN
ejpam-5844	90	8	mn	mn	PROPN
ejpam-5844	90	9	(	(	PUNCT
ejpam-5844	90	10	c	c	X
ejpam-5844	90	11	)	)	PUNCT
ejpam-5844	90	12	be	be	AUX
ejpam-5844	90	13	such	such	ADJ
ejpam-5844	90	14	that	that	SCONJ
ejpam-5844	90	15	a	a	PRON
ejpam-5844	90	16	and	and	CCONJ
ejpam-5844	90	17	b	b	NOUN
ejpam-5844	90	18	are	be	AUX
ejpam-5844	90	19	positive	positive	ADJ
ejpam-5844	90	20	semidefinite	semidefinite	NOUN
ejpam-5844	90	21	.	.	PUNCT
ejpam-5844	91	1	then	then	ADV
ejpam-5844	91	2	for	for	ADP
ejpam-5844	91	3	j	j	PROPN
ejpam-5844	91	4	=	=	SYM
ejpam-5844	91	5	1	1	NUM
ejpam-5844	91	6	,	,	PUNCT
ejpam-5844	91	7	...	...	PUNCT
ejpam-5844	91	8	,	,	PUNCT
ejpam-5844	91	9	2n	2n	NUM
ejpam-5844	91	10	,	,	PUNCT
ejpam-5844	91	11	we	we	PRON
ejpam-5844	91	12	have	have	VERB
ejpam-5844	91	13	sj	sj	INTJ
ejpam-5844	91	14	(	(	PUNCT
ejpam-5844	91	15	(	(	PUNCT
ejpam-5844	91	16	abh	abh	PROPN
ejpam-5844	91	17	(	(	PUNCT
ejpam-5844	91	18	b	b	NOUN
ejpam-5844	91	19	)	)	PUNCT
ejpam-5844	92	1	+	+	CCONJ
ejpam-5844	92	2	g	g	PROPN
ejpam-5844	92	3	(	(	PUNCT
ejpam-5844	92	4	a)ab)⊕	a)ab)⊕	PROPN
ejpam-5844	92	5	0	0	NUM
ejpam-5844	92	6	)	)	PUNCT
ejpam-5844	92	7	≤	≤	NUM
ejpam-5844	92	8	max	max	NOUN
ejpam-5844	92	9	(	(	PUNCT
ejpam-5844	92	10	∥g(a)∥	∥g(a)∥	PROPN
ejpam-5844	92	11	,	,	PUNCT
ejpam-5844	92	12	∥h(b)∥	∥h(b)∥	PROPN
ejpam-5844	92	13	)	)	PUNCT
ejpam-5844	92	14	sj	sj	PROPN
ejpam-5844	92	15	(	(	PUNCT
ejpam-5844	92	16	a2	a2	PROPN
ejpam-5844	92	17	⊕b2	⊕b2	NOUN
ejpam-5844	92	18	⊕ab	⊕ab	NUM
ejpam-5844	92	19	⊕ab	⊕ab	NUM
ejpam-5844	92	20	)	)	PUNCT
ejpam-5844	93	1	+	+	CCONJ
ejpam-5844	93	2	1	1	NUM
ejpam-5844	93	3	2	2	NUM
ejpam-5844	93	4	∥∥a2	∥∥a2	PROPN
ejpam-5844	93	5	+	+	ADJ
ejpam-5844	93	6	b2	b2	NOUN
ejpam-5844	93	7	∥∥	∥∥	X
ejpam-5844	93	8	.	.	PUNCT
ejpam-5844	94	1	a.	a.	PROPN
ejpam-5844	94	2	al	al	PROPN
ejpam-5844	94	3	-	-	PUNCT
ejpam-5844	94	4	natoor	natoor	NOUN
ejpam-5844	94	5	,	,	PUNCT
ejpam-5844	94	6	r.	r.	PROPN
ejpam-5844	94	7	al	al	PROPN
ejpam-5844	94	8	-	-	PUNCT
ejpam-5844	94	9	smadi	smadi	PROPN
ejpam-5844	94	10	,	,	PUNCT
ejpam-5844	94	11	a.	a.	NOUN
ejpam-5844	94	12	burqan	burqan	PROPN
ejpam-5844	94	13	/	/	SYM
ejpam-5844	94	14	eur	eur	PROPN
ejpam-5844	94	15	.	.	PUNCT
ejpam-5844	95	1	j.	j.	PROPN
ejpam-5844	95	2	pure	pure	PROPN
ejpam-5844	95	3	appl	appl	PROPN
ejpam-5844	95	4	.	.	PROPN
ejpam-5844	95	5	math	math	PROPN
ejpam-5844	95	6	,	,	PUNCT
ejpam-5844	95	7	18	18	NUM
ejpam-5844	95	8	(	(	PUNCT
ejpam-5844	95	9	2	2	NUM
ejpam-5844	95	10	)	)	PUNCT
ejpam-5844	95	11	(	(	PUNCT
ejpam-5844	95	12	2025	2025	NUM
ejpam-5844	95	13	)	)	PUNCT
ejpam-5844	95	14	,	,	PUNCT
ejpam-5844	95	15	5844	5844	NUM
ejpam-5844	95	16	5	5	NUM
ejpam-5844	95	17	of	of	ADP
ejpam-5844	95	18	10	10	NUM
ejpam-5844	95	19	proof	proof	NOUN
ejpam-5844	95	20	.	.	PUNCT
ejpam-5844	96	1	by	by	ADP
ejpam-5844	96	2	inequality	inequality	NOUN
ejpam-5844	96	3	(	(	PUNCT
ejpam-5844	96	4	6	6	NUM
ejpam-5844	96	5	)	)	PUNCT
ejpam-5844	96	6	,	,	PUNCT
ejpam-5844	96	7	we	we	PRON
ejpam-5844	96	8	have	have	VERB
ejpam-5844	96	9	sj	sj	INTJ
ejpam-5844	96	10	(	(	PUNCT
ejpam-5844	96	11	(	(	PUNCT
ejpam-5844	96	12	abh	abh	PROPN
ejpam-5844	96	13	(	(	PUNCT
ejpam-5844	96	14	b	b	NOUN
ejpam-5844	96	15	)	)	PUNCT
ejpam-5844	97	1	+	+	CCONJ
ejpam-5844	97	2	g	g	PROPN
ejpam-5844	97	3	(	(	PUNCT
ejpam-5844	97	4	a)ab)⊕	a)ab)⊕	PROPN
ejpam-5844	97	5	0	0	NUM
ejpam-5844	97	6	)	)	PUNCT
ejpam-5844	97	7	≤	≤	NUM
ejpam-5844	97	8	max	max	NOUN
ejpam-5844	97	9	(	(	PUNCT
ejpam-5844	97	10	∥g(a)∥	∥g(a)∥	PROPN
ejpam-5844	97	11	,	,	PUNCT
ejpam-5844	97	12	∥h(b)∥	∥h(b)∥	PROPN
ejpam-5844	97	13	)	)	PUNCT
ejpam-5844	97	14	sj	sj	INTJ
ejpam-5844	97	15	(	(	PUNCT
ejpam-5844	97	16	[	[	PUNCT
ejpam-5844	97	17	a2	a2	PROPN
ejpam-5844	97	18	ab	ab	PROPN
ejpam-5844	97	19	ba	ba	PROPN
ejpam-5844	97	20	b2	b2	PROPN
ejpam-5844	97	21	]	]	PUNCT
ejpam-5844	97	22	)	)	PUNCT
ejpam-5844	97	23	=	=	SYM
ejpam-5844	97	24	max	max	PROPN
ejpam-5844	97	25	(	(	PUNCT
ejpam-5844	97	26	∥g(a)∥	∥g(a)∥	PROPN
ejpam-5844	97	27	,	,	PUNCT
ejpam-5844	97	28	∥h(b)∥	∥h(b)∥	PROPN
ejpam-5844	97	29	)	)	PUNCT
ejpam-5844	97	30	sj	sj	INTJ
ejpam-5844	97	31	(	(	PUNCT
ejpam-5844	97	32	[	[	PUNCT
ejpam-5844	97	33	a2	a2	NOUN
ejpam-5844	97	34	0	0	NUM
ejpam-5844	97	35	0	0	NUM
ejpam-5844	97	36	b2	b2	NOUN
ejpam-5844	97	37	]	]	PUNCT
ejpam-5844	98	1	+	+	CCONJ
ejpam-5844	98	2	[	[	PUNCT
ejpam-5844	98	3	0	0	NUM
ejpam-5844	98	4	ab	ab	PROPN
ejpam-5844	98	5	ba	ba	PROPN
ejpam-5844	98	6	0	0	NUM
ejpam-5844	98	7	]	]	PUNCT
ejpam-5844	98	8	)	)	PUNCT
ejpam-5844	98	9	≤	≤	NUM
ejpam-5844	98	10	max	max	NOUN
ejpam-5844	98	11	(	(	PUNCT
ejpam-5844	98	12	∥g(a)∥	∥g(a)∥	PROPN
ejpam-5844	98	13	,	,	PUNCT
ejpam-5844	98	14	∥h(b)∥	∥h(b)∥	PROPN
ejpam-5844	98	15	)	)	PUNCT
ejpam-5844	98	16			PROPN
ejpam-5844	98	17	sj	sj	INTJ
ejpam-5844	98	18	(	(	PUNCT
ejpam-5844	98	19	[	[	PUNCT
ejpam-5844	98	20	a2	a2	NOUN
ejpam-5844	98	21	0	0	NUM
ejpam-5844	98	22	0	0	NUM
ejpam-5844	98	23	b2	b2	NOUN
ejpam-5844	98	24	]	]	PUNCT
ejpam-5844	98	25	⊕	⊕	PROPN
ejpam-5844	98	26	[	[	PUNCT
ejpam-5844	98	27	0	0	NUM
ejpam-5844	98	28	ab	ab	PROPN
ejpam-5844	98	29	ba	ba	PROPN
ejpam-5844	98	30	0	0	NUM
ejpam-5844	98	31	]	]	PUNCT
ejpam-5844	98	32	)	)	PUNCT
ejpam-5844	99	1	+1	+1	PROPN
ejpam-5844	99	2	2	2	NUM
ejpam-5844	99	3	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5844	99	4	[	[	SYM
ejpam-5844	99	5	a2	a2	NOUN
ejpam-5844	99	6	0	0	NUM
ejpam-5844	99	7	0	0	NUM
ejpam-5844	99	8	b2	b2	NOUN
ejpam-5844	99	9	]	]	PUNCT
ejpam-5844	100	1	+	+	CCONJ
ejpam-5844	100	2	[	[	PUNCT
ejpam-5844	100	3	0	0	NUM
ejpam-5844	100	4	ab	ab	PROPN
ejpam-5844	100	5	ba	ba	PROPN
ejpam-5844	100	6	0	0	NUM
ejpam-5844	100	7	]	]	SYM
ejpam-5844	100	8	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	100	9			NOUN
ejpam-5844	100	10	(	(	PUNCT
ejpam-5844	100	11	by	by	ADP
ejpam-5844	100	12	lemma	lemma	PROPN
ejpam-5844	100	13	3	3	NUM
ejpam-5844	100	14	)	)	PUNCT
ejpam-5844	100	15	=	=	SYM
ejpam-5844	100	16	max	max	PROPN
ejpam-5844	100	17	(	(	PUNCT
ejpam-5844	100	18	∥g(a)∥	∥g(a)∥	PROPN
ejpam-5844	100	19	,	,	PUNCT
ejpam-5844	100	20	∥h(b)∥	∥h(b)∥	PROPN
ejpam-5844	100	21	)	)	PUNCT
ejpam-5844	100	22			PROPN
ejpam-5844	100	23	sj	sj	INTJ
ejpam-5844	100	24	(	(	PUNCT
ejpam-5844	100	25	[	[	PUNCT
ejpam-5844	100	26	a2	a2	NOUN
ejpam-5844	100	27	0	0	NUM
ejpam-5844	100	28	0	0	NUM
ejpam-5844	100	29	b2	b2	NOUN
ejpam-5844	100	30	]	]	PUNCT
ejpam-5844	100	31	⊕	⊕	PROPN
ejpam-5844	100	32	[	[	PUNCT
ejpam-5844	100	33	0	0	NUM
ejpam-5844	100	34	ab	ab	PROPN
ejpam-5844	100	35	ba	ba	PROPN
ejpam-5844	100	36	0	0	NUM
ejpam-5844	100	37	]	]	PUNCT
ejpam-5844	100	38	)	)	PUNCT
ejpam-5844	101	1	+1	+1	PROPN
ejpam-5844	101	2	2	2	NUM
ejpam-5844	101	3	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5844	101	4	[	[	SYM
ejpam-5844	101	5	a2	a2	PROPN
ejpam-5844	101	6	ab	ab	PROPN
ejpam-5844	101	7	ba	ba	PROPN
ejpam-5844	101	8	b2	b2	PROPN
ejpam-5844	101	9	]	]	PUNCT
ejpam-5844	101	10	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	101	11			NOUN
ejpam-5844	101	12	=	=	SYM
ejpam-5844	101	13	max	max	PROPN
ejpam-5844	101	14	(	(	PUNCT
ejpam-5844	101	15	∥g(a)∥	∥g(a)∥	PROPN
ejpam-5844	101	16	,	,	PUNCT
ejpam-5844	101	17	∥h(b)∥	∥h(b)∥	PROPN
ejpam-5844	101	18	)	)	PUNCT
ejpam-5844	101	19	(	(	PUNCT
ejpam-5844	101	20	sj	sj	INTJ
ejpam-5844	101	21	(	(	PUNCT
ejpam-5844	101	22	a2	a2	PROPN
ejpam-5844	101	23	⊕b2	⊕b2	NOUN
ejpam-5844	101	24	⊕ab	⊕ab	NUM
ejpam-5844	101	25	⊕ab	⊕ab	NUM
ejpam-5844	101	26	)	)	PUNCT
ejpam-5844	102	1	+	+	CCONJ
ejpam-5844	102	2	1	1	NUM
ejpam-5844	102	3	2	2	NUM
ejpam-5844	102	4	∥∥a2	∥∥a2	PROPN
ejpam-5844	102	5	+	+	ADJ
ejpam-5844	102	6	b2	b2	NOUN
ejpam-5844	102	7	∥∥	∥∥	X
ejpam-5844	102	8	)	)	PUNCT
ejpam-5844	102	9	,	,	PUNCT
ejpam-5844	102	10	as	as	SCONJ
ejpam-5844	102	11	required	require	VERB
ejpam-5844	102	12	.	.	PUNCT
ejpam-5844	103	1	theorem	theorem	NOUN
ejpam-5844	103	2	3	3	X
ejpam-5844	103	3	.	.	PUNCT
ejpam-5844	104	1	let	let	VERB
ejpam-5844	104	2	a	a	DET
ejpam-5844	104	3	,	,	PUNCT
ejpam-5844	104	4	b	b	PROPN
ejpam-5844	104	5	∈	∈	PROPN
ejpam-5844	104	6	mn	mn	PROPN
ejpam-5844	104	7	(	(	PUNCT
ejpam-5844	104	8	c	c	AUX
ejpam-5844	104	9	)	)	PUNCT
ejpam-5844	104	10	be	be	AUX
ejpam-5844	104	11	positive	positive	ADJ
ejpam-5844	104	12	semidefinite	semidefinite	NOUN
ejpam-5844	104	13	and	and	CCONJ
ejpam-5844	104	14	let	let	VERB
ejpam-5844	104	15	g(t	g(t	PROPN
ejpam-5844	104	16	)	)	PUNCT
ejpam-5844	104	17	,	,	PUNCT
ejpam-5844	104	18	h(t	h(t	PROPN
ejpam-5844	104	19	)	)	PUNCT
ejpam-5844	105	1	be	be	AUX
ejpam-5844	105	2	real	real	ADJ
ejpam-5844	105	3	polynomials	polynomial	NOUN
ejpam-5844	105	4	.	.	PUNCT
ejpam-5844	106	1	then	then	ADV
ejpam-5844	106	2	for	for	ADP
ejpam-5844	106	3	j	j	PROPN
ejpam-5844	106	4	=	=	SYM
ejpam-5844	106	5	1	1	NUM
ejpam-5844	106	6	,	,	PUNCT
ejpam-5844	106	7	2	2	NUM
ejpam-5844	106	8	,	,	PUNCT
ejpam-5844	106	9	...	...	PUNCT
ejpam-5844	106	10	,	,	PUNCT
ejpam-5844	106	11	2n	2n	NUM
ejpam-5844	106	12	,	,	PUNCT
ejpam-5844	106	13	we	we	PRON
ejpam-5844	106	14	have	have	VERB
ejpam-5844	106	15	sj	sj	INTJ
ejpam-5844	106	16	(	(	PUNCT
ejpam-5844	106	17	abh(b	abh(b	NOUN
ejpam-5844	106	18	)	)	PUNCT
ejpam-5844	107	1	+	+	NUM
ejpam-5844	107	2	g(a)ab	g(a)ab	VERB
ejpam-5844	107	3	⊕	⊕	PROPN
ejpam-5844	107	4	0	0	NUM
ejpam-5844	107	5	)	)	PUNCT
ejpam-5844	107	6	≤	≤	NUM
ejpam-5844	107	7	sj	sj	INTJ
ejpam-5844	107	8	(	(	PUNCT
ejpam-5844	107	9	[	[	PUNCT
ejpam-5844	107	10	a2	a2	PROPN
ejpam-5844	107	11	g	g	NOUN
ejpam-5844	107	12	(	(	PUNCT
ejpam-5844	107	13	a	a	PRON
ejpam-5844	107	14	)	)	PUNCT
ejpam-5844	107	15	abh(b	abh(b	PROPN
ejpam-5844	107	16	)	)	PUNCT
ejpam-5844	107	17	bag(a	bag(a	PROPN
ejpam-5844	107	18	)	)	PUNCT
ejpam-5844	107	19	b2h	b2h	PROPN
ejpam-5844	107	20	(	(	PUNCT
ejpam-5844	107	21	b	b	NOUN
ejpam-5844	107	22	)	)	PUNCT
ejpam-5844	107	23	]	]	PUNCT
ejpam-5844	107	24	)	)	PUNCT
ejpam-5844	108	1	+	+	CCONJ
ejpam-5844	108	2	1	1	NUM
ejpam-5844	108	3	2	2	NUM
ejpam-5844	108	4	∥abh(b	∥abh(b	NUM
ejpam-5844	108	5	)	)	PUNCT
ejpam-5844	108	6	+	+	CCONJ
ejpam-5844	108	7	g(a)ab∥	g(a)ab∥	ADJ
ejpam-5844	108	8	.	.	PUNCT
ejpam-5844	109	1	(	(	PUNCT
ejpam-5844	109	2	8)	8)	NUM
ejpam-5844	109	3	in	in	ADP
ejpam-5844	109	4	particular	particular	ADJ
ejpam-5844	109	5	,	,	PUNCT
ejpam-5844	109	6	if	if	SCONJ
ejpam-5844	109	7	j	j	PROPN
ejpam-5844	109	8	=	=	SYM
ejpam-5844	109	9	1	1	NUM
ejpam-5844	109	10	,	,	PUNCT
ejpam-5844	109	11	then	then	ADV
ejpam-5844	109	12	∥abh(b	∥abh(b	NUM
ejpam-5844	109	13	)	)	PUNCT
ejpam-5844	110	1	+	+	CCONJ
ejpam-5844	110	2	g(a)ab∥	g(a)ab∥	ADJ
ejpam-5844	110	3	≤	≤	NUM
ejpam-5844	110	4	2	2	NUM
ejpam-5844	110	5	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	110	6	[	[	PUNCT
ejpam-5844	110	7	a2	a2	PROPN
ejpam-5844	110	8	g	g	PROPN
ejpam-5844	110	9	(	(	PUNCT
ejpam-5844	110	10	a	a	PRON
ejpam-5844	110	11	)	)	PUNCT
ejpam-5844	110	12	abh(b	abh(b	PROPN
ejpam-5844	110	13	)	)	PUNCT
ejpam-5844	110	14	bag(a	bag(a	PROPN
ejpam-5844	110	15	)	)	PUNCT
ejpam-5844	110	16	b2h	b2h	PROPN
ejpam-5844	110	17	(	(	PUNCT
ejpam-5844	110	18	b	b	NOUN
ejpam-5844	110	19	)	)	PUNCT
ejpam-5844	110	20	]	]	PUNCT
ejpam-5844	110	21	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	110	22	.	.	PUNCT
ejpam-5844	111	1	proof	proof	NOUN
ejpam-5844	111	2	.	.	PUNCT
ejpam-5844	112	1	let	let	VERB
ejpam-5844	112	2	q1	q1	PROPN
ejpam-5844	112	3	,	,	PUNCT
ejpam-5844	112	4	q2	q2	NOUN
ejpam-5844	112	5	,	,	PUNCT
ejpam-5844	112	6	q	q	X
ejpam-5844	112	7	,	,	PUNCT
ejpam-5844	112	8	and	and	CCONJ
ejpam-5844	112	9	u	u	NOUN
ejpam-5844	112	10	be	be	VERB
ejpam-5844	112	11	as	as	ADP
ejpam-5844	112	12	in	in	ADP
ejpam-5844	112	13	the	the	DET
ejpam-5844	112	14	proof	proof	NOUN
ejpam-5844	112	15	of	of	ADP
ejpam-5844	112	16	theorem	theorem	NOUN
ejpam-5844	112	17	1	1	NUM
ejpam-5844	112	18	.	.	PUNCT
ejpam-5844	112	19	then	then	ADV
ejpam-5844	112	20	by	by	ADP
ejpam-5844	112	21	equation	equation	NOUN
ejpam-5844	112	22	(	(	PUNCT
ejpam-5844	112	23	4	4	NUM
ejpam-5844	112	24	)	)	PUNCT
ejpam-5844	112	25	,	,	PUNCT
ejpam-5844	112	26	we	we	PRON
ejpam-5844	112	27	have	have	VERB
ejpam-5844	112	28	sj	sj	INTJ
ejpam-5844	112	29	(	(	PUNCT
ejpam-5844	112	30	(	(	PUNCT
ejpam-5844	112	31	abh(b	abh(b	NOUN
ejpam-5844	112	32	)	)	PUNCT
ejpam-5844	113	1	+	+	CCONJ
ejpam-5844	113	2	g	g	PROPN
ejpam-5844	113	3	(	(	PUNCT
ejpam-5844	113	4	a)ab)⊕	a)ab)⊕	PROPN
ejpam-5844	113	5	(	(	PUNCT
ejpam-5844	113	6	abh(b	abh(b	PROPN
ejpam-5844	113	7	)	)	PUNCT
ejpam-5844	113	8	+	+	CCONJ
ejpam-5844	113	9	g	g	PROPN
ejpam-5844	113	10	(	(	PUNCT
ejpam-5844	113	11	a)ab	a)ab	PROPN
ejpam-5844	113	12	)	)	PUNCT
ejpam-5844	113	13	)	)	PUNCT
ejpam-5844	114	1	=	=	PUNCT
ejpam-5844	114	2	sj	sj	INTJ
ejpam-5844	114	3	(	(	PUNCT
ejpam-5844	114	4	q1	q1	PROPN
ejpam-5844	114	5	−q2	−q2	PROPN
ejpam-5844	114	6	)	)	PUNCT
ejpam-5844	114	7	≤	≤	PUNCT
ejpam-5844	115	1	sj	sj	PROPN
ejpam-5844	115	2	(	(	PUNCT
ejpam-5844	115	3	q1	q1	PROPN
ejpam-5844	115	4	⊕q2	⊕q2	PROPN
ejpam-5844	115	5	)	)	PUNCT
ejpam-5844	115	6	+	+	CCONJ
ejpam-5844	115	7	1	1	NUM
ejpam-5844	115	8	2	2	NUM
ejpam-5844	115	9	∥q1	∥q1	NOUN
ejpam-5844	115	10	−q2∥	−q2∥	PROPN
ejpam-5844	115	11	a.	a.	PROPN
ejpam-5844	115	12	al	al	PROPN
ejpam-5844	115	13	-	-	PUNCT
ejpam-5844	115	14	natoor	natoor	NOUN
ejpam-5844	115	15	,	,	PUNCT
ejpam-5844	115	16	r.	r.	PROPN
ejpam-5844	115	17	al	al	PROPN
ejpam-5844	115	18	-	-	PUNCT
ejpam-5844	115	19	smadi	smadi	PROPN
ejpam-5844	115	20	,	,	PUNCT
ejpam-5844	115	21	a.	a.	NOUN
ejpam-5844	115	22	burqan	burqan	PROPN
ejpam-5844	115	23	/	/	SYM
ejpam-5844	115	24	eur	eur	PROPN
ejpam-5844	115	25	.	.	PUNCT
ejpam-5844	116	1	j.	j.	PROPN
ejpam-5844	116	2	pure	pure	PROPN
ejpam-5844	116	3	appl	appl	PROPN
ejpam-5844	116	4	.	.	PROPN
ejpam-5844	116	5	math	math	PROPN
ejpam-5844	116	6	,	,	PUNCT
ejpam-5844	116	7	18	18	NUM
ejpam-5844	116	8	(	(	PUNCT
ejpam-5844	116	9	2	2	NUM
ejpam-5844	116	10	)	)	PUNCT
ejpam-5844	116	11	(	(	PUNCT
ejpam-5844	116	12	2025	2025	NUM
ejpam-5844	116	13	)	)	PUNCT
ejpam-5844	116	14	,	,	PUNCT
ejpam-5844	116	15	5844	5844	NUM
ejpam-5844	116	16	6	6	NUM
ejpam-5844	116	17	of	of	ADP
ejpam-5844	116	18	10	10	NUM
ejpam-5844	116	19	(	(	PUNCT
ejpam-5844	116	20	by	by	ADP
ejpam-5844	116	21	lemma	lemma	PROPN
ejpam-5844	116	22	3	3	NUM
ejpam-5844	116	23	)	)	PUNCT
ejpam-5844	116	24	≤	≤	NUM
ejpam-5844	116	25	sj	sj	INTJ
ejpam-5844	116	26	(	(	PUNCT
ejpam-5844	116	27	[	[	PUNCT
ejpam-5844	116	28	a2	a2	PROPN
ejpam-5844	116	29	g	g	NOUN
ejpam-5844	116	30	(	(	PUNCT
ejpam-5844	116	31	a	a	NOUN
ejpam-5844	116	32	)	)	PUNCT
ejpam-5844	116	33	abh	abh	NOUN
ejpam-5844	116	34	(	(	PUNCT
ejpam-5844	116	35	b	b	NOUN
ejpam-5844	116	36	)	)	PUNCT
ejpam-5844	116	37	bag	bag	NOUN
ejpam-5844	116	38	(	(	PUNCT
ejpam-5844	116	39	a	a	NOUN
ejpam-5844	116	40	)	)	PUNCT
ejpam-5844	116	41	b2h	b2h	PROPN
ejpam-5844	116	42	(	(	PUNCT
ejpam-5844	116	43	b	b	NOUN
ejpam-5844	116	44	)	)	PUNCT
ejpam-5844	116	45	]	]	PUNCT
ejpam-5844	117	1	⊕	⊕	PROPN
ejpam-5844	117	2	[	[	PUNCT
ejpam-5844	117	3	g	g	PROPN
ejpam-5844	117	4	(	(	PUNCT
ejpam-5844	117	5	a)a2	a)a2	PROPN
ejpam-5844	117	6	−g	−g	NOUN
ejpam-5844	117	7	(	(	PUNCT
ejpam-5844	117	8	a)ab	a)ab	PROPN
ejpam-5844	117	9	−h	−h	VERB
ejpam-5844	117	10	(	(	PUNCT
ejpam-5844	117	11	b)ba	b)ba	PROPN
ejpam-5844	117	12	h	h	NOUN
ejpam-5844	117	13	(	(	PUNCT
ejpam-5844	117	14	b)b2	b)b2	PROPN
ejpam-5844	117	15	]	]	PUNCT
ejpam-5844	117	16	)	)	PUNCT
ejpam-5844	118	1	+	+	CCONJ
ejpam-5844	118	2	1	1	NUM
ejpam-5844	118	3	2	2	NUM
ejpam-5844	118	4	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	118	5	[	[	PUNCT
ejpam-5844	118	6	0	0	NUM
ejpam-5844	118	7	abhb	abhb	NOUN
ejpam-5844	118	8	+	+	CCONJ
ejpam-5844	118	9	g	g	PROPN
ejpam-5844	118	10	(	(	PUNCT
ejpam-5844	118	11	a)ab	a)ab	PROPN
ejpam-5844	118	12	bag	bag	NOUN
ejpam-5844	118	13	(	(	PUNCT
ejpam-5844	118	14	a	a	NOUN
ejpam-5844	118	15	)	)	PUNCT
ejpam-5844	119	1	+	+	NUM
ejpam-5844	119	2	h	h	NOUN
ejpam-5844	119	3	(	(	PUNCT
ejpam-5844	119	4	b)ba	b)ba	PROPN
ejpam-5844	119	5	0	0	NUM
ejpam-5844	119	6	]	]	SYM
ejpam-5844	119	7	∥∥∥∥	∥∥∥∥	NUM
ejpam-5844	119	8	=	=	SYM
ejpam-5844	119	9	sj	sj	INTJ
ejpam-5844	119	10	(	(	PUNCT
ejpam-5844	119	11	[	[	PUNCT
ejpam-5844	119	12	a2	a2	PROPN
ejpam-5844	119	13	g	g	NOUN
ejpam-5844	119	14	(	(	PUNCT
ejpam-5844	119	15	a	a	NOUN
ejpam-5844	119	16	)	)	PUNCT
ejpam-5844	119	17	abh	abh	NOUN
ejpam-5844	119	18	(	(	PUNCT
ejpam-5844	119	19	b	b	NOUN
ejpam-5844	119	20	)	)	PUNCT
ejpam-5844	119	21	bag	bag	NOUN
ejpam-5844	119	22	(	(	PUNCT
ejpam-5844	119	23	a	a	NOUN
ejpam-5844	119	24	)	)	PUNCT
ejpam-5844	119	25	b2h	b2h	PROPN
ejpam-5844	119	26	(	(	PUNCT
ejpam-5844	119	27	b	b	NOUN
ejpam-5844	119	28	)	)	PUNCT
ejpam-5844	119	29	]	]	PUNCT
ejpam-5844	120	1	⊕	⊕	PROPN
ejpam-5844	120	2	(	(	PUNCT
ejpam-5844	120	3	u	u	X
ejpam-5844	120	4	[	[	PUNCT
ejpam-5844	120	5	g	g	PROPN
ejpam-5844	120	6	(	(	PUNCT
ejpam-5844	120	7	a)a2	a)a2	PROPN
ejpam-5844	120	8	−g	−g	NOUN
ejpam-5844	120	9	(	(	PUNCT
ejpam-5844	120	10	a)ab	a)ab	PROPN
ejpam-5844	120	11	−h	−h	VERB
ejpam-5844	120	12	(	(	PUNCT
ejpam-5844	120	13	b)ba	b)ba	PROPN
ejpam-5844	120	14	h	h	NOUN
ejpam-5844	120	15	(	(	PUNCT
ejpam-5844	120	16	b)b2	b)b2	PROPN
ejpam-5844	120	17	]	]	PUNCT
ejpam-5844	120	18	u∗	u∗	ADV
ejpam-5844	120	19	)	)	PUNCT
ejpam-5844	120	20	)	)	PUNCT
ejpam-5844	121	1	+	+	CCONJ
ejpam-5844	121	2	1	1	NUM
ejpam-5844	121	3	2	2	NUM
ejpam-5844	121	4	max	max	NOUN
ejpam-5844	121	5	(	(	PUNCT
ejpam-5844	121	6	∥abh	∥abh	PROPN
ejpam-5844	121	7	(	(	PUNCT
ejpam-5844	121	8	b	b	NOUN
ejpam-5844	121	9	)	)	PUNCT
ejpam-5844	122	1	+	+	CCONJ
ejpam-5844	122	2	g	g	NOUN
ejpam-5844	122	3	(	(	PUNCT
ejpam-5844	122	4	a)ab∥	a)ab∥	ADJ
ejpam-5844	122	5	,	,	PUNCT
ejpam-5844	122	6	∥bag	∥bag	PROPN
ejpam-5844	122	7	(	(	PUNCT
ejpam-5844	122	8	a	a	NOUN
ejpam-5844	122	9	)	)	PUNCT
ejpam-5844	122	10	+	+	NUM
ejpam-5844	122	11	h	h	NOUN
ejpam-5844	122	12	(	(	PUNCT
ejpam-5844	122	13	b)ba∥	b)ba∥	NOUN
ejpam-5844	122	14	)	)	PUNCT
ejpam-5844	122	15	=	=	SYM
ejpam-5844	122	16	sj	sj	INTJ
ejpam-5844	122	17	(	(	PUNCT
ejpam-5844	122	18	[	[	PUNCT
ejpam-5844	122	19	a2	a2	PROPN
ejpam-5844	122	20	g	g	NOUN
ejpam-5844	122	21	(	(	PUNCT
ejpam-5844	122	22	a	a	NOUN
ejpam-5844	122	23	)	)	PUNCT
ejpam-5844	122	24	abh	abh	NOUN
ejpam-5844	122	25	(	(	PUNCT
ejpam-5844	122	26	b	b	NOUN
ejpam-5844	122	27	)	)	PUNCT
ejpam-5844	122	28	bag	bag	NOUN
ejpam-5844	122	29	(	(	PUNCT
ejpam-5844	122	30	a	a	NOUN
ejpam-5844	122	31	)	)	PUNCT
ejpam-5844	122	32	b2h	b2h	PROPN
ejpam-5844	122	33	(	(	PUNCT
ejpam-5844	122	34	b	b	NOUN
ejpam-5844	122	35	)	)	PUNCT
ejpam-5844	122	36	]	]	PUNCT
ejpam-5844	123	1	⊕	⊕	PROPN
ejpam-5844	123	2	[	[	PUNCT
ejpam-5844	123	3	g	g	PROPN
ejpam-5844	123	4	(	(	PUNCT
ejpam-5844	123	5	a)a2	a)a2	PROPN
ejpam-5844	123	6	g	g	PROPN
ejpam-5844	123	7	(	(	PUNCT
ejpam-5844	123	8	a)ab	a)ab	PROPN
ejpam-5844	123	9	h	h	NOUN
ejpam-5844	123	10	(	(	PUNCT
ejpam-5844	123	11	b)ba	b)ba	PROPN
ejpam-5844	123	12	h	h	NOUN
ejpam-5844	123	13	(	(	PUNCT
ejpam-5844	123	14	b)b2	b)b2	PROPN
ejpam-5844	123	15	]	]	PUNCT
ejpam-5844	123	16	)	)	PUNCT
ejpam-5844	124	1	+	+	CCONJ
ejpam-5844	124	2	1	1	NUM
ejpam-5844	124	3	2	2	NUM
ejpam-5844	124	4	∥abh	∥abh	PROPN
ejpam-5844	124	5	(	(	PUNCT
ejpam-5844	124	6	b	b	NOUN
ejpam-5844	124	7	)	)	PUNCT
ejpam-5844	125	1	+	+	CCONJ
ejpam-5844	125	2	g	g	NOUN
ejpam-5844	125	3	(	(	PUNCT
ejpam-5844	125	4	a)ab∥	a)ab∥	ADJ
ejpam-5844	125	5	.	.	PUNCT
ejpam-5844	126	1	consequently	consequently	ADV
ejpam-5844	126	2	,	,	PUNCT
ejpam-5844	126	3	sj((abh(b	sj((abh(b	ADJ
ejpam-5844	126	4	)	)	PUNCT
ejpam-5844	126	5	+	+	CCONJ
ejpam-5844	126	6	g(a)ab)⊕(abh(b	g(a)ab)⊕(abh(b	NOUN
ejpam-5844	126	7	)	)	PUNCT
ejpam-5844	127	1	+	+	CCONJ
ejpam-5844	127	2	g(a)ab	g(a)ab	NOUN
ejpam-5844	127	3	)	)	PUNCT
ejpam-5844	127	4	)	)	PUNCT
ejpam-5844	128	1	≤	≤	NUM
ejpam-5844	128	2	sj	sj	INTJ
ejpam-5844	128	3	(	(	PUNCT
ejpam-5844	128	4	[	[	PUNCT
ejpam-5844	128	5	a2	a2	PROPN
ejpam-5844	128	6	g	g	NOUN
ejpam-5844	128	7	(	(	PUNCT
ejpam-5844	128	8	a	a	NOUN
ejpam-5844	128	9	)	)	PUNCT
ejpam-5844	128	10	abh	abh	NOUN
ejpam-5844	128	11	(	(	PUNCT
ejpam-5844	128	12	b	b	NOUN
ejpam-5844	128	13	)	)	PUNCT
ejpam-5844	128	14	bag	bag	NOUN
ejpam-5844	128	15	(	(	PUNCT
ejpam-5844	128	16	a	a	NOUN
ejpam-5844	128	17	)	)	PUNCT
ejpam-5844	128	18	b2h	b2h	PROPN
ejpam-5844	128	19	(	(	PUNCT
ejpam-5844	128	20	b	b	NOUN
ejpam-5844	128	21	)	)	PUNCT
ejpam-5844	128	22	]	]	PUNCT
ejpam-5844	129	1	⊕	⊕	PROPN
ejpam-5844	129	2	[	[	PUNCT
ejpam-5844	129	3	g	g	PROPN
ejpam-5844	129	4	(	(	PUNCT
ejpam-5844	129	5	a)a2	a)a2	PROPN
ejpam-5844	129	6	g	g	PROPN
ejpam-5844	129	7	(	(	PUNCT
ejpam-5844	129	8	a)ab	a)ab	PROPN
ejpam-5844	129	9	h	h	NOUN
ejpam-5844	129	10	(	(	PUNCT
ejpam-5844	129	11	b)ba	b)ba	PROPN
ejpam-5844	129	12	h	h	NOUN
ejpam-5844	129	13	(	(	PUNCT
ejpam-5844	129	14	b)b2	b)b2	PROPN
ejpam-5844	129	15	]	]	PUNCT
ejpam-5844	129	16	)	)	PUNCT
ejpam-5844	130	1	+	+	CCONJ
ejpam-5844	130	2	1	1	NUM
ejpam-5844	130	3	2	2	NUM
ejpam-5844	130	4	∥abh	∥abh	PROPN
ejpam-5844	130	5	(	(	PUNCT
ejpam-5844	130	6	b	b	NOUN
ejpam-5844	130	7	)	)	PUNCT
ejpam-5844	131	1	+	+	CCONJ
ejpam-5844	131	2	g	g	NOUN
ejpam-5844	131	3	(	(	PUNCT
ejpam-5844	131	4	a)ab∥	a)ab∥	ADJ
ejpam-5844	131	5	.	.	PUNCT
ejpam-5844	132	1	(	(	PUNCT
ejpam-5844	132	2	9	9	X
ejpam-5844	132	3	)	)	PUNCT
ejpam-5844	132	4	now	now	ADV
ejpam-5844	132	5	,	,	PUNCT
ejpam-5844	132	6	the	the	DET
ejpam-5844	132	7	desired	desire	VERB
ejpam-5844	132	8	result	result	NOUN
ejpam-5844	132	9	follows	follow	VERB
ejpam-5844	132	10	from	from	ADP
ejpam-5844	132	11	inequalities	inequality	NOUN
ejpam-5844	132	12	(	(	PUNCT
ejpam-5844	132	13	3	3	NUM
ejpam-5844	132	14	)	)	PUNCT
ejpam-5844	132	15	and	and	CCONJ
ejpam-5844	132	16	(	(	PUNCT
ejpam-5844	132	17	9	9	NUM
ejpam-5844	132	18	)	)	PUNCT
ejpam-5844	132	19	.	.	PUNCT
ejpam-5844	133	1	lemma	lemma	PROPN
ejpam-5844	133	2	4	4	NUM
ejpam-5844	133	3	.	.	PUNCT
ejpam-5844	134	1	[	[	X
ejpam-5844	134	2	10]let	10]let	NUM
ejpam-5844	134	3	a	a	PRON
ejpam-5844	134	4	,	,	PUNCT
ejpam-5844	134	5	b	b	X
ejpam-5844	134	6	∈	∈	PROPN
ejpam-5844	134	7	mn(c	mn(c	X
ejpam-5844	134	8	)	)	PUNCT
ejpam-5844	134	9	be	be	AUX
ejpam-5844	134	10	positive	positive	ADJ
ejpam-5844	134	11	semidefinite	semidefinite	NOUN
ejpam-5844	134	12	.	.	PUNCT
ejpam-5844	135	1	then	then	ADV
ejpam-5844	135	2	for	for	ADP
ejpam-5844	135	3	r	r	PROPN
ejpam-5844	135	4	≥	≥	NOUN
ejpam-5844	135	5	0	0	NUM
ejpam-5844	135	6	,	,	PUNCT
ejpam-5844	135	7	we	we	PRON
ejpam-5844	135	8	have∥∥∥a1/2(a+b)rb1/2	have∥∥∥a1/2(a+b)rb1/2	VERB
ejpam-5844	135	9	∥∥∥	∥∥∥	PROPN
ejpam-5844	135	10	≤	≤	NUM
ejpam-5844	135	11	1	1	NUM
ejpam-5844	135	12	2	2	NUM
ejpam-5844	135	13	∥∥(a+b)r+1	∥∥(a+b)r+1	X
ejpam-5844	135	14	∥∥	∥∥	X
ejpam-5844	135	15	.	.	PUNCT
ejpam-5844	136	1	corollary	corollary	ADJ
ejpam-5844	136	2	2	2	NUM
ejpam-5844	136	3	.	.	PUNCT
ejpam-5844	137	1	let	let	VERB
ejpam-5844	137	2	a	a	DET
ejpam-5844	137	3	,	,	PUNCT
ejpam-5844	137	4	b	b	NOUN
ejpam-5844	137	5	∈	∈	PROPN
ejpam-5844	137	6	mn(c	mn(c	X
ejpam-5844	137	7	)	)	PUNCT
ejpam-5844	137	8	be	be	AUX
ejpam-5844	137	9	positive	positive	ADJ
ejpam-5844	137	10	semidefinite	semidefinite	NOUN
ejpam-5844	137	11	.	.	PUNCT
ejpam-5844	138	1	then	then	ADV
ejpam-5844	138	2	for	for	ADP
ejpam-5844	138	3	j	j	PROPN
ejpam-5844	138	4	=	=	SYM
ejpam-5844	138	5	1	1	NUM
ejpam-5844	138	6	,	,	PUNCT
ejpam-5844	138	7	...	...	PUNCT
ejpam-5844	138	8	,	,	PUNCT
ejpam-5844	138	9	2n	2n	NUM
ejpam-5844	138	10	,	,	PUNCT
ejpam-5844	138	11	we	we	PRON
ejpam-5844	138	12	have	have	VERB
ejpam-5844	138	13	sj	sj	INTJ
ejpam-5844	138	14	(	(	PUNCT
ejpam-5844	138	15	(	(	PUNCT
ejpam-5844	138	16	a1/2b3/2	a1/2b3/2	ADJ
ejpam-5844	138	17	+	+	ADJ
ejpam-5844	138	18	a3/2b12	a3/2b12	PROPN
ejpam-5844	138	19	)	)	PUNCT
ejpam-5844	138	20	⊕	⊕	PROPN
ejpam-5844	138	21	0	0	NUM
ejpam-5844	138	22	)	)	PUNCT
ejpam-5844	138	23	≤	≤	PUNCT
ejpam-5844	138	24	sj	sj	INTJ
ejpam-5844	138	25	(	(	PUNCT
ejpam-5844	138	26	[	[	PUNCT
ejpam-5844	138	27	a2	a2	PROPN
ejpam-5844	138	28	a1/2b3/2	a1/2b3/2	ADJ
ejpam-5844	138	29	b1/2a3/2	b1/2a3/2	NOUN
ejpam-5844	138	30	b2	b2	NOUN
ejpam-5844	138	31	]	]	PUNCT
ejpam-5844	138	32	)	)	PUNCT
ejpam-5844	139	1	+	+	CCONJ
ejpam-5844	139	2	1	1	NUM
ejpam-5844	139	3	4	4	NUM
ejpam-5844	139	4	∥∥(a+b)2	∥∥(a+b)2	ADJ
ejpam-5844	139	5	∥∥	∥∥	X
ejpam-5844	139	6	proof	proof	NOUN
ejpam-5844	139	7	.	.	PUNCT
ejpam-5844	140	1	let	let	VERB
ejpam-5844	140	2	g(t	g(t	PROPN
ejpam-5844	140	3	)	)	PUNCT
ejpam-5844	140	4	=	=	SYM
ejpam-5844	140	5	h(t	h(t	X
ejpam-5844	140	6	)	)	PUNCT
ejpam-5844	141	1	=	=	SYM
ejpam-5844	141	2	t2	t2	PROPN
ejpam-5844	141	3	in	in	ADP
ejpam-5844	141	4	inequality	inequality	NOUN
ejpam-5844	141	5	(	(	PUNCT
ejpam-5844	141	6	8)	8)	NUM
ejpam-5844	141	7	.	.	PUNCT
ejpam-5844	142	1	then	then	ADV
ejpam-5844	142	2	sj	sj	INTJ
ejpam-5844	142	3	(	(	PUNCT
ejpam-5844	142	4	(	(	PUNCT
ejpam-5844	142	5	ab3	ab3	PROPN
ejpam-5844	142	6	+	+	PROPN
ejpam-5844	142	7	a3b	a3b	ADJ
ejpam-5844	142	8	)	)	PUNCT
ejpam-5844	142	9	⊕	⊕	PROPN
ejpam-5844	142	10	0	0	NUM
ejpam-5844	142	11	)	)	PUNCT
ejpam-5844	142	12	≤	≤	PUNCT
ejpam-5844	142	13	sj	sj	INTJ
ejpam-5844	142	14	(	(	PUNCT
ejpam-5844	142	15	[	[	PUNCT
ejpam-5844	142	16	a4	a4	INTJ
ejpam-5844	142	17	ab3	ab3	PROPN
ejpam-5844	142	18	ba3	ba3	PROPN
ejpam-5844	142	19	b4	b4	PROPN
ejpam-5844	142	20	]	]	PUNCT
ejpam-5844	142	21	)	)	PUNCT
ejpam-5844	143	1	+	+	CCONJ
ejpam-5844	143	2	1	1	NUM
ejpam-5844	143	3	2	2	NUM
ejpam-5844	143	4	∥∥ab3	∥∥ab3	NOUN
ejpam-5844	143	5	+	+	PROPN
ejpam-5844	143	6	a3b	a3b	VERB
ejpam-5844	143	7	∥∥	∥∥	X
ejpam-5844	143	8	≤	≤	ADV
ejpam-5844	143	9	sj	sj	INTJ
ejpam-5844	143	10	(	(	PUNCT
ejpam-5844	143	11	[	[	PUNCT
ejpam-5844	143	12	a4	a4	INTJ
ejpam-5844	143	13	ab3	ab3	PROPN
ejpam-5844	143	14	ba3	ba3	PROPN
ejpam-5844	143	15	b4	b4	PROPN
ejpam-5844	143	16	]	]	PUNCT
ejpam-5844	143	17	)	)	PUNCT
ejpam-5844	144	1	+	+	CCONJ
ejpam-5844	144	2	1	1	NUM
ejpam-5844	144	3	2	2	NUM
ejpam-5844	144	4	∥∥a(b2	∥∥a(b2	NOUN
ejpam-5844	144	5	+	+	NOUN
ejpam-5844	144	6	a2)b	a2)b	NOUN
ejpam-5844	144	7	∥∥	∥∥	X
ejpam-5844	144	8	.	.	PUNCT
ejpam-5844	145	1	replacing	replace	VERB
ejpam-5844	145	2	a	a	DET
ejpam-5844	145	3	by	by	ADP
ejpam-5844	145	4	a1/2	a1/2	NOUN
ejpam-5844	145	5	and	and	CCONJ
ejpam-5844	145	6	b	b	NOUN
ejpam-5844	145	7	by	by	ADP
ejpam-5844	145	8	b1/2	b1/2	NOUN
ejpam-5844	145	9	,	,	PUNCT
ejpam-5844	145	10	we	we	PRON
ejpam-5844	145	11	have	have	VERB
ejpam-5844	145	12	sj	sj	INTJ
ejpam-5844	145	13	(	(	PUNCT
ejpam-5844	145	14	(	(	PUNCT
ejpam-5844	145	15	a1/2b3/2	a1/2b3/2	ADJ
ejpam-5844	145	16	+	+	ADJ
ejpam-5844	145	17	a3/2b12	a3/2b12	PROPN
ejpam-5844	145	18	)	)	PUNCT
ejpam-5844	145	19	⊕	⊕	PROPN
ejpam-5844	145	20	0	0	NUM
ejpam-5844	145	21	)	)	PUNCT
ejpam-5844	145	22	≤	≤	PUNCT
ejpam-5844	145	23	sj	sj	INTJ
ejpam-5844	145	24	(	(	PUNCT
ejpam-5844	145	25	[	[	PUNCT
ejpam-5844	145	26	a2	a2	PROPN
ejpam-5844	145	27	a1/2b3/2	a1/2b3/2	ADJ
ejpam-5844	145	28	b1/2a3/2	b1/2a3/2	NOUN
ejpam-5844	145	29	b2	b2	NOUN
ejpam-5844	145	30	]	]	PUNCT
ejpam-5844	145	31	)	)	PUNCT
ejpam-5844	145	32	a.	a.	PROPN
ejpam-5844	145	33	al	al	PROPN
ejpam-5844	145	34	-	-	PUNCT
ejpam-5844	145	35	natoor	natoor	NOUN
ejpam-5844	145	36	,	,	PUNCT
ejpam-5844	145	37	r.	r.	PROPN
ejpam-5844	145	38	al	al	PROPN
ejpam-5844	145	39	-	-	PUNCT
ejpam-5844	145	40	smadi	smadi	PROPN
ejpam-5844	145	41	,	,	PUNCT
ejpam-5844	145	42	a.	a.	NOUN
ejpam-5844	145	43	burqan	burqan	PROPN
ejpam-5844	145	44	/	/	SYM
ejpam-5844	145	45	eur	eur	PROPN
ejpam-5844	145	46	.	.	PUNCT
ejpam-5844	146	1	j.	j.	PROPN
ejpam-5844	146	2	pure	pure	PROPN
ejpam-5844	146	3	appl	appl	PROPN
ejpam-5844	146	4	.	.	PROPN
ejpam-5844	146	5	math	math	PROPN
ejpam-5844	146	6	,	,	PUNCT
ejpam-5844	146	7	18	18	NUM
ejpam-5844	146	8	(	(	PUNCT
ejpam-5844	146	9	2	2	NUM
ejpam-5844	146	10	)	)	PUNCT
ejpam-5844	146	11	(	(	PUNCT
ejpam-5844	146	12	2025	2025	NUM
ejpam-5844	146	13	)	)	PUNCT
ejpam-5844	146	14	,	,	PUNCT
ejpam-5844	146	15	5844	5844	NUM
ejpam-5844	146	16	7	7	NUM
ejpam-5844	146	17	of	of	ADP
ejpam-5844	146	18	10	10	NUM
ejpam-5844	146	19	+	+	CCONJ
ejpam-5844	146	20	1	1	NUM
ejpam-5844	146	21	2	2	NUM
ejpam-5844	146	22	∥∥∥a1/2(b	∥∥∥a1/2(b	NOUN
ejpam-5844	146	23	+	+	ADJ
ejpam-5844	146	24	a)b1/2	a)b1/2	ADJ
ejpam-5844	146	25	∥∥∥	∥∥∥	PROPN
ejpam-5844	146	26	≤	≤	NUM
ejpam-5844	146	27	sj	sj	INTJ
ejpam-5844	146	28	(	(	PUNCT
ejpam-5844	146	29	[	[	PUNCT
ejpam-5844	146	30	a2	a2	PROPN
ejpam-5844	146	31	a1/2b3/2	a1/2b3/2	ADJ
ejpam-5844	146	32	b1/2a3/2	b1/2a3/2	NOUN
ejpam-5844	146	33	b2	b2	NOUN
ejpam-5844	146	34	]	]	PUNCT
ejpam-5844	146	35	)	)	PUNCT
ejpam-5844	147	1	+	+	CCONJ
ejpam-5844	147	2	1	1	NUM
ejpam-5844	147	3	4	4	NUM
ejpam-5844	147	4	∥∥(a+b)2	∥∥(a+b)2	ADJ
ejpam-5844	147	5	∥∥	∥∥	X
ejpam-5844	147	6	(	(	PUNCT
ejpam-5844	147	7	by	by	ADP
ejpam-5844	147	8	lemma	lemma	PROPN
ejpam-5844	147	9	4	4	NUM
ejpam-5844	147	10	)	)	PUNCT
ejpam-5844	147	11	as	as	SCONJ
ejpam-5844	147	12	required	require	VERB
ejpam-5844	147	13	.	.	PUNCT
ejpam-5844	148	1	the	the	DET
ejpam-5844	148	2	author	author	NOUN
ejpam-5844	148	3	in	in	ADP
ejpam-5844	148	4	[	[	X
ejpam-5844	148	5	11	11	NUM
ejpam-5844	148	6	]	]	PUNCT
ejpam-5844	148	7	proved	prove	VERB
ejpam-5844	148	8	that	that	SCONJ
ejpam-5844	148	9	if	if	SCONJ
ejpam-5844	148	10	a	a	DET
ejpam-5844	148	11	,	,	PUNCT
ejpam-5844	148	12	b	b	NOUN
ejpam-5844	148	13	,	,	PUNCT
ejpam-5844	148	14	y	y	PROPN
ejpam-5844	148	15	∈	∈	PROPN
ejpam-5844	148	16	mn(c	mn(c	X
ejpam-5844	148	17	)	)	PUNCT
ejpam-5844	148	18	are	be	AUX
ejpam-5844	148	19	such	such	ADJ
ejpam-5844	148	20	that	that	SCONJ
ejpam-5844	148	21	y	y	PROPN
ejpam-5844	148	22	is	be	AUX
ejpam-5844	148	23	positive	positive	ADJ
ejpam-5844	148	24	semidefinite	semidefinite	NOUN
ejpam-5844	148	25	,	,	PUNCT
ejpam-5844	148	26	then	then	ADV
ejpam-5844	148	27	sj	sj	INTJ
ejpam-5844	148	28	(	(	PUNCT
ejpam-5844	148	29	ay	ay	NOUN
ejpam-5844	148	30	b∗	b∗	ADJ
ejpam-5844	148	31	)	)	PUNCT
ejpam-5844	148	32	≤	≤	NUM
ejpam-5844	148	33	1	1	NUM
ejpam-5844	148	34	2	2	NUM
ejpam-5844	148	35	∥y	∥y	PROPN
ejpam-5844	148	36	∥	∥	PUNCT
ejpam-5844	148	37	sj	sj	NOUN
ejpam-5844	148	38	(	(	PUNCT
ejpam-5844	148	39	a∗a+b∗b	a∗a+b∗b	PROPN
ejpam-5844	148	40	)	)	PUNCT
ejpam-5844	148	41	(	(	PUNCT
ejpam-5844	148	42	10	10	NUM
ejpam-5844	148	43	)	)	PUNCT
ejpam-5844	148	44	for	for	ADP
ejpam-5844	148	45	j	j	PROPN
ejpam-5844	148	46	=	=	SYM
ejpam-5844	148	47	1	1	NUM
ejpam-5844	148	48	,	,	PUNCT
ejpam-5844	148	49	2	2	NUM
ejpam-5844	148	50	,	,	PUNCT
ejpam-5844	148	51	...	...	PUNCT
ejpam-5844	148	52	,	,	PUNCT
ejpam-5844	148	53	n.	n.	PROPN
ejpam-5844	148	54	based	base	VERB
ejpam-5844	148	55	on	on	ADP
ejpam-5844	148	56	this	this	DET
ejpam-5844	148	57	inequality	inequality	NOUN
ejpam-5844	148	58	,	,	PUNCT
ejpam-5844	148	59	we	we	PRON
ejpam-5844	148	60	have	have	VERB
ejpam-5844	148	61	the	the	DET
ejpam-5844	148	62	following	follow	VERB
ejpam-5844	148	63	lemma	lemma	PROPN
ejpam-5844	148	64	.	.	PUNCT
ejpam-5844	149	1	lemma	lemma	PROPN
ejpam-5844	149	2	5	5	X
ejpam-5844	149	3	.	.	PUNCT
ejpam-5844	150	1	let	let	VERB
ejpam-5844	150	2	a	a	DET
ejpam-5844	150	3	,	,	PUNCT
ejpam-5844	150	4	b	b	NOUN
ejpam-5844	150	5	,	,	PUNCT
ejpam-5844	150	6	y	y	PROPN
ejpam-5844	150	7	∈	∈	PROPN
ejpam-5844	150	8	mn(c	mn(c	X
ejpam-5844	150	9	)	)	PUNCT
ejpam-5844	150	10	be	be	AUX
ejpam-5844	150	11	such	such	ADJ
ejpam-5844	150	12	that	that	SCONJ
ejpam-5844	150	13	y	y	PROPN
ejpam-5844	150	14	is	be	AUX
ejpam-5844	150	15	positive	positive	ADJ
ejpam-5844	150	16	semidefinite	semidefinite	NOUN
ejpam-5844	150	17	.	.	PUNCT
ejpam-5844	151	1	then	then	ADV
ejpam-5844	151	2	sj	sj	INTJ
ejpam-5844	151	3	(	(	PUNCT
ejpam-5844	151	4	ay	ay	NOUN
ejpam-5844	151	5	b∗	b∗	ADJ
ejpam-5844	151	6	)	)	PUNCT
ejpam-5844	151	7	≤	≤	NUM
ejpam-5844	151	8	1	1	NUM
ejpam-5844	151	9	2	2	NUM
ejpam-5844	151	10	∥y	∥y	PROPN
ejpam-5844	151	11	∥	∥	PUNCT
ejpam-5844	151	12	∥a∥	∥a∥	NOUN
ejpam-5844	151	13	∥b∥	∥b∥	VERB
ejpam-5844	151	14	sj	sj	NOUN
ejpam-5844	151	15	(	(	PUNCT
ejpam-5844	151	16	a∗a	a∗a	X
ejpam-5844	151	17	∥a∥2	∥a∥2	X
ejpam-5844	151	18	+	+	CCONJ
ejpam-5844	151	19	b∗b	b∗b	PROPN
ejpam-5844	151	20	∥b∥2	∥b∥2	PROPN
ejpam-5844	151	21	)	)	PUNCT
ejpam-5844	151	22	(	(	PUNCT
ejpam-5844	151	23	11	11	NUM
ejpam-5844	151	24	)	)	PUNCT
ejpam-5844	151	25	for	for	ADP
ejpam-5844	151	26	j	j	PROPN
ejpam-5844	151	27	=	=	SYM
ejpam-5844	151	28	1	1	NUM
ejpam-5844	151	29	,	,	PUNCT
ejpam-5844	151	30	...	...	PUNCT
ejpam-5844	151	31	,	,	PUNCT
ejpam-5844	151	32	n.	n.	NOUN
ejpam-5844	151	33	proof	proof	NOUN
ejpam-5844	151	34	.	.	PUNCT
ejpam-5844	152	1	in	in	ADP
ejpam-5844	152	2	inequality	inequality	NOUN
ejpam-5844	152	3	(	(	PUNCT
ejpam-5844	152	4	10	10	NUM
ejpam-5844	152	5	)	)	PUNCT
ejpam-5844	152	6	,	,	PUNCT
ejpam-5844	152	7	replacing	replace	VERB
ejpam-5844	152	8	a	a	PRON
ejpam-5844	152	9	and	and	CCONJ
ejpam-5844	152	10	b	b	NOUN
ejpam-5844	152	11	by	by	ADP
ejpam-5844	152	12	√	√	NUM
ejpam-5844	152	13	∥b∥	∥b∥	NUM
ejpam-5844	152	14	∥a∥a	∥a∥a	PROPN
ejpam-5844	152	15	and	and	CCONJ
ejpam-5844	152	16	√	√	ADP
ejpam-5844	152	17	∥a∥	∥a∥	NOUN
ejpam-5844	152	18	∥b∥b	∥b∥b	NOUN
ejpam-5844	152	19	respectively	respectively	ADV
ejpam-5844	152	20	,	,	PUNCT
ejpam-5844	152	21	we	we	PRON
ejpam-5844	152	22	have	have	VERB
ejpam-5844	152	23	sj	sj	INTJ
ejpam-5844	152	24	(	(	PUNCT
ejpam-5844	152	25	ay	ay	NOUN
ejpam-5844	152	26	b∗	b∗	ADJ
ejpam-5844	152	27	)	)	PUNCT
ejpam-5844	152	28	≤	≤	NUM
ejpam-5844	152	29	1	1	NUM
ejpam-5844	152	30	2	2	NUM
ejpam-5844	152	31	∥y	∥y	PROPN
ejpam-5844	152	32	∥	∥	PUNCT
ejpam-5844	152	33	sj	sj	NOUN
ejpam-5844	152	34	(	(	PUNCT
ejpam-5844	152	35	∥b∥a∗a	∥b∥a∗a	PROPN
ejpam-5844	152	36	∥a∥	∥a∥	NOUN
ejpam-5844	152	37	+	+	CCONJ
ejpam-5844	153	1	∥a∥b∗b	∥a∥b∗b	PROPN
ejpam-5844	153	2	∥b∥	∥b∥	NUM
ejpam-5844	153	3	)	)	PUNCT
ejpam-5844	153	4	=	=	SYM
ejpam-5844	153	5	1	1	NUM
ejpam-5844	153	6	2	2	NUM
ejpam-5844	153	7	∥y	∥y	PROPN
ejpam-5844	153	8	∥	∥	PUNCT
ejpam-5844	153	9	∥a∥	∥a∥	NOUN
ejpam-5844	153	10	∥b∥	∥b∥	VERB
ejpam-5844	153	11	sj	sj	NOUN
ejpam-5844	153	12	(	(	PUNCT
ejpam-5844	153	13	a∗a	a∗a	X
ejpam-5844	153	14	∥a∥2	∥a∥2	X
ejpam-5844	153	15	+	+	CCONJ
ejpam-5844	153	16	b∗b	b∗b	PROPN
ejpam-5844	153	17	∥b∥2	∥b∥2	PROPN
ejpam-5844	153	18	)	)	PUNCT
ejpam-5844	153	19	,	,	PUNCT
ejpam-5844	153	20	as	as	SCONJ
ejpam-5844	153	21	required	require	VERB
ejpam-5844	153	22	.	.	PUNCT
ejpam-5844	154	1	theorem	theorem	ADJ
ejpam-5844	154	2	4	4	NUM
ejpam-5844	154	3	.	.	PUNCT
ejpam-5844	155	1	let	let	VERB
ejpam-5844	155	2	a	a	DET
ejpam-5844	155	3	,	,	PUNCT
ejpam-5844	155	4	b	b	NOUN
ejpam-5844	155	5	,	,	PUNCT
ejpam-5844	155	6	c	c	NOUN
ejpam-5844	155	7	,	,	PUNCT
ejpam-5844	155	8	d	d	NOUN
ejpam-5844	155	9	,	,	PUNCT
ejpam-5844	155	10	e	e	NOUN
ejpam-5844	155	11	,	,	PUNCT
ejpam-5844	155	12	f	f	PROPN
ejpam-5844	155	13	∈	∈	PROPN
ejpam-5844	155	14	mn(c	mn(c	X
ejpam-5844	155	15	)	)	PUNCT
ejpam-5844	155	16	be	be	AUX
ejpam-5844	155	17	such	such	ADJ
ejpam-5844	155	18	that	that	SCONJ
ejpam-5844	155	19	c	c	PROPN
ejpam-5844	156	1	and	and	CCONJ
ejpam-5844	156	2	d	d	NOUN
ejpam-5844	156	3	are	be	AUX
ejpam-5844	156	4	positive	positive	ADJ
ejpam-5844	156	5	semidefinite	semidefinite	NOUN
ejpam-5844	156	6	.	.	PUNCT
ejpam-5844	157	1	then	then	ADV
ejpam-5844	157	2	for	for	ADP
ejpam-5844	157	3	j	j	PROPN
ejpam-5844	157	4	=	=	SYM
ejpam-5844	157	5	1	1	NUM
ejpam-5844	157	6	,	,	PUNCT
ejpam-5844	157	7	...	...	PUNCT
ejpam-5844	157	8	,	,	PUNCT
ejpam-5844	157	9	2n	2n	NUM
ejpam-5844	157	10	,	,	PUNCT
ejpam-5844	157	11	we	we	PRON
ejpam-5844	157	12	have	have	VERB
ejpam-5844	157	13	sj	sj	INTJ
ejpam-5844	157	14	(	(	PUNCT
ejpam-5844	157	15	(	(	PUNCT
ejpam-5844	157	16	ace∗	ace∗	NOUN
ejpam-5844	157	17	+	+	PROPN
ejpam-5844	157	18	bdf	bdf	NOUN
ejpam-5844	157	19	∗)⊕	∗)⊕	ADP
ejpam-5844	157	20	0	0	NUM
ejpam-5844	157	21	)	)	PUNCT
ejpam-5844	157	22	≤	≤	NUM
ejpam-5844	157	23	max	max	NOUN
ejpam-5844	157	24	(	(	PUNCT
ejpam-5844	157	25	∥c∥	∥c∥	X
ejpam-5844	157	26	,	,	PUNCT
ejpam-5844	157	27	∥d∥	∥d∥	NOUN
ejpam-5844	157	28	)	)	PUNCT
ejpam-5844	157	29	2	2	NUM
ejpam-5844	157	30	√	√	NUM
ejpam-5844	157	31	k1k2	k1k2	PROPN
ejpam-5844	157	32	sj	sj	INTJ
ejpam-5844	157	33	(	(	PUNCT
ejpam-5844	157	34	[	[	PUNCT
ejpam-5844	157	35	k2a	k2a	X
ejpam-5844	157	36	∗a+	∗a+	X
ejpam-5844	158	1	k1e	k1e	PROPN
ejpam-5844	158	2	∗e	∗e	PROPN
ejpam-5844	158	3	k2a	k2a	VERB
ejpam-5844	159	1	∗b	∗b	X
ejpam-5844	159	2	+	+	CCONJ
ejpam-5844	159	3	k1e	k1e	PROPN
ejpam-5844	159	4	∗f	∗f	PROPN
ejpam-5844	159	5	k2b	k2b	PROPN
ejpam-5844	159	6	∗a+	∗a+	NUM
ejpam-5844	159	7	k1f	k1f	PROPN
ejpam-5844	159	8	∗e	∗e	PROPN
ejpam-5844	159	9	k2b	k2b	PROPN
ejpam-5844	160	1	∗b	∗b	PROPN
ejpam-5844	160	2	+	+	CCONJ
ejpam-5844	160	3	k1f	k1f	PROPN
ejpam-5844	160	4	∗f	∗f	PROPN
ejpam-5844	160	5	]	]	PUNCT
ejpam-5844	160	6	)	)	PUNCT
ejpam-5844	160	7	,	,	PUNCT
ejpam-5844	160	8	(	(	PUNCT
ejpam-5844	160	9	12	12	NUM
ejpam-5844	160	10	)	)	PUNCT
ejpam-5844	161	1	where	where	SCONJ
ejpam-5844	161	2	k1	k1	NOUN
ejpam-5844	161	3	=	=	PUNCT
ejpam-5844	161	4	∥aa∗	∥aa∗	X
ejpam-5844	161	5	+	+	ADJ
ejpam-5844	161	6	bb∗∥	bb∗∥	NOUN
ejpam-5844	161	7	and	and	CCONJ
ejpam-5844	161	8	k2	k2	PROPN
ejpam-5844	161	9	=	=	PROPN
ejpam-5844	161	10	∥ee∗	∥ee∗	PROPN
ejpam-5844	161	11	+	+	CCONJ
ejpam-5844	161	12	ff	ff	PROPN
ejpam-5844	161	13	∗∥	∗∥	PUNCT
ejpam-5844	161	14	.	.	PUNCT
ejpam-5844	162	1	proof	proof	NOUN
ejpam-5844	162	2	.	.	PUNCT
ejpam-5844	163	1	let	let	VERB
ejpam-5844	163	2	t1	t1	NOUN
ejpam-5844	163	3	=	=	PUNCT
ejpam-5844	164	1	[	[	PUNCT
ejpam-5844	164	2	a	a	DET
ejpam-5844	164	3	b	b	NOUN
ejpam-5844	164	4	0	0	NUM
ejpam-5844	164	5	0	0	NUM
ejpam-5844	164	6	]	]	PUNCT
ejpam-5844	164	7	,	,	PUNCT
ejpam-5844	164	8	t2	t2	NOUN
ejpam-5844	164	9	=	=	PUNCT
ejpam-5844	164	10	[	[	PUNCT
ejpam-5844	164	11	c	c	NOUN
ejpam-5844	164	12	0	0	NUM
ejpam-5844	164	13	0	0	NUM
ejpam-5844	164	14	d	d	NOUN
ejpam-5844	164	15	]	]	X
ejpam-5844	164	16	,	,	PUNCT
ejpam-5844	164	17	and	and	CCONJ
ejpam-5844	164	18	t3	t3	NOUN
ejpam-5844	164	19	=	=	PUNCT
ejpam-5844	165	1	[	[	PUNCT
ejpam-5844	165	2	e	e	X
ejpam-5844	165	3	f	f	X
ejpam-5844	165	4	0	0	NUM
ejpam-5844	165	5	0	0	NUM
ejpam-5844	165	6	]	]	PUNCT
ejpam-5844	165	7	.	.	PUNCT
ejpam-5844	166	1	then	then	ADV
ejpam-5844	166	2	∥t1∥	∥t1∥	PROPN
ejpam-5844	166	3	=	=	PUNCT
ejpam-5844	166	4	√	√	NUM
ejpam-5844	166	5	∥t1	∥t1	NOUN
ejpam-5844	166	6	t	t	NOUN
ejpam-5844	166	7	∗	∗	NOUN
ejpam-5844	166	8	1	1	NUM
ejpam-5844	166	9	∥	∥	NOUN
ejpam-5844	166	10	=	=	PUNCT
ejpam-5844	166	11	√	√	ADP
ejpam-5844	166	12	∥aa∗	∥aa∗	NOUN
ejpam-5844	167	1	+	+	ADJ
ejpam-5844	167	2	bb∗∥	bb∗∥	NOUN
ejpam-5844	167	3	=	=	SYM
ejpam-5844	167	4	√	√	NUM
ejpam-5844	167	5	k1	k1	NOUN
ejpam-5844	167	6	,	,	PUNCT
ejpam-5844	167	7	∥t3∥	∥t3∥	PROPN
ejpam-5844	167	8	=	=	PUNCT
ejpam-5844	167	9	√	√	NUM
ejpam-5844	167	10	∥t3	∥t3	NOUN
ejpam-5844	167	11	t	t	PROPN
ejpam-5844	167	12	∗	∗	NOUN
ejpam-5844	167	13	3	3	NUM
ejpam-5844	167	14	∥	∥	NOUN
ejpam-5844	167	15	=	=	SYM
ejpam-5844	167	16	√	√	NUM
ejpam-5844	167	17	∥ee∗	∥ee∗	NOUN
ejpam-5844	167	18	+	+	CCONJ
ejpam-5844	167	19	ff	ff	PROPN
ejpam-5844	167	20	∗∥	∗∥	PRON
ejpam-5844	167	21	=	=	SYM
ejpam-5844	167	22	√	√	PROPN
ejpam-5844	167	23	k2	k2	PROPN
ejpam-5844	167	24	a.	a.	PROPN
ejpam-5844	167	25	al	al	PROPN
ejpam-5844	167	26	-	-	PUNCT
ejpam-5844	167	27	natoor	natoor	NOUN
ejpam-5844	167	28	,	,	PUNCT
ejpam-5844	167	29	r.	r.	PROPN
ejpam-5844	167	30	al	al	PROPN
ejpam-5844	167	31	-	-	PUNCT
ejpam-5844	167	32	smadi	smadi	PROPN
ejpam-5844	167	33	,	,	PUNCT
ejpam-5844	167	34	a.	a.	NOUN
ejpam-5844	167	35	burqan	burqan	PROPN
ejpam-5844	167	36	/	/	SYM
ejpam-5844	167	37	eur	eur	PROPN
ejpam-5844	167	38	.	.	PUNCT
ejpam-5844	168	1	j.	j.	PROPN
ejpam-5844	168	2	pure	pure	PROPN
ejpam-5844	168	3	appl	appl	PROPN
ejpam-5844	168	4	.	.	PROPN
ejpam-5844	168	5	math	math	PROPN
ejpam-5844	168	6	,	,	PUNCT
ejpam-5844	168	7	18	18	NUM
ejpam-5844	168	8	(	(	PUNCT
ejpam-5844	168	9	2	2	NUM
ejpam-5844	168	10	)	)	PUNCT
ejpam-5844	168	11	(	(	PUNCT
ejpam-5844	168	12	2025	2025	NUM
ejpam-5844	168	13	)	)	PUNCT
ejpam-5844	168	14	,	,	PUNCT
ejpam-5844	168	15	5844	5844	NUM
ejpam-5844	168	16	8	8	NUM
ejpam-5844	168	17	of	of	ADP
ejpam-5844	168	18	10	10	NUM
ejpam-5844	168	19	and	and	CCONJ
ejpam-5844	168	20	∥t2∥	∥t2∥	PROPN
ejpam-5844	168	21	=	=	SYM
ejpam-5844	168	22	max	max	PROPN
ejpam-5844	168	23	(	(	PUNCT
ejpam-5844	168	24	∥c∥	∥c∥	X
ejpam-5844	168	25	,	,	PUNCT
ejpam-5844	168	26	∥d∥	∥d∥	NOUN
ejpam-5844	168	27	)	)	PUNCT
ejpam-5844	168	28	.	.	PUNCT
ejpam-5844	169	1	so	so	ADV
ejpam-5844	169	2	,	,	PUNCT
ejpam-5844	169	3	sj	sj	INTJ
ejpam-5844	169	4	(	(	PUNCT
ejpam-5844	169	5	ace∗	ace∗	NOUN
ejpam-5844	169	6	+	+	PROPN
ejpam-5844	169	7	bdf	bdf	NOUN
ejpam-5844	169	8	∗	∗	NOUN
ejpam-5844	169	9	⊕	⊕	PROPN
ejpam-5844	169	10	0	0	NUM
ejpam-5844	169	11	)	)	PUNCT
ejpam-5844	170	1	=	=	PRON
ejpam-5844	170	2	sj	sj	INTJ
ejpam-5844	170	3	(	(	PUNCT
ejpam-5844	170	4	t1t2	t1t2	ADP
ejpam-5844	170	5	t	t	PROPN
ejpam-5844	170	6	∗	∗	X
ejpam-5844	170	7	3	3	NUM
ejpam-5844	170	8	)	)	PUNCT
ejpam-5844	170	9	≤	≤	NUM
ejpam-5844	170	10	1	1	NUM
ejpam-5844	170	11	2	2	NUM
ejpam-5844	170	12	∥t1∥	∥t1∥	PROPN
ejpam-5844	170	13	∥t2∥	∥t2∥	PROPN
ejpam-5844	170	14	∥t3∥	∥t3∥	PROPN
ejpam-5844	170	15	sj	sj	PROPN
ejpam-5844	170	16	(	(	PUNCT
ejpam-5844	170	17	t	t	PROPN
ejpam-5844	170	18	∗	∗	PROPN
ejpam-5844	170	19	1	1	NUM
ejpam-5844	170	20	t1	t1	NOUN
ejpam-5844	170	21	∥t1∥2	∥t1∥2	PROPN
ejpam-5844	171	1	+	+	PROPN
ejpam-5844	172	1	t	t	PROPN
ejpam-5844	172	2	∗	∗	NOUN
ejpam-5844	172	3	3	3	NUM
ejpam-5844	172	4	t3	t3	PROPN
ejpam-5844	172	5	∥t3∥2	∥t3∥2	PROPN
ejpam-5844	172	6	)	)	PUNCT
ejpam-5844	173	1	=	=	PUNCT
ejpam-5844	173	2	1	1	NUM
ejpam-5844	173	3	2	2	NUM
ejpam-5844	173	4	√	√	NUM
ejpam-5844	173	5	k1k2max	k1k2max	PRON
ejpam-5844	173	6	(	(	PUNCT
ejpam-5844	173	7	∥c∥	∥c∥	X
ejpam-5844	173	8	,	,	PUNCT
ejpam-5844	173	9	∥d∥	∥d∥	NOUN
ejpam-5844	173	10	)	)	PUNCT
ejpam-5844	173	11	sj	sj	PART
ejpam-5844	173	12			PROPN
ejpam-5844	173	13	[	[	PUNCT
ejpam-5844	173	14	a∗a	a∗a	X
ejpam-5844	173	15	a∗b	a∗b	NUM
ejpam-5844	173	16	b∗a	b∗a	X
ejpam-5844	173	17	bb	bb	NOUN
ejpam-5844	173	18	]	]	PUNCT
ejpam-5844	173	19	k1	k1	NOUN
ejpam-5844	174	1	+	+	CCONJ
ejpam-5844	174	2	[	[	PUNCT
ejpam-5844	174	3	e∗e	e∗e	NUM
ejpam-5844	174	4	e∗f	e∗f	NUM
ejpam-5844	174	5	f	f	PROPN
ejpam-5844	174	6	∗e	∗e	NOUN
ejpam-5844	174	7	f	f	PROPN
ejpam-5844	174	8	∗f	∗f	PROPN
ejpam-5844	174	9	]	]	PUNCT
ejpam-5844	174	10	k2	k2	ADJ
ejpam-5844	174	11			NOUN
ejpam-5844	174	12	=	=	NOUN
ejpam-5844	174	13	1	1	NUM
ejpam-5844	174	14	2	2	NUM
ejpam-5844	174	15	√	√	NUM
ejpam-5844	174	16	k1k2max	k1k2max	PRON
ejpam-5844	174	17	(	(	PUNCT
ejpam-5844	174	18	∥c∥	∥c∥	X
ejpam-5844	174	19	,	,	PUNCT
ejpam-5844	174	20	∥d∥	∥d∥	NOUN
ejpam-5844	174	21	)	)	PUNCT
ejpam-5844	174	22	sj	sj	VERB
ejpam-5844	174	23	k2	k2	PROPN
ejpam-5844	174	24	[	[	PUNCT
ejpam-5844	174	25	a∗a	a∗a	NUM
ejpam-5844	174	26	a∗b	a∗b	NUM
ejpam-5844	174	27	b∗a	b∗a	X
ejpam-5844	174	28	b∗b	b∗b	X
ejpam-5844	174	29	]	]	PUNCT
ejpam-5844	174	30	+	+	CCONJ
ejpam-5844	174	31	k1	k1	X
ejpam-5844	174	32	[	[	PUNCT
ejpam-5844	174	33	e∗e	e∗e	NUM
ejpam-5844	174	34	e∗f	e∗f	NUM
ejpam-5844	174	35	f	f	PROPN
ejpam-5844	174	36	∗e	∗e	NOUN
ejpam-5844	174	37	f	f	PROPN
ejpam-5844	174	38	∗f	∗f	PROPN
ejpam-5844	174	39	]	]	PUNCT
ejpam-5844	174	40	k1k2	k1k2	PROPN
ejpam-5844	174	41			PROPN
ejpam-5844	174	42	=	=	SYM
ejpam-5844	174	43	max	max	PROPN
ejpam-5844	174	44	(	(	PUNCT
ejpam-5844	174	45	∥c∥	∥c∥	X
ejpam-5844	174	46	,	,	PUNCT
ejpam-5844	174	47	∥d∥	∥d∥	NOUN
ejpam-5844	174	48	)	)	PUNCT
ejpam-5844	174	49	2	2	NUM
ejpam-5844	175	1	√	√	NUM
ejpam-5844	176	1	k1k2	k1k2	PROPN
ejpam-5844	176	2	sj	sj	INTJ
ejpam-5844	176	3	(	(	PUNCT
ejpam-5844	176	4	[	[	PUNCT
ejpam-5844	176	5	k2a	k2a	X
ejpam-5844	176	6	∗a+	∗a+	X
ejpam-5844	177	1	k1e	k1e	PROPN
ejpam-5844	177	2	∗e	∗e	PROPN
ejpam-5844	177	3	k2a	k2a	VERB
ejpam-5844	178	1	∗b	∗b	X
ejpam-5844	178	2	+	+	CCONJ
ejpam-5844	178	3	k1e	k1e	PROPN
ejpam-5844	178	4	∗f	∗f	PROPN
ejpam-5844	178	5	k2b	k2b	PROPN
ejpam-5844	178	6	∗a+	∗a+	NUM
ejpam-5844	178	7	k1f	k1f	PROPN
ejpam-5844	178	8	∗e	∗e	PROPN
ejpam-5844	178	9	k2b	k2b	PROPN
ejpam-5844	179	1	∗b	∗b	PROPN
ejpam-5844	179	2	+	+	CCONJ
ejpam-5844	179	3	k1f	k1f	PROPN
ejpam-5844	179	4	∗f	∗f	PROPN
ejpam-5844	179	5	]	]	PUNCT
ejpam-5844	179	6	)	)	PUNCT
ejpam-5844	179	7	,	,	PUNCT
ejpam-5844	179	8	as	as	SCONJ
ejpam-5844	179	9	required	require	VERB
ejpam-5844	179	10	.	.	PUNCT
ejpam-5844	180	1	corollary	corollary	ADJ
ejpam-5844	180	2	3	3	X
ejpam-5844	180	3	.	.	PUNCT
ejpam-5844	181	1	let	let	VERB
ejpam-5844	181	2	a	a	DET
ejpam-5844	181	3	,	,	PUNCT
ejpam-5844	181	4	b	b	NOUN
ejpam-5844	181	5	,	,	PUNCT
ejpam-5844	181	6	c	c	NOUN
ejpam-5844	181	7	,	,	PUNCT
ejpam-5844	181	8	d	d	PROPN
ejpam-5844	181	9	∈	∈	PROPN
ejpam-5844	181	10	mn(c	mn(c	X
ejpam-5844	181	11	)	)	PUNCT
ejpam-5844	181	12	be	be	AUX
ejpam-5844	181	13	such	such	ADJ
ejpam-5844	181	14	that	that	SCONJ
ejpam-5844	181	15	c	c	PROPN
ejpam-5844	182	1	and	and	CCONJ
ejpam-5844	182	2	d	d	NOUN
ejpam-5844	182	3	are	be	AUX
ejpam-5844	182	4	positive	positive	ADJ
ejpam-5844	182	5	semidefinite	semidefinite	NOUN
ejpam-5844	182	6	.	.	PUNCT
ejpam-5844	183	1	then	then	ADV
ejpam-5844	183	2	for	for	ADP
ejpam-5844	183	3	j	j	PROPN
ejpam-5844	183	4	=	=	SYM
ejpam-5844	183	5	1	1	NUM
ejpam-5844	183	6	,	,	PUNCT
ejpam-5844	183	7	...	...	PUNCT
ejpam-5844	183	8	,	,	PUNCT
ejpam-5844	183	9	2n	2n	NUM
ejpam-5844	183	10	,	,	PUNCT
ejpam-5844	183	11	we	we	PRON
ejpam-5844	183	12	have	have	VERB
ejpam-5844	183	13	sj	sj	INTJ
ejpam-5844	183	14	(	(	PUNCT
ejpam-5844	183	15	(	(	PUNCT
ejpam-5844	183	16	acb∗	acb∗	X
ejpam-5844	183	17	+	+	ADJ
ejpam-5844	183	18	bda∗)⊕	bda∗)⊕	X
ejpam-5844	183	19	0	0	NUM
ejpam-5844	183	20	)	)	PUNCT
ejpam-5844	183	21	≤	≤	NUM
ejpam-5844	183	22	max	max	NOUN
ejpam-5844	183	23	(	(	PUNCT
ejpam-5844	183	24	∥c∥	∥c∥	X
ejpam-5844	183	25	,	,	PUNCT
ejpam-5844	183	26	∥d∥	∥d∥	NOUN
ejpam-5844	183	27	)	)	PUNCT
ejpam-5844	183	28	2	2	NUM
ejpam-5844	183	29	s2j	s2j	NOUN
ejpam-5844	183	30	(	(	PUNCT
ejpam-5844	183	31	[	[	PUNCT
ejpam-5844	183	32	a	a	PRON
ejpam-5844	183	33	b	b	PROPN
ejpam-5844	183	34	b	b	PROPN
ejpam-5844	183	35	a	a	PRON
ejpam-5844	183	36	]	]	X
ejpam-5844	183	37	)	)	PUNCT
ejpam-5844	183	38	.	.	PUNCT
ejpam-5844	184	1	in	in	ADP
ejpam-5844	184	2	particular	particular	ADJ
ejpam-5844	184	3	,	,	PUNCT
ejpam-5844	184	4	if	if	SCONJ
ejpam-5844	184	5	c	c	NOUN
ejpam-5844	184	6	=	=	SYM
ejpam-5844	185	1	d	d	PROPN
ejpam-5844	185	2	=	=	SYM
ejpam-5844	185	3	i	i	PROPN
ejpam-5844	185	4	,	,	PUNCT
ejpam-5844	185	5	we	we	PRON
ejpam-5844	185	6	have	have	AUX
ejpam-5844	185	7	sj	sj	INTJ
ejpam-5844	185	8	(	(	PUNCT
ejpam-5844	185	9	(	(	PUNCT
ejpam-5844	185	10	re	re	X
ejpam-5844	185	11	(	(	PUNCT
ejpam-5844	185	12	ab	ab	PROPN
ejpam-5844	185	13	∗))⊕	∗))⊕	NOUN
ejpam-5844	185	14	0	0	NUM
ejpam-5844	185	15	)	)	PUNCT
ejpam-5844	185	16	≤	≤	NUM
ejpam-5844	185	17	1	1	NUM
ejpam-5844	185	18	4	4	NUM
ejpam-5844	185	19	s2j	s2j	NOUN
ejpam-5844	185	20	(	(	PUNCT
ejpam-5844	185	21	[	[	PUNCT
ejpam-5844	185	22	a	a	PRON
ejpam-5844	185	23	b	b	PROPN
ejpam-5844	185	24	b	b	PROPN
ejpam-5844	185	25	a	a	DET
ejpam-5844	185	26	]	]	X
ejpam-5844	185	27	)	)	PUNCT
ejpam-5844	185	28	where	where	SCONJ
ejpam-5844	185	29	re(t	re(t	PUNCT
ejpam-5844	185	30	)	)	PUNCT
ejpam-5844	185	31	=	=	SYM
ejpam-5844	185	32	t+t	t+t	NUM
ejpam-5844	185	33	∗	∗	NOUN
ejpam-5844	185	34	2	2	NUM
ejpam-5844	185	35	denotes	denote	NOUN
ejpam-5844	185	36	the	the	DET
ejpam-5844	185	37	real	real	ADJ
ejpam-5844	185	38	part	part	NOUN
ejpam-5844	185	39	of	of	ADP
ejpam-5844	185	40	t	t	PROPN
ejpam-5844	185	41	∈	∈	PROPN
ejpam-5844	185	42	mn(c	mn(c	X
ejpam-5844	185	43	)	)	PUNCT
ejpam-5844	185	44	.	.	PUNCT
ejpam-5844	186	1	proof	proof	NOUN
ejpam-5844	186	2	.	.	PUNCT
ejpam-5844	187	1	letting	let	VERB
ejpam-5844	187	2	e	e	PROPN
ejpam-5844	187	3	=	=	SYM
ejpam-5844	187	4	b	b	PROPN
ejpam-5844	187	5	and	and	CCONJ
ejpam-5844	187	6	f	f	PROPN
ejpam-5844	188	1	=	=	NOUN
ejpam-5844	188	2	a	a	PRON
ejpam-5844	188	3	in	in	ADP
ejpam-5844	188	4	inequality	inequality	NOUN
ejpam-5844	188	5	(	(	PUNCT
ejpam-5844	188	6	12	12	NUM
ejpam-5844	188	7	)	)	PUNCT
ejpam-5844	188	8	,	,	PUNCT
ejpam-5844	188	9	we	we	PRON
ejpam-5844	188	10	have	have	VERB
ejpam-5844	188	11	sj	sj	INTJ
ejpam-5844	188	12	(	(	PUNCT
ejpam-5844	188	13	(	(	PUNCT
ejpam-5844	188	14	acb∗	acb∗	X
ejpam-5844	188	15	+	+	ADJ
ejpam-5844	188	16	bda∗)⊕	bda∗)⊕	X
ejpam-5844	188	17	0	0	NUM
ejpam-5844	188	18	)	)	PUNCT
ejpam-5844	188	19	≤	≤	NUM
ejpam-5844	188	20	max	max	NOUN
ejpam-5844	188	21	(	(	PUNCT
ejpam-5844	188	22	∥c∥	∥c∥	X
ejpam-5844	188	23	,	,	PUNCT
ejpam-5844	188	24	∥d∥	∥d∥	NOUN
ejpam-5844	188	25	)	)	PUNCT
ejpam-5844	188	26	2k1	2k1	NUM
ejpam-5844	189	1	sj	sj	INTJ
ejpam-5844	189	2	(	(	PUNCT
ejpam-5844	189	3	[	[	PUNCT
ejpam-5844	189	4	k1a	k1a	PROPN
ejpam-5844	189	5	∗a+	∗a+	NUM
ejpam-5844	189	6	k1b	k1b	PROPN
ejpam-5844	189	7	∗b	∗b	PROPN
ejpam-5844	189	8	k1a	k1a	PROPN
ejpam-5844	189	9	∗b	∗b	PROPN
ejpam-5844	189	10	+	+	CCONJ
ejpam-5844	189	11	k1b	k1b	X
ejpam-5844	189	12	∗a	∗a	ADJ
ejpam-5844	189	13	k1b	k1b	PROPN
ejpam-5844	189	14	∗a+	∗a+	PROPN
ejpam-5844	189	15	k1a	k1a	PROPN
ejpam-5844	189	16	∗b	∗b	PROPN
ejpam-5844	189	17	k1b	k1b	PROPN
ejpam-5844	190	1	∗b	∗b	PROPN
ejpam-5844	190	2	+	+	CCONJ
ejpam-5844	190	3	k1a	k1a	ADJ
ejpam-5844	190	4	∗a	∗a	ADJ
ejpam-5844	190	5	]	]	PUNCT
ejpam-5844	190	6	)	)	PUNCT
ejpam-5844	190	7	=	=	SYM
ejpam-5844	190	8	max	max	PROPN
ejpam-5844	190	9	(	(	PUNCT
ejpam-5844	190	10	∥c∥	∥c∥	X
ejpam-5844	190	11	,	,	PUNCT
ejpam-5844	190	12	∥d∥	∥d∥	NOUN
ejpam-5844	190	13	)	)	PUNCT
ejpam-5844	190	14	2	2	NUM
ejpam-5844	190	15	sj	sj	INTJ
ejpam-5844	190	16	(	(	PUNCT
ejpam-5844	190	17	[	[	PUNCT
ejpam-5844	190	18	a∗a+b∗b	a∗a+b∗b	NOUN
ejpam-5844	190	19	a∗b	a∗b	CCONJ
ejpam-5844	190	20	+	+	ADV
ejpam-5844	190	21	b∗a	b∗a	X
ejpam-5844	190	22	b∗a+a∗b	b∗a+a∗b	NOUN
ejpam-5844	190	23	b∗b	b∗b	NOUN
ejpam-5844	190	24	+	+	NOUN
ejpam-5844	190	25	a∗a	a∗a	X
ejpam-5844	190	26	]	]	PUNCT
ejpam-5844	190	27	)	)	PUNCT
ejpam-5844	190	28	a.	a.	PROPN
ejpam-5844	190	29	al	al	PROPN
ejpam-5844	190	30	-	-	PUNCT
ejpam-5844	190	31	natoor	natoor	NOUN
ejpam-5844	190	32	,	,	PUNCT
ejpam-5844	190	33	r.	r.	PROPN
ejpam-5844	190	34	al	al	PROPN
ejpam-5844	190	35	-	-	PUNCT
ejpam-5844	190	36	smadi	smadi	PROPN
ejpam-5844	190	37	,	,	PUNCT
ejpam-5844	190	38	a.	a.	NOUN
ejpam-5844	190	39	burqan	burqan	PROPN
ejpam-5844	190	40	/	/	SYM
ejpam-5844	190	41	eur	eur	PROPN
ejpam-5844	190	42	.	.	PUNCT
ejpam-5844	191	1	j.	j.	PROPN
ejpam-5844	191	2	pure	pure	PROPN
ejpam-5844	191	3	appl	appl	PROPN
ejpam-5844	191	4	.	.	PROPN
ejpam-5844	191	5	math	math	PROPN
ejpam-5844	191	6	,	,	PUNCT
ejpam-5844	191	7	18	18	NUM
ejpam-5844	191	8	(	(	PUNCT
ejpam-5844	191	9	2	2	NUM
ejpam-5844	191	10	)	)	PUNCT
ejpam-5844	191	11	(	(	PUNCT
ejpam-5844	191	12	2025	2025	NUM
ejpam-5844	191	13	)	)	PUNCT
ejpam-5844	191	14	,	,	PUNCT
ejpam-5844	191	15	5844	5844	NUM
ejpam-5844	191	16	9	9	NUM
ejpam-5844	191	17	of	of	ADP
ejpam-5844	191	18	10	10	NUM
ejpam-5844	191	19	=	=	SYM
ejpam-5844	191	20	max	max	X
ejpam-5844	191	21	(	(	PUNCT
ejpam-5844	191	22	∥c∥	∥c∥	X
ejpam-5844	191	23	,	,	PUNCT
ejpam-5844	191	24	∥d∥	∥d∥	NOUN
ejpam-5844	191	25	)	)	PUNCT
ejpam-5844	191	26	2	2	NUM
ejpam-5844	191	27	sj	sj	INTJ
ejpam-5844	191	28	(	(	PUNCT
ejpam-5844	191	29	[	[	PUNCT
ejpam-5844	191	30	a∗	a∗	ADJ
ejpam-5844	191	31	b∗	b∗	ADJ
ejpam-5844	191	32	b∗	b∗	ADJ
ejpam-5844	191	33	a∗	a∗	NOUN
ejpam-5844	191	34	]	]	PUNCT
ejpam-5844	191	35	[	[	PUNCT
ejpam-5844	191	36	a	a	PRON
ejpam-5844	191	37	b	b	PROPN
ejpam-5844	191	38	b	b	PROPN
ejpam-5844	191	39	a	a	PRON
ejpam-5844	191	40	]	]	X
ejpam-5844	191	41	)	)	PUNCT
ejpam-5844	192	1	=	=	SYM
ejpam-5844	192	2	max	max	PROPN
ejpam-5844	192	3	(	(	PUNCT
ejpam-5844	192	4	∥c∥	∥c∥	X
ejpam-5844	192	5	,	,	PUNCT
ejpam-5844	192	6	∥d∥	∥d∥	NOUN
ejpam-5844	192	7	)	)	PUNCT
ejpam-5844	192	8	2	2	NUM
ejpam-5844	192	9	sj	sj	NOUN
ejpam-5844	192	10	(	(	PUNCT
ejpam-5844	192	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5844	192	12	[	[	PUNCT
ejpam-5844	192	13	a	a	DET
ejpam-5844	192	14	b	b	PROPN
ejpam-5844	192	15	b	b	PROPN
ejpam-5844	192	16	a	a	DET
ejpam-5844	192	17	]	]	X
ejpam-5844	192	18	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-5844	192	19	)	)	PUNCT
ejpam-5844	193	1	=	=	SYM
ejpam-5844	193	2	max	max	PROPN
ejpam-5844	193	3	(	(	PUNCT
ejpam-5844	193	4	∥c∥	∥c∥	X
ejpam-5844	193	5	,	,	PUNCT
ejpam-5844	193	6	∥d∥	∥d∥	NOUN
ejpam-5844	193	7	)	)	PUNCT
ejpam-5844	193	8	2	2	NUM
ejpam-5844	193	9	s2j	s2j	NOUN
ejpam-5844	193	10	(	(	PUNCT
ejpam-5844	193	11	[	[	PUNCT
ejpam-5844	193	12	a	a	PRON
ejpam-5844	193	13	b	b	PROPN
ejpam-5844	193	14	b	b	PROPN
ejpam-5844	193	15	a	a	PRON
ejpam-5844	193	16	]	]	X
ejpam-5844	193	17	)	)	PUNCT
ejpam-5844	193	18	=	=	SYM
ejpam-5844	193	19	max	max	PROPN
ejpam-5844	193	20	(	(	PUNCT
ejpam-5844	193	21	∥c∥	∥c∥	X
ejpam-5844	193	22	,	,	PUNCT
ejpam-5844	193	23	∥d∥	∥d∥	NOUN
ejpam-5844	193	24	)	)	PUNCT
ejpam-5844	193	25	2	2	NUM
ejpam-5844	193	26	s2j	s2j	NOUN
ejpam-5844	193	27	(	(	PUNCT
ejpam-5844	193	28	[	[	PUNCT
ejpam-5844	193	29	a	a	PRON
ejpam-5844	193	30	b	b	PROPN
ejpam-5844	193	31	b	b	PROPN
ejpam-5844	193	32	a	a	PRON
ejpam-5844	193	33	]	]	X
ejpam-5844	193	34	)	)	PUNCT
ejpam-5844	193	35	.	.	PUNCT
ejpam-5844	194	1	we	we	PRON
ejpam-5844	194	2	end	end	VERB
ejpam-5844	194	3	this	this	DET
ejpam-5844	194	4	paper	paper	NOUN
ejpam-5844	194	5	by	by	ADP
ejpam-5844	194	6	the	the	DET
ejpam-5844	194	7	following	follow	VERB
ejpam-5844	194	8	result	result	NOUN
ejpam-5844	194	9	,	,	PUNCT
ejpam-5844	194	10	which	which	PRON
ejpam-5844	194	11	gives	give	VERB
ejpam-5844	194	12	a	a	DET
ejpam-5844	194	13	lower	low	ADJ
ejpam-5844	194	14	bound	bind	VERB
ejpam-5844	194	15	for	for	ADP
ejpam-5844	194	16	singular	singular	ADJ
ejpam-5844	194	17	values	value	NOUN
ejpam-5844	194	18	of	of	ADP
ejpam-5844	194	19	products	product	NOUN
ejpam-5844	194	20	and	and	CCONJ
ejpam-5844	194	21	sums	sum	NOUN
ejpam-5844	194	22	of	of	ADP
ejpam-5844	194	23	matrices	matrix	NOUN
ejpam-5844	194	24	lemma	lemma	PROPN
ejpam-5844	194	25	6	6	NUM
ejpam-5844	194	26	.	.	PUNCT
ejpam-5844	195	1	[	[	X
ejpam-5844	195	2	12]let	12]let	NUM
ejpam-5844	195	3	a	a	PRON
ejpam-5844	195	4	,	,	PUNCT
ejpam-5844	195	5	b	b	X
ejpam-5844	195	6	∈	∈	NOUN
ejpam-5844	195	7	mn(c	mn(c	X
ejpam-5844	195	8	)	)	PUNCT
ejpam-5844	195	9	.	.	PUNCT
ejpam-5844	196	1	then	then	ADV
ejpam-5844	196	2	for	for	ADP
ejpam-5844	196	3	j	j	PROPN
ejpam-5844	196	4	=	=	SYM
ejpam-5844	196	5	1	1	NUM
ejpam-5844	196	6	,	,	PUNCT
ejpam-5844	196	7	...	...	PUNCT
ejpam-5844	196	8	,	,	PUNCT
ejpam-5844	196	9	n	n	CCONJ
ejpam-5844	196	10	,	,	PUNCT
ejpam-5844	196	11	we	we	PRON
ejpam-5844	196	12	have	have	VERB
ejpam-5844	196	13	sj	sj	INTJ
ejpam-5844	196	14	(	(	PUNCT
ejpam-5844	196	15	ab	ab	PROPN
ejpam-5844	196	16	)	)	PUNCT
ejpam-5844	196	17	≥	≥	PROPN
ejpam-5844	196	18	sn	sn	PROPN
ejpam-5844	196	19	(	(	PUNCT
ejpam-5844	196	20	a	a	X
ejpam-5844	196	21	)	)	PUNCT
ejpam-5844	196	22	sj	sj	NOUN
ejpam-5844	196	23	(	(	PUNCT
ejpam-5844	196	24	b	b	NOUN
ejpam-5844	196	25	)	)	PUNCT
ejpam-5844	196	26	(	(	PUNCT
ejpam-5844	196	27	13	13	NUM
ejpam-5844	196	28	)	)	PUNCT
ejpam-5844	196	29	and	and	CCONJ
ejpam-5844	196	30	sj	sj	INTJ
ejpam-5844	196	31	(	(	PUNCT
ejpam-5844	196	32	ab	ab	NOUN
ejpam-5844	196	33	)	)	PUNCT
ejpam-5844	196	34	≤	≤	NOUN
ejpam-5844	196	35	sj	sj	PROPN
ejpam-5844	196	36	(	(	PUNCT
ejpam-5844	196	37	a	a	PRON
ejpam-5844	196	38	)	)	PUNCT
ejpam-5844	196	39	s1	s1	NOUN
ejpam-5844	196	40	(	(	PUNCT
ejpam-5844	196	41	b	b	NOUN
ejpam-5844	196	42	)	)	PUNCT
ejpam-5844	196	43	.	.	PUNCT
ejpam-5844	197	1	(	(	PUNCT
ejpam-5844	197	2	14	14	NUM
ejpam-5844	197	3	)	)	PUNCT
ejpam-5844	197	4	theorem	theorem	NOUN
ejpam-5844	197	5	5	5	NUM
ejpam-5844	197	6	.	.	PUNCT
ejpam-5844	198	1	let	let	VERB
ejpam-5844	198	2	a	a	DET
ejpam-5844	198	3	,	,	PUNCT
ejpam-5844	198	4	b	b	NOUN
ejpam-5844	198	5	,	,	PUNCT
ejpam-5844	198	6	c	c	NOUN
ejpam-5844	198	7	,	,	PUNCT
ejpam-5844	198	8	d	d	PROPN
ejpam-5844	198	9	∈	∈	PROPN
ejpam-5844	198	10	mn(c	mn(c	X
ejpam-5844	198	11	)	)	PUNCT
ejpam-5844	198	12	.	.	PUNCT
ejpam-5844	199	1	then	then	ADV
ejpam-5844	199	2	sj	sj	INTJ
ejpam-5844	199	3	(	(	PUNCT
ejpam-5844	199	4	(	(	PUNCT
ejpam-5844	199	5	ac	ac	ADP
ejpam-5844	199	6	+	+	NOUN
ejpam-5844	199	7	bd)⊕	bd)⊕	NOUN
ejpam-5844	199	8	0	0	X
ejpam-5844	199	9	)	)	PUNCT
ejpam-5844	199	10	≥	≥	NOUN
ejpam-5844	199	11	sn	sn	INTJ
ejpam-5844	199	12	(	(	PUNCT
ejpam-5844	199	13	(	(	PUNCT
ejpam-5844	199	14	√	√	INTJ
ejpam-5844	199	15	aa∗	aa∗	NOUN
ejpam-5844	200	1	+	+	NOUN
ejpam-5844	200	2	bb∗	bb∗	NOUN
ejpam-5844	200	3	)	)	PUNCT
ejpam-5844	200	4	⊕	⊕	PROPN
ejpam-5844	200	5	0	0	NUM
ejpam-5844	200	6	)	)	PUNCT
ejpam-5844	200	7	sj	sj	INTJ
ejpam-5844	200	8	(	(	PUNCT
ejpam-5844	200	9	(	(	PUNCT
ejpam-5844	200	10	√	√	ADP
ejpam-5844	200	11	c∗c	c∗c	NUM
ejpam-5844	200	12	+	+	NOUN
ejpam-5844	200	13	d∗d	d∗d	NUM
ejpam-5844	200	14	)	)	PUNCT
ejpam-5844	200	15	⊕	⊕	PROPN
ejpam-5844	200	16	0	0	NUM
ejpam-5844	200	17	)	)	PUNCT
ejpam-5844	200	18	(	(	PUNCT
ejpam-5844	200	19	15	15	NUM
ejpam-5844	200	20	)	)	PUNCT
ejpam-5844	200	21	and	and	CCONJ
ejpam-5844	200	22	sj	sj	INTJ
ejpam-5844	200	23	(	(	PUNCT
ejpam-5844	200	24	(	(	PUNCT
ejpam-5844	200	25	ac	ac	ADP
ejpam-5844	200	26	+	+	NOUN
ejpam-5844	200	27	bd)⊕	bd)⊕	NOUN
ejpam-5844	200	28	0	0	X
ejpam-5844	200	29	)	)	PUNCT
ejpam-5844	200	30	≤	≤	NOUN
ejpam-5844	200	31	s1	s1	NOUN
ejpam-5844	200	32	(	(	PUNCT
ejpam-5844	200	33	(	(	PUNCT
ejpam-5844	200	34	√	√	INTJ
ejpam-5844	200	35	aa∗	aa∗	NOUN
ejpam-5844	201	1	+	+	NOUN
ejpam-5844	201	2	bb∗	bb∗	NOUN
ejpam-5844	201	3	)	)	PUNCT
ejpam-5844	201	4	⊕	⊕	PROPN
ejpam-5844	201	5	0	0	NUM
ejpam-5844	201	6	)	)	PUNCT
ejpam-5844	201	7	sj	sj	INTJ
ejpam-5844	201	8	(	(	PUNCT
ejpam-5844	201	9	(	(	PUNCT
ejpam-5844	201	10	√	√	ADP
ejpam-5844	201	11	c∗c	c∗c	NUM
ejpam-5844	201	12	+	+	NOUN
ejpam-5844	201	13	d∗d	d∗d	NUM
ejpam-5844	201	14	)	)	PUNCT
ejpam-5844	201	15	⊕	⊕	PROPN
ejpam-5844	201	16	0	0	NUM
ejpam-5844	201	17	)	)	PUNCT
ejpam-5844	201	18	.	.	PUNCT
ejpam-5844	202	1	(	(	PUNCT
ejpam-5844	202	2	16	16	X
ejpam-5844	202	3	)	)	PUNCT
ejpam-5844	202	4	proof	proof	NOUN
ejpam-5844	202	5	.	.	PUNCT
ejpam-5844	203	1	we	we	PRON
ejpam-5844	203	2	have	have	VERB
ejpam-5844	203	3	sj	sj	INTJ
ejpam-5844	203	4	(	(	PUNCT
ejpam-5844	203	5	(	(	PUNCT
ejpam-5844	203	6	ac	ac	ADP
ejpam-5844	203	7	+	+	NOUN
ejpam-5844	203	8	bd)⊕	bd)⊕	NOUN
ejpam-5844	203	9	0	0	X
ejpam-5844	203	10	)	)	PUNCT
ejpam-5844	203	11	=	=	VERB
ejpam-5844	203	12	sj	sj	INTJ
ejpam-5844	203	13	(	(	PUNCT
ejpam-5844	203	14	[	[	PUNCT
ejpam-5844	203	15	a	a	DET
ejpam-5844	203	16	b	b	NOUN
ejpam-5844	203	17	0	0	NUM
ejpam-5844	203	18	0	0	NUM
ejpam-5844	203	19	]	]	PUNCT
ejpam-5844	204	1	[	[	PUNCT
ejpam-5844	204	2	c	c	NOUN
ejpam-5844	204	3	0	0	PUNCT
ejpam-5844	204	4	d	d	NOUN
ejpam-5844	204	5	0	0	NUM
ejpam-5844	204	6	]	]	PUNCT
ejpam-5844	204	7	)	)	PUNCT
ejpam-5844	204	8	≥	≥	PROPN
ejpam-5844	204	9	sn	sn	INTJ
ejpam-5844	204	10	(	(	PUNCT
ejpam-5844	204	11	[	[	PUNCT
ejpam-5844	204	12	a	a	DET
ejpam-5844	204	13	b	b	NOUN
ejpam-5844	204	14	0	0	NUM
ejpam-5844	204	15	0	0	NUM
ejpam-5844	204	16	]	]	PUNCT
ejpam-5844	204	17	)	)	PUNCT
ejpam-5844	204	18	sj	sj	INTJ
ejpam-5844	204	19	(	(	PUNCT
ejpam-5844	204	20	[	[	PUNCT
ejpam-5844	204	21	c	c	NOUN
ejpam-5844	204	22	0	0	PUNCT
ejpam-5844	205	1	d	d	NOUN
ejpam-5844	205	2	0	0	NUM
ejpam-5844	205	3	]	]	PUNCT
ejpam-5844	205	4	)	)	PUNCT
ejpam-5844	205	5	(	(	PUNCT
ejpam-5844	205	6	by	by	ADP
ejpam-5844	205	7	inequality	inequality	NOUN
ejpam-5844	205	8	(	(	PUNCT
ejpam-5844	205	9	13	13	NUM
ejpam-5844	205	10	)	)	PUNCT
ejpam-5844	205	11	=	=	SYM
ejpam-5844	205	12	sn	sn	PROPN
ejpam-5844	205	13	(	(	PUNCT
ejpam-5844	205	14	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5844	205	15	[	[	PUNCT
ejpam-5844	205	16	a	a	DET
ejpam-5844	205	17	b	b	NOUN
ejpam-5844	205	18	0	0	NUM
ejpam-5844	205	19	0	0	NUM
ejpam-5844	205	20	]	]	X
ejpam-5844	205	21	∣∣∣∣	∣∣∣∣	X
ejpam-5844	205	22	)	)	PUNCT
ejpam-5844	205	23	sj	sj	NOUN
ejpam-5844	205	24	(	(	PUNCT
ejpam-5844	205	25	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5844	205	26	[	[	PUNCT
ejpam-5844	205	27	c	c	NOUN
ejpam-5844	205	28	0	0	NUM
ejpam-5844	206	1	d	d	NOUN
ejpam-5844	206	2	0	0	NUM
ejpam-5844	206	3	]	]	SYM
ejpam-5844	206	4	∣∣∣∣	∣∣∣∣	X
ejpam-5844	206	5	)	)	PUNCT
ejpam-5844	206	6	=	=	SYM
ejpam-5844	206	7	sn	sn	PROPN
ejpam-5844	206	8	(	(	PUNCT
ejpam-5844	206	9	(	(	PUNCT
ejpam-5844	206	10	[	[	PUNCT
ejpam-5844	206	11	a∗	a∗	ADJ
ejpam-5844	206	12	0	0	SYM
ejpam-5844	206	13	b∗	b∗	ADJ
ejpam-5844	206	14	0	0	NUM
ejpam-5844	206	15	]	]	PUNCT
ejpam-5844	207	1	[	[	PUNCT
ejpam-5844	207	2	a	a	DET
ejpam-5844	207	3	b	b	NOUN
ejpam-5844	207	4	0	0	NUM
ejpam-5844	207	5	0	0	NUM
ejpam-5844	207	6	]	]	SYM
ejpam-5844	207	7	)	)	PUNCT
ejpam-5844	207	8	1/2	1/2	NUM
ejpam-5844	207	9	)	)	PUNCT
ejpam-5844	207	10	sj	sj	INTJ
ejpam-5844	207	11	(	(	PUNCT
ejpam-5844	207	12	(	(	PUNCT
ejpam-5844	207	13	[	[	PUNCT
ejpam-5844	207	14	c∗	c∗	ADJ
ejpam-5844	207	15	d∗	d∗	NOUN
ejpam-5844	207	16	0	0	NUM
ejpam-5844	207	17	0	0	NUM
ejpam-5844	207	18	]	]	PUNCT
ejpam-5844	208	1	[	[	PUNCT
ejpam-5844	208	2	c	c	NOUN
ejpam-5844	208	3	0	0	PUNCT
ejpam-5844	208	4	d	d	NOUN
ejpam-5844	208	5	0	0	NUM
ejpam-5844	208	6	]	]	SYM
ejpam-5844	208	7	)	)	PUNCT
ejpam-5844	208	8	1/2	1/2	NUM
ejpam-5844	208	9	)	)	PUNCT
ejpam-5844	209	1	=	=	SYM
ejpam-5844	209	2	s1/2n	s1/2n	NOUN
ejpam-5844	209	3	(	(	PUNCT
ejpam-5844	209	4	[	[	PUNCT
ejpam-5844	209	5	a∗	a∗	ADJ
ejpam-5844	209	6	0	0	SYM
ejpam-5844	209	7	b∗	b∗	ADJ
ejpam-5844	209	8	0	0	NUM
ejpam-5844	209	9	]	]	PUNCT
ejpam-5844	210	1	[	[	PUNCT
ejpam-5844	210	2	a	a	DET
ejpam-5844	210	3	b	b	NOUN
ejpam-5844	210	4	0	0	NUM
ejpam-5844	210	5	0	0	NUM
ejpam-5844	210	6	]	]	PUNCT
ejpam-5844	210	7	)	)	PUNCT
ejpam-5844	210	8	s	s	PART
ejpam-5844	210	9	1/2	1/2	NUM
ejpam-5844	210	10	j	j	NOUN
ejpam-5844	210	11	(	(	PUNCT
ejpam-5844	210	12	[	[	PUNCT
ejpam-5844	210	13	c∗	c∗	ADJ
ejpam-5844	210	14	d∗	d∗	NOUN
ejpam-5844	210	15	0	0	NUM
ejpam-5844	210	16	0	0	NUM
ejpam-5844	210	17	]	]	PUNCT
ejpam-5844	211	1	[	[	PUNCT
ejpam-5844	211	2	c	c	NOUN
ejpam-5844	211	3	0	0	PUNCT
ejpam-5844	211	4	d	d	NOUN
ejpam-5844	211	5	0	0	NUM
ejpam-5844	211	6	]	]	PUNCT
ejpam-5844	211	7	)	)	PUNCT
ejpam-5844	211	8	a.	a.	PROPN
ejpam-5844	211	9	al	al	PROPN
ejpam-5844	211	10	-	-	PUNCT
ejpam-5844	211	11	natoor	natoor	NOUN
ejpam-5844	211	12	,	,	PUNCT
ejpam-5844	211	13	r.	r.	PROPN
ejpam-5844	211	14	al	al	PROPN
ejpam-5844	211	15	-	-	PUNCT
ejpam-5844	211	16	smadi	smadi	PROPN
ejpam-5844	211	17	,	,	PUNCT
ejpam-5844	211	18	a.	a.	NOUN
ejpam-5844	211	19	burqan	burqan	PROPN
ejpam-5844	211	20	/	/	SYM
ejpam-5844	211	21	eur	eur	PROPN
ejpam-5844	211	22	.	.	PUNCT
ejpam-5844	212	1	j.	j.	PROPN
ejpam-5844	212	2	pure	pure	PROPN
ejpam-5844	212	3	appl	appl	PROPN
ejpam-5844	212	4	.	.	PROPN
ejpam-5844	212	5	math	math	PROPN
ejpam-5844	212	6	,	,	PUNCT
ejpam-5844	212	7	18	18	NUM
ejpam-5844	212	8	(	(	PUNCT
ejpam-5844	212	9	2	2	NUM
ejpam-5844	212	10	)	)	PUNCT
ejpam-5844	212	11	(	(	PUNCT
ejpam-5844	212	12	2025	2025	NUM
ejpam-5844	212	13	)	)	PUNCT
ejpam-5844	212	14	,	,	PUNCT
ejpam-5844	212	15	5844	5844	NUM
ejpam-5844	212	16	10	10	NUM
ejpam-5844	212	17	of	of	ADP
ejpam-5844	212	18	10	10	NUM
ejpam-5844	212	19	=	=	SYM
ejpam-5844	212	20	s1/2n	s1/2n	NOUN
ejpam-5844	212	21	(	(	PUNCT
ejpam-5844	212	22	[	[	PUNCT
ejpam-5844	212	23	a	a	DET
ejpam-5844	212	24	b	b	NOUN
ejpam-5844	212	25	0	0	NUM
ejpam-5844	212	26	0	0	NUM
ejpam-5844	212	27	]	]	PUNCT
ejpam-5844	213	1	[	[	PUNCT
ejpam-5844	213	2	a∗	a∗	ADJ
ejpam-5844	213	3	0	0	SYM
ejpam-5844	213	4	b∗	b∗	ADJ
ejpam-5844	213	5	0	0	NUM
ejpam-5844	213	6	]	]	PUNCT
ejpam-5844	213	7	)	)	PUNCT
ejpam-5844	213	8	s	s	PART
ejpam-5844	213	9	1/2	1/2	NUM
ejpam-5844	213	10	j	j	NOUN
ejpam-5844	213	11	(	(	PUNCT
ejpam-5844	213	12	[	[	PUNCT
ejpam-5844	213	13	c∗	c∗	ADJ
ejpam-5844	213	14	d∗	d∗	NOUN
ejpam-5844	213	15	0	0	NUM
ejpam-5844	213	16	0	0	NUM
ejpam-5844	213	17	]	]	PUNCT
ejpam-5844	214	1	[	[	PUNCT
ejpam-5844	214	2	c	c	NOUN
ejpam-5844	214	3	0	0	PUNCT
ejpam-5844	214	4	d	d	NOUN
ejpam-5844	214	5	0	0	NUM
ejpam-5844	214	6	]	]	PUNCT
ejpam-5844	214	7	)	)	PUNCT
ejpam-5844	215	1	=	=	SYM
ejpam-5844	215	2	s1/2n	s1/2n	NOUN
ejpam-5844	215	3	(	(	PUNCT
ejpam-5844	215	4	[	[	PUNCT
ejpam-5844	215	5	aa∗	aa∗	NOUN
ejpam-5844	215	6	+	+	NOUN
ejpam-5844	215	7	bb∗	bb∗	NOUN
ejpam-5844	215	8	0	0	NUM
ejpam-5844	215	9	0	0	NUM
ejpam-5844	215	10	0	0	NUM
ejpam-5844	215	11	]	]	PUNCT
ejpam-5844	215	12	)	)	PUNCT
ejpam-5844	215	13	s	s	PART
ejpam-5844	215	14	1/2	1/2	NUM
ejpam-5844	215	15	j	j	NOUN
ejpam-5844	215	16	(	(	PUNCT
ejpam-5844	215	17	[	[	PUNCT
ejpam-5844	215	18	c∗c	c∗c	X
ejpam-5844	215	19	+	+	NOUN
ejpam-5844	215	20	d∗d	d∗d	NUM
ejpam-5844	215	21	0	0	NUM
ejpam-5844	215	22	0	0	NUM
ejpam-5844	215	23	0	0	NUM
ejpam-5844	215	24	]	]	PUNCT
ejpam-5844	215	25	)	)	PUNCT
ejpam-5844	215	26	=	=	SYM
ejpam-5844	215	27	sn	sn	INTJ
ejpam-5844	215	28	(	(	PUNCT
ejpam-5844	215	29	[	[	PUNCT
ejpam-5844	215	30	√	√	ADJ
ejpam-5844	215	31	aa∗	aa∗	NOUN
ejpam-5844	216	1	+	+	NOUN
ejpam-5844	216	2	bb∗	bb∗	NOUN
ejpam-5844	216	3	0	0	NUM
ejpam-5844	216	4	0	0	NUM
ejpam-5844	216	5	0	0	NUM
ejpam-5844	216	6	]	]	PUNCT
ejpam-5844	216	7	)	)	PUNCT
ejpam-5844	216	8	sj	sj	INTJ
ejpam-5844	216	9	(	(	PUNCT
ejpam-5844	216	10	[	[	PUNCT
ejpam-5844	216	11	√	√	ADP
ejpam-5844	216	12	c∗c	c∗c	NUM
ejpam-5844	216	13	+	+	NOUN
ejpam-5844	216	14	d∗d	d∗d	NUM
ejpam-5844	216	15	0	0	NUM
ejpam-5844	216	16	0	0	NUM
ejpam-5844	216	17	0	0	NUM
ejpam-5844	216	18	]	]	PUNCT
ejpam-5844	216	19	)	)	PUNCT
ejpam-5844	216	20	=	=	SYM
ejpam-5844	216	21	sn	sn	PROPN
ejpam-5844	216	22	(	(	PUNCT
ejpam-5844	216	23	(	(	PUNCT
ejpam-5844	216	24	√	√	X
ejpam-5844	216	25	aa∗	aa∗	NOUN
ejpam-5844	217	1	+	+	NOUN
ejpam-5844	217	2	bb∗	bb∗	NOUN
ejpam-5844	217	3	)	)	PUNCT
ejpam-5844	217	4	⊕	⊕	PROPN
ejpam-5844	217	5	0	0	NUM
ejpam-5844	217	6	)	)	PUNCT
ejpam-5844	217	7	sj	sj	INTJ
ejpam-5844	217	8	(	(	PUNCT
ejpam-5844	217	9	(	(	PUNCT
ejpam-5844	217	10	√	√	ADP
ejpam-5844	217	11	c∗c	c∗c	NUM
ejpam-5844	217	12	+	+	NOUN
ejpam-5844	217	13	d∗d	d∗d	NUM
ejpam-5844	217	14	)	)	PUNCT
ejpam-5844	217	15	⊕	⊕	PROPN
ejpam-5844	217	16	0	0	NUM
ejpam-5844	217	17	)	)	PUNCT
ejpam-5844	217	18	.	.	PUNCT
ejpam-5844	218	1	which	which	PRON
ejpam-5844	218	2	proves	prove	VERB
ejpam-5844	218	3	inequality	inequality	NOUN
ejpam-5844	218	4	(	(	PUNCT
ejpam-5844	218	5	15	15	NUM
ejpam-5844	218	6	)	)	PUNCT
ejpam-5844	218	7	.	.	PUNCT
ejpam-5844	219	1	the	the	DET
ejpam-5844	219	2	inequality	inequality	NOUN
ejpam-5844	219	3	(	(	PUNCT
ejpam-5844	219	4	16	16	NUM
ejpam-5844	219	5	)	)	PUNCT
ejpam-5844	219	6	follows	follow	VERB
ejpam-5844	219	7	by	by	ADP
ejpam-5844	219	8	applying	apply	VERB
ejpam-5844	219	9	inequality	inequality	NOUN
ejpam-5844	219	10	(	(	PUNCT
ejpam-5844	219	11	14	14	NUM
ejpam-5844	219	12	)	)	PUNCT
ejpam-5844	219	13	and	and	CCONJ
ejpam-5844	219	14	using	use	VERB
ejpam-5844	219	15	the	the	DET
ejpam-5844	219	16	same	same	ADJ
ejpam-5844	219	17	argument	argument	NOUN
ejpam-5844	219	18	that	that	SCONJ
ejpam-5844	219	19	we	we	PRON
ejpam-5844	219	20	use	use	VERB
ejpam-5844	219	21	in	in	ADP
ejpam-5844	219	22	proving	prove	VERB
ejpam-5844	219	23	inequality	inequality	NOUN
ejpam-5844	219	24	(	(	PUNCT
ejpam-5844	219	25	15	15	NUM
ejpam-5844	219	26	)	)	PUNCT
ejpam-5844	219	27	.	.	PUNCT
ejpam-5844	220	1	references	reference	NOUN
ejpam-5844	220	2	[	[	X
ejpam-5844	220	3	1	1	NUM
ejpam-5844	220	4	]	]	X
ejpam-5844	220	5	y.	y.	PROPN
ejpam-5844	220	6	tao	tao	PROPN
ejpam-5844	220	7	.	.	PUNCT
ejpam-5844	221	1	more	more	ADJ
ejpam-5844	221	2	results	result	NOUN
ejpam-5844	221	3	on	on	ADP
ejpam-5844	221	4	singular	singular	ADJ
ejpam-5844	221	5	value	value	NOUN
ejpam-5844	221	6	inequalities	inequality	NOUN
ejpam-5844	221	7	of	of	ADP
ejpam-5844	221	8	matrices	matrix	NOUN
ejpam-5844	221	9	.	.	PUNCT
ejpam-5844	222	1	linear	linear	ADJ
ejpam-5844	222	2	algebra	algebra	NOUN
ejpam-5844	222	3	and	and	CCONJ
ejpam-5844	222	4	its	its	PRON
ejpam-5844	222	5	applications	application	NOUN
ejpam-5844	222	6	,	,	PUNCT
ejpam-5844	222	7	416(2	416(2	NUM
ejpam-5844	222	8	-	-	SYM
ejpam-5844	222	9	3):724–729	3):724–729	NUM
ejpam-5844	222	10	,	,	PUNCT
ejpam-5844	222	11	2006	2006	NUM
ejpam-5844	222	12	.	.	PUNCT
ejpam-5844	223	1	[	[	X
ejpam-5844	223	2	2	2	NUM
ejpam-5844	223	3	]	]	PUNCT
ejpam-5844	223	4	a.	a.	NOUN
ejpam-5844	223	5	al	al	PROPN
ejpam-5844	223	6	-	-	PUNCT
ejpam-5844	223	7	natoor	natoor	NOUN
ejpam-5844	223	8	,	,	PUNCT
ejpam-5844	223	9	o.	o.	PROPN
ejpam-5844	223	10	hirzallah	hirzallah	PROPN
ejpam-5844	223	11	,	,	PUNCT
ejpam-5844	223	12	and	and	CCONJ
ejpam-5844	223	13	f.	f.	PROPN
ejpam-5844	223	14	kittaneh	kittaneh	PROPN
ejpam-5844	223	15	.	.	PUNCT
ejpam-5844	224	1	singular	singular	PROPN
ejpam-5844	224	2	value	value	NOUN
ejpam-5844	224	3	inequalities	inequality	NOUN
ejpam-5844	224	4	for	for	ADP
ejpam-5844	224	5	convex	convex	NOUN
ejpam-5844	224	6	functions	function	NOUN
ejpam-5844	224	7	of	of	ADP
ejpam-5844	224	8	positive	positive	ADJ
ejpam-5844	224	9	semidefinite	semidefinite	NOUN
ejpam-5844	224	10	matrices	matrix	NOUN
ejpam-5844	224	11	.	.	PUNCT
ejpam-5844	225	1	annals	annal	NOUN
ejpam-5844	225	2	of	of	ADP
ejpam-5844	225	3	functional	functional	ADJ
ejpam-5844	225	4	analysis	analysis	NOUN
ejpam-5844	225	5	,	,	PUNCT
ejpam-5844	225	6	14(1):7	14(1):7	PROPN
ejpam-5844	225	7	,	,	PUNCT
ejpam-5844	225	8	2023	2023	NUM
ejpam-5844	225	9	.	.	PUNCT
ejpam-5844	226	1	[	[	X
ejpam-5844	226	2	3	3	NUM
ejpam-5844	226	3	]	]	PUNCT
ejpam-5844	226	4	a.	a.	NOUN
ejpam-5844	226	5	al	al	PROPN
ejpam-5844	226	6	-	-	PUNCT
ejpam-5844	226	7	natoor	natoor	PROPN
ejpam-5844	226	8	and	and	CCONJ
ejpam-5844	226	9	f.	f.	PROPN
ejpam-5844	226	10	alrimawi	alrimawi	PROPN
ejpam-5844	226	11	.	.	PUNCT
ejpam-5844	227	1	singular	singular	PROPN
ejpam-5844	227	2	value	value	NOUN
ejpam-5844	227	3	inequalities	inequality	NOUN
ejpam-5844	227	4	for	for	ADP
ejpam-5844	227	5	concave	concave	NOUN
ejpam-5844	227	6	and	and	CCONJ
ejpam-5844	227	7	convex	convex	NOUN
ejpam-5844	227	8	functions	function	NOUN
ejpam-5844	227	9	of	of	ADP
ejpam-5844	227	10	matrix	matrix	NOUN
ejpam-5844	227	11	sums	sum	NOUN
ejpam-5844	227	12	and	and	CCONJ
ejpam-5844	227	13	products	product	NOUN
ejpam-5844	227	14	.	.	PUNCT
ejpam-5844	228	1	european	european	ADJ
ejpam-5844	228	2	journal	journal	PROPN
ejpam-5844	228	3	of	of	ADP
ejpam-5844	228	4	pure	pure	ADJ
ejpam-5844	228	5	and	and	CCONJ
ejpam-5844	228	6	applied	applied	ADJ
ejpam-5844	228	7	mathematics	mathematic	NOUN
ejpam-5844	228	8	,	,	PUNCT
ejpam-5844	228	9	18(1):558–578	18(1):558–578	NUM
ejpam-5844	228	10	,	,	PUNCT
ejpam-5844	228	11	2025	2025	NUM
ejpam-5844	228	12	.	.	PUNCT
ejpam-5844	229	1	[	[	X
ejpam-5844	229	2	4	4	NUM
ejpam-5844	229	3	]	]	PUNCT
ejpam-5844	229	4	a.	a.	NOUN
ejpam-5844	229	5	al	al	PROPN
ejpam-5844	229	6	-	-	PUNCT
ejpam-5844	229	7	natoor	natoor	NOUN
ejpam-5844	229	8	,	,	PUNCT
ejpam-5844	229	9	m.	m.	NOUN
ejpam-5844	229	10	a.	a.	NOUN
ejpam-5844	229	11	amleh	amleh	PROPN
ejpam-5844	229	12	,	,	PUNCT
ejpam-5844	229	13	b.	b.	PROPN
ejpam-5844	229	14	abughazaleh	abughazaleh	PROPN
ejpam-5844	229	15	,	,	PUNCT
ejpam-5844	229	16	and	and	CCONJ
ejpam-5844	229	17	a.	a.	NOUN
ejpam-5844	229	18	burqan	burqan	PROPN
ejpam-5844	229	19	.	.	PUNCT
ejpam-5844	230	1	generalization	generalization	NOUN
ejpam-5844	230	2	of	of	ADP
ejpam-5844	230	3	some	some	DET
ejpam-5844	230	4	unitarily	unitarily	ADV
ejpam-5844	230	5	invariant	invariant	ADJ
ejpam-5844	230	6	norm	norm	NOUN
ejpam-5844	230	7	inequalities	inequality	NOUN
ejpam-5844	230	8	for	for	ADP
ejpam-5844	230	9	matrices	matrix	NOUN
ejpam-5844	230	10	.	.	PUNCT
ejpam-5844	231	1	journal	journal	PROPN
ejpam-5844	231	2	of	of	ADP
ejpam-5844	231	3	mathematical	mathematical	ADJ
ejpam-5844	231	4	inequalities	inequality	NOUN
ejpam-5844	231	5	,	,	PUNCT
ejpam-5844	231	6	17(2):581–589	17(2):581–589	PROPN
ejpam-5844	231	7	,	,	PUNCT
ejpam-5844	231	8	2023	2023	NUM
ejpam-5844	231	9	.	.	PUNCT
ejpam-5844	232	1	[	[	X
ejpam-5844	232	2	5	5	NUM
ejpam-5844	232	3	]	]	PUNCT
ejpam-5844	232	4	a.	a.	NOUN
ejpam-5844	232	5	al	al	PROPN
ejpam-5844	232	6	-	-	PUNCT
ejpam-5844	232	7	natoor	natoor	NOUN
ejpam-5844	232	8	,	,	PUNCT
ejpam-5844	232	9	a.	a.	NOUN
ejpam-5844	232	10	burqan	burqan	PROPN
ejpam-5844	232	11	,	,	PUNCT
ejpam-5844	232	12	m.	m.	NOUN
ejpam-5844	232	13	a.	a.	NOUN
ejpam-5844	232	14	amleh	amleh	PROPN
ejpam-5844	232	15	,	,	PUNCT
ejpam-5844	232	16	and	and	CCONJ
ejpam-5844	232	17	c.	c.	PROPN
ejpam-5844	232	18	conde	conde	PROPN
ejpam-5844	232	19	.	.	PUNCT
ejpam-5844	233	1	some	some	DET
ejpam-5844	233	2	singular	singular	ADJ
ejpam-5844	233	3	value	value	NOUN
ejpam-5844	233	4	inequalities	inequality	NOUN
ejpam-5844	233	5	for	for	ADP
ejpam-5844	233	6	matrices	matrix	NOUN
ejpam-5844	233	7	.	.	PUNCT
ejpam-5844	234	1	journal	journal	PROPN
ejpam-5844	234	2	of	of	ADP
ejpam-5844	234	3	mathematical	mathematical	ADJ
ejpam-5844	234	4	inequalities	inequality	NOUN
ejpam-5844	234	5	,	,	PUNCT
ejpam-5844	234	6	18(3):911–919	18(3):911–919	PROPN
ejpam-5844	234	7	,	,	PUNCT
ejpam-5844	234	8	2024	2024	NUM
ejpam-5844	234	9	.	.	PUNCT
ejpam-5844	235	1	[	[	X
ejpam-5844	235	2	6	6	NUM
ejpam-5844	235	3	]	]	PUNCT
ejpam-5844	235	4	a.	a.	NOUN
ejpam-5844	235	5	burqan	burqan	PROPN
ejpam-5844	235	6	and	and	CCONJ
ejpam-5844	235	7	f.	f.	PROPN
ejpam-5844	235	8	kittaneh	kittaneh	PROPN
ejpam-5844	235	9	.	.	PUNCT
ejpam-5844	236	1	singular	singular	PROPN
ejpam-5844	236	2	value	value	NOUN
ejpam-5844	236	3	and	and	CCONJ
ejpam-5844	236	4	norm	norm	NOUN
ejpam-5844	236	5	inequalities	inequality	NOUN
ejpam-5844	236	6	associated	associate	VERB
ejpam-5844	236	7	with	with	ADP
ejpam-5844	236	8	2	2	NUM
ejpam-5844	236	9	×	×	NOUN
ejpam-5844	236	10	2	2	NUM
ejpam-5844	236	11	positive	positive	ADJ
ejpam-5844	236	12	semidefinite	semidefinite	NOUN
ejpam-5844	236	13	block	block	NOUN
ejpam-5844	236	14	matrices	matrix	NOUN
ejpam-5844	236	15	.	.	PUNCT
ejpam-5844	237	1	electronic	electronic	ADJ
ejpam-5844	237	2	journal	journal	NOUN
ejpam-5844	237	3	of	of	ADP
ejpam-5844	237	4	linear	linear	PROPN
ejpam-5844	237	5	algebra	algebra	PROPN
ejpam-5844	237	6	,	,	PUNCT
ejpam-5844	237	7	32:116–124	32:116–124	NUM
ejpam-5844	237	8	,	,	PUNCT
ejpam-5844	237	9	2017	2017	NUM
ejpam-5844	237	10	.	.	PUNCT
ejpam-5844	238	1	[	[	X
ejpam-5844	238	2	7	7	X
ejpam-5844	238	3	]	]	X
ejpam-5844	238	4	f.	f.	PROPN
ejpam-5844	238	5	kittaneh	kittaneh	PROPN
ejpam-5844	238	6	,	,	PUNCT
ejpam-5844	238	7	h.	h.	PROPN
ejpam-5844	238	8	r.	r.	PROPN
ejpam-5844	238	9	moradi	moradi	PROPN
ejpam-5844	238	10	,	,	PUNCT
ejpam-5844	238	11	and	and	CCONJ
ejpam-5844	238	12	m.	m.	NOUN
ejpam-5844	238	13	sababheh	sababheh	NOUN
ejpam-5844	238	14	.	.	PUNCT
ejpam-5844	239	1	singular	singular	ADJ
ejpam-5844	239	2	values	value	NOUN
ejpam-5844	239	3	of	of	ADP
ejpam-5844	239	4	compact	compact	ADJ
ejpam-5844	239	5	operators	operator	NOUN
ejpam-5844	239	6	via	via	ADP
ejpam-5844	239	7	operator	operator	NOUN
ejpam-5844	239	8	matrices	matrix	NOUN
ejpam-5844	239	9	.	.	PUNCT
ejpam-5844	240	1	mathematical	mathematical	ADJ
ejpam-5844	240	2	inequalities	inequality	NOUN
ejpam-5844	240	3	&	&	CCONJ
ejpam-5844	240	4	applications	application	NOUN
ejpam-5844	240	5	,	,	PUNCT
ejpam-5844	240	6	27(3):759–774	27(3):759–774	NUM
ejpam-5844	240	7	,	,	PUNCT
ejpam-5844	240	8	2024	2024	NUM
ejpam-5844	240	9	.	.	PUNCT
ejpam-5844	241	1	[	[	X
ejpam-5844	241	2	8	8	NUM
ejpam-5844	241	3	]	]	PUNCT
ejpam-5844	241	4	a.	a.	NOUN
ejpam-5844	241	5	al	al	PROPN
ejpam-5844	241	6	-	-	PUNCT
ejpam-5844	241	7	natoor	natoor	PROPN
ejpam-5844	241	8	and	and	CCONJ
ejpam-5844	241	9	f.	f.	PROPN
ejpam-5844	241	10	kittaneh	kittaneh	PROPN
ejpam-5844	241	11	.	.	PUNCT
ejpam-5844	242	1	singular	singular	PROPN
ejpam-5844	242	2	value	value	NOUN
ejpam-5844	242	3	and	and	CCONJ
ejpam-5844	242	4	norm	norm	NOUN
ejpam-5844	242	5	inequalities	inequality	NOUN
ejpam-5844	242	6	for	for	ADP
ejpam-5844	242	7	positive	positive	ADJ
ejpam-5844	242	8	semidefinite	semidefinite	NOUN
ejpam-5844	242	9	matrices	matrix	NOUN
ejpam-5844	242	10	.	.	PUNCT
ejpam-5844	243	1	linear	linear	ADJ
ejpam-5844	243	2	and	and	CCONJ
ejpam-5844	243	3	multilinear	multilinear	PROPN
ejpam-5844	243	4	algebra	algebra	PROPN
ejpam-5844	243	5	,	,	PUNCT
ejpam-5844	243	6	70(21):4498–4509	70(21):4498–4509	NUM
ejpam-5844	243	7	,	,	PUNCT
ejpam-5844	243	8	2022	2022	NUM
ejpam-5844	243	9	.	.	PUNCT
ejpam-5844	244	1	[	[	X
ejpam-5844	244	2	9	9	NUM
ejpam-5844	244	3	]	]	PUNCT
ejpam-5844	244	4	a.	a.	NOUN
ejpam-5844	244	5	al	al	PROPN
ejpam-5844	244	6	-	-	PUNCT
ejpam-5844	244	7	natoor	natoor	NOUN
ejpam-5844	244	8	,	,	PUNCT
ejpam-5844	244	9	o.	o.	PROPN
ejpam-5844	244	10	hirzallah	hirzallah	PROPN
ejpam-5844	244	11	,	,	PUNCT
ejpam-5844	244	12	and	and	CCONJ
ejpam-5844	244	13	f.	f.	PROPN
ejpam-5844	244	14	kittaneh	kittaneh	PROPN
ejpam-5844	244	15	.	.	PUNCT
ejpam-5844	245	1	singular	singular	PROPN
ejpam-5844	245	2	value	value	NOUN
ejpam-5844	245	3	and	and	CCONJ
ejpam-5844	245	4	unitarily	unitarily	ADV
ejpam-5844	245	5	invariant	invariant	ADJ
ejpam-5844	245	6	norm	norm	NOUN
ejpam-5844	245	7	inequalities	inequality	NOUN
ejpam-5844	245	8	for	for	ADP
ejpam-5844	245	9	matrices	matrix	NOUN
ejpam-5844	245	10	.	.	PUNCT
ejpam-5844	246	1	annals	annal	NOUN
ejpam-5844	246	2	of	of	ADP
ejpam-5844	246	3	functional	functional	ADJ
ejpam-5844	246	4	analysis	analysis	NOUN
ejpam-5844	246	5	,	,	PUNCT
ejpam-5844	246	6	15(2):21	15(2):21	NUM
ejpam-5844	246	7	,	,	PUNCT
ejpam-5844	246	8	2024	2024	NUM
ejpam-5844	246	9	.	.	PUNCT
ejpam-5844	247	1	[	[	X
ejpam-5844	247	2	10	10	NUM
ejpam-5844	247	3	]	]	X
ejpam-5844	247	4	r.	r.	PROPN
ejpam-5844	247	5	bhatia	bhatia	PROPN
ejpam-5844	247	6	and	and	CCONJ
ejpam-5844	247	7	f.	f.	PROPN
ejpam-5844	247	8	kittaneh	kittaneh	PROPN
ejpam-5844	247	9	.	.	PUNCT
ejpam-5844	248	1	the	the	DET
ejpam-5844	248	2	matrix	matrix	NOUN
ejpam-5844	248	3	arithmetic	arithmetic	ADJ
ejpam-5844	248	4	-	-	PUNCT
ejpam-5844	248	5	geometric	geometric	ADJ
ejpam-5844	248	6	mean	mean	NOUN
ejpam-5844	248	7	inequality	inequality	NOUN
ejpam-5844	248	8	revisited	revisit	VERB
ejpam-5844	248	9	.	.	PUNCT
ejpam-5844	249	1	linear	linear	ADJ
ejpam-5844	249	2	algebra	algebra	NOUN
ejpam-5844	249	3	and	and	CCONJ
ejpam-5844	249	4	its	its	PRON
ejpam-5844	249	5	applications	application	NOUN
ejpam-5844	249	6	,	,	PUNCT
ejpam-5844	249	7	428(8	428(8	NUM
ejpam-5844	249	8	-	-	PUNCT
ejpam-5844	249	9	9):2177–2191	9):2177–2191	NUM
ejpam-5844	249	10	,	,	PUNCT
ejpam-5844	249	11	2008	2008	NUM
ejpam-5844	249	12	.	.	PUNCT
ejpam-5844	250	1	[	[	X
ejpam-5844	250	2	11	11	NUM
ejpam-5844	250	3	]	]	X
ejpam-5844	250	4	h.	h.	PROPN
ejpam-5844	250	5	albadawi	albadawi	PROPN
ejpam-5844	250	6	.	.	PUNCT
ejpam-5844	251	1	singular	singular	PROPN
ejpam-5844	251	2	values	value	NOUN
ejpam-5844	251	3	and	and	CCONJ
ejpam-5844	251	4	arithmetic	arithmetic	ADJ
ejpam-5844	251	5	-	-	PUNCT
ejpam-5844	251	6	geometric	geometric	ADJ
ejpam-5844	251	7	mean	mean	NOUN
ejpam-5844	251	8	inequalities	inequality	NOUN
ejpam-5844	251	9	for	for	ADP
ejpam-5844	251	10	operators	operator	NOUN
ejpam-5844	251	11	.	.	PUNCT
ejpam-5844	252	1	annals	annal	NOUN
ejpam-5844	252	2	of	of	ADP
ejpam-5844	252	3	functional	functional	ADJ
ejpam-5844	252	4	analysis	analysis	NOUN
ejpam-5844	252	5	,	,	PUNCT
ejpam-5844	252	6	3(2):10–18	3(2):10–18	NUM
ejpam-5844	252	7	,	,	PUNCT
ejpam-5844	252	8	2012	2012	NUM
ejpam-5844	252	9	.	.	PUNCT
ejpam-5844	253	1	[	[	X
ejpam-5844	253	2	12	12	NUM
ejpam-5844	253	3	]	]	PUNCT
ejpam-5844	253	4	f.	f.	PROPN
ejpam-5844	253	5	zhang	zhang	PROPN
ejpam-5844	253	6	.	.	PROPN
ejpam-5844	253	7	matrix	matrix	NOUN
ejpam-5844	253	8	theory	theory	NOUN
ejpam-5844	253	9	:	:	PUNCT
ejpam-5844	253	10	basic	basic	ADJ
ejpam-5844	253	11	results	result	NOUN
ejpam-5844	253	12	and	and	CCONJ
ejpam-5844	253	13	techniques	technique	NOUN
ejpam-5844	253	14	.	.	PUNCT
ejpam-5844	254	1	springer	springer	NOUN
ejpam-5844	254	2	,	,	PUNCT
ejpam-5844	254	3	new	new	PROPN
ejpam-5844	254	4	york	york	PROPN
ejpam-5844	254	5	,	,	PUNCT
ejpam-5844	254	6	2	2	NUM
ejpam-5844	254	7	edition	edition	NOUN
ejpam-5844	254	8	,	,	PUNCT
ejpam-5844	254	9	2011	2011	NUM
ejpam-5844	254	10	.	.	PUNCT