id	sid	tid	token	lemma	pos
ejpam-6590	1	1	european	european	PROPN
ejpam-6590	1	2	journal	journal	PROPN
ejpam-6590	1	3	of	of	ADP
ejpam-6590	1	4	pure	pure	ADJ
ejpam-6590	1	5	and	and	CCONJ
ejpam-6590	1	6	applied	applied	ADJ
ejpam-6590	1	7	mathematics	mathematic	NOUN
ejpam-6590	1	8	2025	2025	NUM
ejpam-6590	1	9	,	,	PUNCT
ejpam-6590	1	10	vol	vol	NOUN
ejpam-6590	1	11	.	.	PROPN
ejpam-6590	1	12	18	18	NUM
ejpam-6590	1	13	,	,	PUNCT
ejpam-6590	1	14	issue	issue	NOUN
ejpam-6590	1	15	3	3	NUM
ejpam-6590	1	16	,	,	PUNCT
ejpam-6590	1	17	article	article	NOUN
ejpam-6590	1	18	number	number	NOUN
ejpam-6590	1	19	6590	6590	NUM
ejpam-6590	1	20	issn	issn	VERB
ejpam-6590	1	21	1307	1307	NUM
ejpam-6590	1	22	-	-	SYM
ejpam-6590	1	23	5543	5543	NUM
ejpam-6590	1	24	–	–	PUNCT
ejpam-6590	1	25	ejpam.com	ejpam.com	X
ejpam-6590	1	26	published	publish	VERB
ejpam-6590	1	27	by	by	ADP
ejpam-6590	1	28	new	new	PROPN
ejpam-6590	1	29	york	york	PROPN
ejpam-6590	1	30	business	business	PROPN
ejpam-6590	1	31	global	global	PROPN
ejpam-6590	1	32	some	some	DET
ejpam-6590	1	33	spectral	spectral	ADJ
ejpam-6590	1	34	radius	radius	NOUN
ejpam-6590	1	35	inequalities	inequality	NOUN
ejpam-6590	1	36	for	for	ADP
ejpam-6590	1	37	certain	certain	ADJ
ejpam-6590	1	38	matrices	matrix	NOUN
ejpam-6590	1	39	mona	mona	PROPN
ejpam-6590	1	40	sakkijha1	sakkijha1	PROPN
ejpam-6590	1	41	,	,	PUNCT
ejpam-6590	1	42	shatha	shatha	PROPN
ejpam-6590	1	43	hasan2,∗	hasan2,∗	PROPN
ejpam-6590	1	44	,	,	PUNCT
ejpam-6590	1	45	maryam	maryam	PROPN
ejpam-6590	1	46	m	m	PROPN
ejpam-6590	1	47	alholi3	alholi3	PROPN
ejpam-6590	1	48	1	1	NUM
ejpam-6590	1	49	department	department	NOUN
ejpam-6590	1	50	of	of	ADP
ejpam-6590	1	51	mathematics	mathematic	NOUN
ejpam-6590	1	52	,	,	PUNCT
ejpam-6590	1	53	faculty	faculty	NOUN
ejpam-6590	1	54	of	of	ADP
ejpam-6590	1	55	science	science	NOUN
ejpam-6590	1	56	,	,	PUNCT
ejpam-6590	1	57	the	the	DET
ejpam-6590	1	58	university	university	PROPN
ejpam-6590	1	59	of	of	ADP
ejpam-6590	1	60	jordan	jordan	PROPN
ejpam-6590	1	61	,	,	PUNCT
ejpam-6590	1	62	amman	amman	PROPN
ejpam-6590	1	63	11942	11942	NUM
ejpam-6590	1	64	,	,	PUNCT
ejpam-6590	1	65	jordan	jordan	PROPN
ejpam-6590	1	66	2	2	NUM
ejpam-6590	1	67	department	department	NOUN
ejpam-6590	1	68	of	of	ADP
ejpam-6590	1	69	applied	apply	VERB
ejpam-6590	1	70	science	science	NOUN
ejpam-6590	1	71	,	,	PUNCT
ejpam-6590	1	72	ajloun	ajloun	PROPN
ejpam-6590	1	73	college	college	PROPN
ejpam-6590	1	74	,	,	PUNCT
ejpam-6590	1	75	al	al	PROPN
ejpam-6590	1	76	-	-	PUNCT
ejpam-6590	1	77	balqa	balqa	NOUN
ejpam-6590	1	78	applied	apply	VERB
ejpam-6590	1	79	university	university	NOUN
ejpam-6590	1	80	,	,	PUNCT
ejpam-6590	1	81	ajloun	ajloun	NOUN
ejpam-6590	1	82	26816	26816	NUM
ejpam-6590	1	83	,	,	PUNCT
ejpam-6590	1	84	jordan	jordan	PROPN
ejpam-6590	1	85	3	3	NUM
ejpam-6590	1	86	department	department	PROPN
ejpam-6590	1	87	of	of	ADP
ejpam-6590	1	88	applied	applied	ADJ
ejpam-6590	1	89	taibah	taibah	PROPN
ejpam-6590	1	90	university	university	PROPN
ejpam-6590	1	91	,	,	PUNCT
ejpam-6590	1	92	al	al	PROPN
ejpam-6590	1	93	ula	ula	PROPN
ejpam-6590	1	94	,	,	PUNCT
ejpam-6590	1	95	saudi	saudi	PROPN
ejpam-6590	1	96	arabia	arabia	PROPN
ejpam-6590	1	97	abstract	abstract	NOUN
ejpam-6590	1	98	.	.	PUNCT
ejpam-6590	2	1	in	in	ADP
ejpam-6590	2	2	this	this	DET
ejpam-6590	2	3	paper	paper	NOUN
ejpam-6590	2	4	we	we	PRON
ejpam-6590	2	5	present	present	VERB
ejpam-6590	2	6	upper	upper	ADJ
ejpam-6590	2	7	bounds	bound	NOUN
ejpam-6590	2	8	for	for	ADP
ejpam-6590	2	9	spectral	spectral	ADJ
ejpam-6590	2	10	radius	radius	NOUN
ejpam-6590	2	11	inequalities	inequality	NOUN
ejpam-6590	2	12	of	of	ADP
ejpam-6590	2	13	2	2	NUM
ejpam-6590	2	14	×	×	NOUN
ejpam-6590	2	15	2	2	NUM
ejpam-6590	2	16	block	block	NOUN
ejpam-6590	2	17	accretive	accretive	ADJ
ejpam-6590	2	18	-	-	PUNCT
ejpam-6590	2	19	dissipative	dissipative	ADJ
ejpam-6590	2	20	matrices	matrix	NOUN
ejpam-6590	2	21	.	.	PUNCT
ejpam-6590	3	1	2020	2020	NUM
ejpam-6590	3	2	mathematics	mathematic	NOUN
ejpam-6590	3	3	subject	subject	NOUN
ejpam-6590	3	4	classifications	classification	NOUN
ejpam-6590	3	5	:	:	PUNCT
ejpam-6590	3	6	15a45	15a45	NUM
ejpam-6590	3	7	,	,	PUNCT
ejpam-6590	3	8	47b44	47b44	NUM
ejpam-6590	3	9	,	,	PUNCT
ejpam-6590	3	10	47a30	47a30	NUM
ejpam-6590	3	11	,	,	PUNCT
ejpam-6590	3	12	47a63	47a63	NUM
ejpam-6590	3	13	key	key	ADJ
ejpam-6590	3	14	words	word	NOUN
ejpam-6590	3	15	and	and	CCONJ
ejpam-6590	3	16	phrases	phrase	NOUN
ejpam-6590	3	17	:	:	PUNCT
ejpam-6590	3	18	spectral	spectral	ADJ
ejpam-6590	3	19	radius	radius	NOUN
ejpam-6590	3	20	,	,	PUNCT
ejpam-6590	3	21	accretive	accretive	ADJ
ejpam-6590	3	22	-	-	PUNCT
ejpam-6590	3	23	dissipative	dissipative	ADJ
ejpam-6590	3	24	matrices	matrix	NOUN
ejpam-6590	3	25	,	,	PUNCT
ejpam-6590	3	26	spectral	spectral	ADJ
ejpam-6590	3	27	norm	norm	NOUN
ejpam-6590	3	28	,	,	PUNCT
ejpam-6590	3	29	unitary	unitary	ADJ
ejpam-6590	3	30	matrix	matrix	NOUN
ejpam-6590	3	31	,	,	PUNCT
ejpam-6590	3	32	cartesian	cartesian	ADJ
ejpam-6590	3	33	decomposition	decomposition	NOUN
ejpam-6590	3	34	,	,	PUNCT
ejpam-6590	3	35	positive	positive	ADJ
ejpam-6590	3	36	semidefinite	semidefinite	NOUN
ejpam-6590	3	37	1	1	NUM
ejpam-6590	3	38	.	.	PUNCT
ejpam-6590	3	39	introduction	introduction	NOUN
ejpam-6590	3	40	the	the	DET
ejpam-6590	3	41	study	study	NOUN
ejpam-6590	3	42	of	of	ADP
ejpam-6590	3	43	matrix	matrix	NOUN
ejpam-6590	3	44	theory	theory	NOUN
ejpam-6590	3	45	has	have	AUX
ejpam-6590	3	46	become	become	VERB
ejpam-6590	3	47	more	more	ADV
ejpam-6590	3	48	and	and	CCONJ
ejpam-6590	3	49	more	more	ADV
ejpam-6590	3	50	popular	popular	ADJ
ejpam-6590	3	51	in	in	ADP
ejpam-6590	3	52	the	the	DET
ejpam-6590	3	53	last	last	ADJ
ejpam-6590	3	54	few	few	ADJ
ejpam-6590	3	55	decades	decade	NOUN
ejpam-6590	3	56	.	.	PUNCT
ejpam-6590	4	1	researchers	researcher	NOUN
ejpam-6590	4	2	are	be	AUX
ejpam-6590	4	3	attracted	attract	VERB
ejpam-6590	4	4	to	to	ADP
ejpam-6590	4	5	this	this	DET
ejpam-6590	4	6	subject	subject	NOUN
ejpam-6590	4	7	because	because	SCONJ
ejpam-6590	4	8	of	of	ADP
ejpam-6590	4	9	its	its	PRON
ejpam-6590	4	10	connections	connection	NOUN
ejpam-6590	4	11	with	with	ADP
ejpam-6590	4	12	other	other	ADJ
ejpam-6590	4	13	pure	pure	ADJ
ejpam-6590	4	14	and	and	CCONJ
ejpam-6590	4	15	applied	applied	ADJ
ejpam-6590	4	16	areas	area	NOUN
ejpam-6590	4	17	.	.	PUNCT
ejpam-6590	5	1	in	in	ADP
ejpam-6590	5	2	particular	particular	ADJ
ejpam-6590	5	3	,	,	PUNCT
ejpam-6590	5	4	the	the	DET
ejpam-6590	5	5	eigenvalues	eigenvalue	NOUN
ejpam-6590	5	6	are	be	AUX
ejpam-6590	5	7	crucial	crucial	ADJ
ejpam-6590	5	8	in	in	ADP
ejpam-6590	5	9	solving	solve	VERB
ejpam-6590	5	10	systems	system	NOUN
ejpam-6590	5	11	of	of	ADP
ejpam-6590	5	12	differential	differential	ADJ
ejpam-6590	5	13	equations	equation	NOUN
ejpam-6590	5	14	,	,	PUNCT
ejpam-6590	5	15	analyzing	analyze	VERB
ejpam-6590	5	16	population	population	NOUN
ejpam-6590	5	17	growth	growth	NOUN
ejpam-6590	5	18	models	model	NOUN
ejpam-6590	5	19	and	and	CCONJ
ejpam-6590	5	20	calculating	calculate	VERB
ejpam-6590	5	21	powers	power	NOUN
ejpam-6590	5	22	of	of	ADP
ejpam-6590	5	23	matrices	matrix	NOUN
ejpam-6590	5	24	.	.	PUNCT
ejpam-6590	6	1	it	it	PRON
ejpam-6590	6	2	is	be	AUX
ejpam-6590	6	3	not	not	PART
ejpam-6590	6	4	always	always	ADV
ejpam-6590	6	5	easy	easy	ADJ
ejpam-6590	6	6	to	to	PART
ejpam-6590	6	7	calculate	calculate	VERB
ejpam-6590	6	8	the	the	DET
ejpam-6590	6	9	eigenvalues	eigenvalue	NOUN
ejpam-6590	6	10	.	.	PUNCT
ejpam-6590	7	1	however	however	ADV
ejpam-6590	7	2	,	,	PUNCT
ejpam-6590	7	3	in	in	ADP
ejpam-6590	7	4	many	many	ADJ
ejpam-6590	7	5	scientific	scientific	ADJ
ejpam-6590	7	6	problems	problem	NOUN
ejpam-6590	7	7	it	it	PRON
ejpam-6590	7	8	is	be	AUX
ejpam-6590	7	9	enough	enough	ADJ
ejpam-6590	7	10	to	to	PART
ejpam-6590	7	11	know	know	VERB
ejpam-6590	7	12	that	that	SCONJ
ejpam-6590	7	13	the	the	DET
ejpam-6590	7	14	eigenvalues	eigenvalue	NOUN
ejpam-6590	7	15	lie	lie	VERB
ejpam-6590	7	16	in	in	ADP
ejpam-6590	7	17	specific	specific	ADJ
ejpam-6590	7	18	region	region	NOUN
ejpam-6590	7	19	.	.	PUNCT
ejpam-6590	8	1	such	such	ADJ
ejpam-6590	8	2	information	information	NOUN
ejpam-6590	8	3	is	be	AUX
ejpam-6590	8	4	provided	provide	VERB
ejpam-6590	8	5	by	by	ADP
ejpam-6590	8	6	comparing	compare	VERB
ejpam-6590	8	7	between	between	ADP
ejpam-6590	8	8	spectral	spectral	ADJ
ejpam-6590	8	9	radius	radius	NOUN
ejpam-6590	8	10	and	and	CCONJ
ejpam-6590	8	11	unitarily	unitarily	ADV
ejpam-6590	8	12	invariant	invariant	ADJ
ejpam-6590	8	13	norms	norm	NOUN
ejpam-6590	8	14	.	.	PUNCT
ejpam-6590	9	1	a	a	DET
ejpam-6590	9	2	large	large	ADJ
ejpam-6590	9	3	number	number	NOUN
ejpam-6590	9	4	of	of	ADP
ejpam-6590	9	5	inequalities	inequality	NOUN
ejpam-6590	9	6	involving	involve	VERB
ejpam-6590	9	7	spectral	spectral	ADJ
ejpam-6590	9	8	radius	radius	NOUN
ejpam-6590	9	9	in	in	ADP
ejpam-6590	9	10	addition	addition	NOUN
ejpam-6590	9	11	to	to	ADP
ejpam-6590	9	12	matrix	matrix	NOUN
ejpam-6590	9	13	norm	norm	NOUN
ejpam-6590	9	14	were	be	AUX
ejpam-6590	9	15	studied	study	VERB
ejpam-6590	9	16	in	in	ADP
ejpam-6590	9	17	many	many	ADJ
ejpam-6590	9	18	books	book	NOUN
ejpam-6590	9	19	that	that	PRON
ejpam-6590	9	20	is	be	AUX
ejpam-6590	9	21	concerning	concern	VERB
ejpam-6590	9	22	with	with	ADP
ejpam-6590	9	23	inequalities	inequality	NOUN
ejpam-6590	9	24	,	,	PUNCT
ejpam-6590	9	25	like	like	ADP
ejpam-6590	9	26	bhatia	bhatia	PROPN
ejpam-6590	9	27	,	,	PUNCT
ejpam-6590	9	28	2007	2007	NUM
ejpam-6590	10	1	[	[	X
ejpam-6590	10	2	1	1	NUM
ejpam-6590	10	3	]	]	PUNCT
ejpam-6590	10	4	.	.	PUNCT
ejpam-6590	11	1	some	some	DET
ejpam-6590	11	2	investigations	investigation	NOUN
ejpam-6590	11	3	on	on	ADP
ejpam-6590	11	4	norm	norm	NOUN
ejpam-6590	11	5	and	and	CCONJ
ejpam-6590	11	6	spectral	spectral	ADJ
ejpam-6590	11	7	radius	radius	NOUN
ejpam-6590	11	8	inequalities	inequality	NOUN
ejpam-6590	11	9	were	be	AUX
ejpam-6590	11	10	obtained	obtain	VERB
ejpam-6590	11	11	by	by	ADP
ejpam-6590	11	12	kittaneh	kittaneh	PROPN
ejpam-6590	11	13	in	in	ADP
ejpam-6590	11	14	2005	2005	NUM
ejpam-6590	12	1	[	[	X
ejpam-6590	12	2	2	2	NUM
ejpam-6590	12	3	]	]	PUNCT
ejpam-6590	12	4	,	,	PUNCT
ejpam-6590	12	5	elhaddad	elhaddad	ADJ
ejpam-6590	12	6	and	and	CCONJ
ejpam-6590	12	7	kittaneh	kittaneh	PROPN
ejpam-6590	12	8	in	in	ADP
ejpam-6590	12	9	2007[3	2007[3	NUM
ejpam-6590	12	10	]	]	PUNCT
ejpam-6590	12	11	.	.	PUNCT
ejpam-6590	13	1	in	in	ADP
ejpam-6590	13	2	2015	2015	NUM
ejpam-6590	13	3	,	,	PUNCT
ejpam-6590	13	4	abu	abu	PROPN
ejpam-6590	13	5	-	-	PUNCT
ejpam-6590	13	6	omar	omar	PROPN
ejpam-6590	13	7	and	and	CCONJ
ejpam-6590	13	8	kittaneh	kittaneh	PROPN
ejpam-6590	13	9	studied	study	VERB
ejpam-6590	13	10	similar	similar	ADJ
ejpam-6590	13	11	topics	topic	NOUN
ejpam-6590	13	12	;	;	PUNCT
ejpam-6590	13	13	they	they	PRON
ejpam-6590	13	14	applied	apply	VERB
ejpam-6590	13	15	spectral	spectral	ADJ
ejpam-6590	13	16	radius	radius	NOUN
ejpam-6590	13	17	and	and	CCONJ
ejpam-6590	13	18	norm	norm	NOUN
ejpam-6590	13	19	inequalities	inequality	NOUN
ejpam-6590	13	20	for	for	ADP
ejpam-6590	13	21	any	any	DET
ejpam-6590	13	22	two	two	NUM
ejpam-6590	13	23	by	by	ADP
ejpam-6590	13	24	two	two	NUM
ejpam-6590	13	25	block	block	NOUN
ejpam-6590	13	26	matrices	matrix	NOUN
ejpam-6590	13	27	[	[	X
ejpam-6590	13	28	4	4	NUM
ejpam-6590	13	29	]	]	PUNCT
ejpam-6590	13	30	.	.	PUNCT
ejpam-6590	14	1	moreover	moreover	ADV
ejpam-6590	14	2	,	,	PUNCT
ejpam-6590	14	3	in	in	ADP
ejpam-6590	14	4	2025	2025	NUM
ejpam-6590	14	5	,	,	PUNCT
ejpam-6590	14	6	sakkijha	sakkijha	NOUN
ejpam-6590	14	7	and	and	CCONJ
ejpam-6590	14	8	hasan	hasan	PROPN
ejpam-6590	14	9	studied	study	VERB
ejpam-6590	14	10	sum	sum	NOUN
ejpam-6590	14	11	,	,	PUNCT
ejpam-6590	14	12	difference	difference	NOUN
ejpam-6590	14	13	and	and	CCONJ
ejpam-6590	14	14	commutators	commutator	NOUN
ejpam-6590	14	15	for	for	ADP
ejpam-6590	14	16	spectral	spectral	ADJ
ejpam-6590	14	17	radius	radius	NOUN
ejpam-6590	14	18	inequalities	inequality	NOUN
ejpam-6590	14	19	involving	involve	VERB
ejpam-6590	14	20	accretive	accretive	ADJ
ejpam-6590	14	21	-	-	PUNCT
ejpam-6590	14	22	dissipative	dissipative	ADJ
ejpam-6590	14	23	matrices	matrix	NOUN
ejpam-6590	14	24	[	[	X
ejpam-6590	14	25	5	5	NUM
ejpam-6590	14	26	]	]	PUNCT
ejpam-6590	14	27	.	.	PUNCT
ejpam-6590	15	1	∗corresponding	∗corresponde	VERB
ejpam-6590	15	2	author	author	NOUN
ejpam-6590	15	3	.	.	PUNCT
ejpam-6590	16	1	doi	doi	NOUN
ejpam-6590	16	2	:	:	PUNCT
ejpam-6590	16	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6590	https://doi.org/10.29020/nybg.ejpam.v18i3.6590	NUM
ejpam-6590	16	4	email	email	NOUN
ejpam-6590	16	5	addresses	address	NOUN
ejpam-6590	16	6	:	:	PUNCT
ejpam-6590	16	7	m.sakkijha@ju.edu.jo	m.sakkijha@ju.edu.jo	PROPN
ejpam-6590	16	8	(	(	PUNCT
ejpam-6590	16	9	m.	m.	NOUN
ejpam-6590	16	10	sakkijha	sakkijha	PROPN
ejpam-6590	16	11	)	)	PUNCT
ejpam-6590	16	12	,	,	PUNCT
ejpam-6590	16	13	shatha@bau.edu.jo	shatha@bau.edu.jo	NOUN
ejpam-6590	16	14	(	(	PUNCT
ejpam-6590	16	15	s.	s.	PROPN
ejpam-6590	16	16	hasan	hasan	PROPN
ejpam-6590	16	17	)	)	PUNCT
ejpam-6590	16	18	,	,	PUNCT
ejpam-6590	16	19	mholi@taibahu.edu.sa	mholi@taibahu.edu.sa	NOUN
ejpam-6590	16	20	(	(	PUNCT
ejpam-6590	16	21	m.	m.	NOUN
ejpam-6590	16	22	alholi	alholi	PROPN
ejpam-6590	16	23	)	)	PUNCT
ejpam-6590	16	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6590	17	1	1	1	NUM
ejpam-6590	17	2	copyright	copyright	NOUN
ejpam-6590	17	3	:	:	PUNCT
ejpam-6590	17	4	©	©	PROPN
ejpam-6590	17	5	2025	2025	NUM
ejpam-6590	17	6	the	the	DET
ejpam-6590	17	7	author(s	author(s	NOUN
ejpam-6590	17	8	)	)	PUNCT
ejpam-6590	17	9	.	.	PUNCT
ejpam-6590	18	1	(	(	PUNCT
ejpam-6590	18	2	cc	cc	NOUN
ejpam-6590	18	3	by	by	ADP
ejpam-6590	18	4	-	-	PUNCT
ejpam-6590	18	5	nc	nc	PROPN
ejpam-6590	18	6	4.0	4.0	NUM
ejpam-6590	18	7	)	)	PUNCT
ejpam-6590	18	8	m.	m.	NOUN
ejpam-6590	18	9	sakkijha	sakkijha	PROPN
ejpam-6590	18	10	,	,	PUNCT
ejpam-6590	18	11	s.	s.	PROPN
ejpam-6590	18	12	hasan	hasan	PROPN
ejpam-6590	18	13	,	,	PUNCT
ejpam-6590	18	14	m.	m.	NOUN
ejpam-6590	18	15	alholi	alholi	PROPN
ejpam-6590	18	16	/	/	SYM
ejpam-6590	18	17	eur	eur	PROPN
ejpam-6590	18	18	.	.	PUNCT
ejpam-6590	19	1	j.	j.	PROPN
ejpam-6590	19	2	pure	pure	PROPN
ejpam-6590	19	3	appl	appl	PROPN
ejpam-6590	19	4	.	.	PROPN
ejpam-6590	19	5	math	math	PROPN
ejpam-6590	19	6	,	,	PUNCT
ejpam-6590	19	7	18	18	NUM
ejpam-6590	19	8	(	(	PUNCT
ejpam-6590	19	9	3	3	NUM
ejpam-6590	19	10	)	)	PUNCT
ejpam-6590	19	11	(	(	PUNCT
ejpam-6590	19	12	2025	2025	NUM
ejpam-6590	19	13	)	)	PUNCT
ejpam-6590	19	14	,	,	PUNCT
ejpam-6590	19	15	6590	6590	NUM
ejpam-6590	19	16	2	2	NUM
ejpam-6590	19	17	of	of	ADP
ejpam-6590	19	18	9	9	NUM
ejpam-6590	19	19	the	the	DET
ejpam-6590	19	20	spectral	spectral	ADJ
ejpam-6590	19	21	radius	radius	PROPN
ejpam-6590	19	22	r(x	r(x	PROPN
ejpam-6590	19	23	)	)	PUNCT
ejpam-6590	19	24	of	of	ADP
ejpam-6590	19	25	a	a	DET
ejpam-6590	19	26	matrix	matrix	NOUN
ejpam-6590	19	27	x	x	PUNCT
ejpam-6590	19	28	∈mn(c	∈mn(c	NOUN
ejpam-6590	19	29	)	)	PUNCT
ejpam-6590	19	30	is	be	AUX
ejpam-6590	19	31	defined	define	VERB
ejpam-6590	19	32	as	as	ADP
ejpam-6590	19	33	r(x	r(x	PROPN
ejpam-6590	19	34	)	)	PUNCT
ejpam-6590	20	1	=	=	SYM
ejpam-6590	20	2	max{|λ|	max{|λ|	NOUN
ejpam-6590	20	3	:	:	PUNCT
ejpam-6590	21	1	λ	λ	X
ejpam-6590	21	2	∈	∈	PROPN
ejpam-6590	21	3	σ(x	σ(x	PROPN
ejpam-6590	21	4	)	)	PUNCT
ejpam-6590	21	5	}	}	PUNCT
ejpam-6590	21	6	.	.	PUNCT
ejpam-6590	22	1	(	(	PUNCT
ejpam-6590	22	2	1	1	X
ejpam-6590	22	3	)	)	PUNCT
ejpam-6590	22	4	it	it	PRON
ejpam-6590	22	5	’s	’	VERB
ejpam-6590	22	6	well	well	ADV
ejpam-6590	22	7	known	know	VERB
ejpam-6590	22	8	that	that	SCONJ
ejpam-6590	22	9	r(x	r(x	PROPN
ejpam-6590	22	10	)	)	PUNCT
ejpam-6590	22	11	⩽	⩽	ADJ
ejpam-6590	22	12	∥x∥	∥x∥	NOUN
ejpam-6590	22	13	for	for	ADP
ejpam-6590	22	14	every	every	DET
ejpam-6590	22	15	x	x	SYM
ejpam-6590	22	16	∈mn(c	∈mn(c	NOUN
ejpam-6590	22	17	)	)	PUNCT
ejpam-6590	22	18	,	,	PUNCT
ejpam-6590	22	19	(	(	PUNCT
ejpam-6590	22	20	2	2	X
ejpam-6590	22	21	)	)	PUNCT
ejpam-6590	22	22	if	if	SCONJ
ejpam-6590	22	23	x	x	PRON
ejpam-6590	22	24	is	be	AUX
ejpam-6590	22	25	positive	positive	ADJ
ejpam-6590	22	26	semidefinite	semidefinite	NOUN
ejpam-6590	22	27	,	,	PUNCT
ejpam-6590	22	28	then	then	ADV
ejpam-6590	22	29	r(x	r(x	PROPN
ejpam-6590	22	30	)	)	PUNCT
ejpam-6590	23	1	=	=	SYM
ejpam-6590	23	2	∥x∥	∥x∥	NOUN
ejpam-6590	23	3	,	,	PUNCT
ejpam-6590	23	4	(	(	PUNCT
ejpam-6590	23	5	3	3	X
ejpam-6590	23	6	)	)	PUNCT
ejpam-6590	23	7	where	where	SCONJ
ejpam-6590	23	8	∥x∥	∥x∥	NOUN
ejpam-6590	23	9	is	be	AUX
ejpam-6590	23	10	the	the	DET
ejpam-6590	23	11	spectral	spectral	ADJ
ejpam-6590	23	12	norm	norm	NOUN
ejpam-6590	23	13	of	of	ADP
ejpam-6590	23	14	x	x	PUNCT
ejpam-6590	23	15	which	which	PRON
ejpam-6590	23	16	is	be	AUX
ejpam-6590	23	17	defined	define	VERB
ejpam-6590	23	18	as	as	ADP
ejpam-6590	23	19	max∥ν∥=1∥xν∥	max∥ν∥=1∥xν∥	NOUN
ejpam-6590	23	20	and	and	CCONJ
ejpam-6590	23	21	satisfies	satisfie	NOUN
ejpam-6590	23	22	∥x∥	∥x∥	NOUN
ejpam-6590	23	23	=	=	SYM
ejpam-6590	23	24	∥x∗∥	∥x∗∥	PROPN
ejpam-6590	23	25	=	=	SYM
ejpam-6590	23	26	∥x∗x∥1/2	∥x∗x∥1/2	PROPN
ejpam-6590	23	27	=	=	PROPN
ejpam-6590	23	28	∥xx∗∥1/2	∥xx∗∥1/2	PROPN
ejpam-6590	23	29	.	.	PUNCT
ejpam-6590	24	1	(	(	PUNCT
ejpam-6590	24	2	4	4	X
ejpam-6590	24	3	)	)	PUNCT
ejpam-6590	24	4	moreover	moreover	ADV
ejpam-6590	24	5	,	,	PUNCT
ejpam-6590	24	6	for	for	ADP
ejpam-6590	24	7	any	any	DET
ejpam-6590	24	8	x	x	NOUN
ejpam-6590	24	9	,	,	PUNCT
ejpam-6590	24	10	υ	υ	PROPN
ejpam-6590	24	11	∈mn(c	∈mn(c	NOUN
ejpam-6590	24	12	)	)	PUNCT
ejpam-6590	24	13	,	,	PUNCT
ejpam-6590	24	14	δ	δ	PROPN
ejpam-6590	24	15	∈	∈	PROPN
ejpam-6590	24	16	c	c	PROPN
ejpam-6590	24	17	and	and	CCONJ
ejpam-6590	24	18	a	a	DET
ejpam-6590	24	19	positive	positive	ADJ
ejpam-6590	24	20	integer	integer	NOUN
ejpam-6590	24	21	n	n	CCONJ
ejpam-6590	24	22	,	,	PUNCT
ejpam-6590	24	23	r(δx	r(δx	NOUN
ejpam-6590	24	24	)	)	PUNCT
ejpam-6590	24	25	=	=	SYM
ejpam-6590	24	26	|δ|r(x	|δ|r(x	PROPN
ejpam-6590	24	27	)	)	PUNCT
ejpam-6590	24	28	.	.	PUNCT
ejpam-6590	25	1	(	(	PUNCT
ejpam-6590	25	2	5	5	X
ejpam-6590	25	3	)	)	PUNCT
ejpam-6590	25	4	a	a	DET
ejpam-6590	25	5	special	special	ADJ
ejpam-6590	25	6	case	case	NOUN
ejpam-6590	25	7	of	of	ADP
ejpam-6590	25	8	the	the	DET
ejpam-6590	25	9	spectral	spectral	ADJ
ejpam-6590	25	10	mapping	mapping	NOUN
ejpam-6590	25	11	theorem	theorem	VERB
ejpam-6590	25	12	,	,	PUNCT
ejpam-6590	25	13	which	which	PRON
ejpam-6590	25	14	asserts	assert	VERB
ejpam-6590	25	15	that	that	SCONJ
ejpam-6590	25	16	r	r	NOUN
ejpam-6590	25	17	(	(	PUNCT
ejpam-6590	25	18	xn	xn	PROPN
ejpam-6590	25	19	)	)	PUNCT
ejpam-6590	25	20	=	=	SYM
ejpam-6590	25	21	rn(x	rn(x	X
ejpam-6590	25	22	)	)	PUNCT
ejpam-6590	25	23	.	.	PUNCT
ejpam-6590	26	1	(	(	PUNCT
ejpam-6590	26	2	6	6	NUM
ejpam-6590	26	3	)	)	PUNCT
ejpam-6590	26	4	in	in	ADP
ejpam-6590	26	5	addition	addition	NOUN
ejpam-6590	26	6	,	,	PUNCT
ejpam-6590	26	7	two	two	NUM
ejpam-6590	26	8	useful	useful	ADJ
ejpam-6590	26	9	facts	fact	NOUN
ejpam-6590	26	10	that	that	PRON
ejpam-6590	26	11	are	be	AUX
ejpam-6590	26	12	related	relate	VERB
ejpam-6590	26	13	to	to	ADP
ejpam-6590	26	14	the	the	DET
ejpam-6590	26	15	spectral	spectral	ADJ
ejpam-6590	26	16	radius	radius	NOUN
ejpam-6590	26	17	are	be	AUX
ejpam-6590	26	18	as	as	SCONJ
ejpam-6590	26	19	follows	follow	VERB
ejpam-6590	26	20	:	:	PUNCT
ejpam-6590	27	1	r	r	NOUN
ejpam-6590	27	2	(	(	PUNCT
ejpam-6590	27	3	x∗	x∗	X
ejpam-6590	27	4	)	)	PUNCT
ejpam-6590	27	5	=	=	SYM
ejpam-6590	27	6	r(x	r(x	PROPN
ejpam-6590	27	7	)	)	PUNCT
ejpam-6590	27	8	(	(	PUNCT
ejpam-6590	27	9	7	7	NUM
ejpam-6590	27	10	)	)	PUNCT
ejpam-6590	27	11	and	and	CCONJ
ejpam-6590	27	12	r	r	NOUN
ejpam-6590	27	13	(	(	PUNCT
ejpam-6590	27	14	uxu∗	uxu∗	NOUN
ejpam-6590	27	15	)	)	PUNCT
ejpam-6590	27	16	=	=	SYM
ejpam-6590	27	17	r(x	r(x	PROPN
ejpam-6590	27	18	)	)	PUNCT
ejpam-6590	27	19	(	(	PUNCT
ejpam-6590	27	20	8)	8)	NUM
ejpam-6590	27	21	for	for	ADP
ejpam-6590	27	22	every	every	DET
ejpam-6590	27	23	unitary	unitary	ADJ
ejpam-6590	27	24	matrix	matrix	NOUN
ejpam-6590	27	25	u	u	NOUN
ejpam-6590	27	26	,	,	PUNCT
ejpam-6590	27	27	i.e.	i.e.	X
ejpam-6590	27	28	u	u	NOUN
ejpam-6590	27	29	∗	∗	NOUN
ejpam-6590	27	30	u	u	NOUN
ejpam-6590	27	31	=	=	PROPN
ejpam-6590	27	32	i	i	PROPN
ejpam-6590	27	33	,	,	PUNCT
ejpam-6590	27	34	a	a	DET
ejpam-6590	27	35	commutative	commutative	ADJ
ejpam-6590	27	36	property	property	NOUN
ejpam-6590	27	37	which	which	PRON
ejpam-6590	27	38	asserts	assert	VERB
ejpam-6590	27	39	that	that	SCONJ
ejpam-6590	27	40	r(xυ	r(xυ	NOUN
ejpam-6590	27	41	)	)	PUNCT
ejpam-6590	27	42	=	=	PUNCT
ejpam-6590	27	43	r(υx	r(υx	PROPN
ejpam-6590	27	44	)	)	PUNCT
ejpam-6590	27	45	.	.	PUNCT
ejpam-6590	28	1	(	(	PUNCT
ejpam-6590	28	2	9	9	X
ejpam-6590	28	3	)	)	PUNCT
ejpam-6590	28	4	the	the	DET
ejpam-6590	28	5	last	last	ADJ
ejpam-6590	28	6	property	property	NOUN
ejpam-6590	28	7	is	be	AUX
ejpam-6590	28	8	an	an	DET
ejpam-6590	28	9	immediate	immediate	ADJ
ejpam-6590	28	10	consequence	consequence	NOUN
ejpam-6590	28	11	of	of	ADP
ejpam-6590	28	12	the	the	DET
ejpam-6590	28	13	fact	fact	NOUN
ejpam-6590	28	14	that	that	SCONJ
ejpam-6590	28	15	the	the	DET
ejpam-6590	28	16	spectra	spectra	NOUN
ejpam-6590	28	17	of	of	ADP
ejpam-6590	28	18	the	the	DET
ejpam-6590	28	19	operators	operator	NOUN
ejpam-6590	28	20	xυ	xυ	NOUN
ejpam-6590	28	21	and	and	CCONJ
ejpam-6590	28	22	υx	υx	PART
ejpam-6590	28	23	have	have	VERB
ejpam-6590	28	24	the	the	DET
ejpam-6590	28	25	same	same	ADJ
ejpam-6590	28	26	nonzero	nonzero	NOUN
ejpam-6590	28	27	elements	element	NOUN
ejpam-6590	28	28	.	.	PUNCT
ejpam-6590	29	1	a	a	DET
ejpam-6590	29	2	matrix	matrix	NOUN
ejpam-6590	29	3	ψ	ψ	ADP
ejpam-6590	29	4	∈	∈	PROPN
ejpam-6590	29	5	mn(c	mn(c	X
ejpam-6590	29	6	)	)	PUNCT
ejpam-6590	29	7	is	be	AUX
ejpam-6590	29	8	referred	refer	VERB
ejpam-6590	29	9	to	to	ADP
ejpam-6590	29	10	as	as	ADP
ejpam-6590	29	11	positive	positive	ADJ
ejpam-6590	29	12	semidefinite	semidefinite	NOUN
ejpam-6590	29	13	(	(	PUNCT
ejpam-6590	29	14	p.s.d	p.s.d	NOUN
ejpam-6590	29	15	.	.	PUNCT
ejpam-6590	29	16	)	)	PUNCT
ejpam-6590	29	17	matrix	matrix	NOUN
ejpam-6590	30	1	if	if	SCONJ
ejpam-6590	30	2	(	(	PUNCT
ejpam-6590	30	3	ψν	ψν	NOUN
ejpam-6590	30	4	,	,	PUNCT
ejpam-6590	30	5	ν	ν	NOUN
ejpam-6590	30	6	)	)	PUNCT
ejpam-6590	30	7	≥	≥	NOUN
ejpam-6590	30	8	0	0	NUM
ejpam-6590	30	9	∀ν	∀ν	PROPN
ejpam-6590	30	10	∈	∈	PROPN
ejpam-6590	31	1	cn	cn	PROPN
ejpam-6590	31	2	.	.	PUNCT
ejpam-6590	32	1	it	it	PRON
ejpam-6590	32	2	is	be	AUX
ejpam-6590	32	3	called	call	VERB
ejpam-6590	32	4	accretive	accretive	ADJ
ejpam-6590	32	5	-	-	PUNCT
ejpam-6590	32	6	dissipative	dissipative	NOUN
ejpam-6590	32	7	(	(	PUNCT
ejpam-6590	32	8	acc	acc	PROPN
ejpam-6590	32	9	-	-	PUNCT
ejpam-6590	32	10	dis	dis	PROPN
ejpam-6590	32	11	)	)	PUNCT
ejpam-6590	32	12	if	if	SCONJ
ejpam-6590	32	13	in	in	ADP
ejpam-6590	32	14	its	its	PRON
ejpam-6590	32	15	cartesian	cartesian	ADJ
ejpam-6590	32	16	decomposition	decomposition	NOUN
ejpam-6590	32	17	(	(	PUNCT
ejpam-6590	32	18	cd	cd	PROPN
ejpam-6590	32	19	)	)	PUNCT
ejpam-6590	32	20	ψ	ψ	NOUN
ejpam-6590	33	1	=	=	SYM
ejpam-6590	33	2	ψ1	ψ1	NOUN
ejpam-6590	33	3	+	+	CCONJ
ejpam-6590	33	4	iψ2	iψ2	PROPN
ejpam-6590	33	5	,	,	PUNCT
ejpam-6590	33	6	the	the	DET
ejpam-6590	33	7	matrices	matrix	NOUN
ejpam-6590	33	8	ψ1	ψ1	NOUN
ejpam-6590	33	9	=	=	PUNCT
ejpam-6590	33	10	re(ψ	re(ψ	PROPN
ejpam-6590	33	11	)	)	PUNCT
ejpam-6590	33	12	=	=	SYM
ejpam-6590	34	1	ψ+ψ∗	ψ+ψ∗	X
ejpam-6590	34	2	2	2	NUM
ejpam-6590	34	3	and	and	CCONJ
ejpam-6590	34	4	ψ2	ψ2	NOUN
ejpam-6590	34	5	=	=	SYM
ejpam-6590	34	6	im(ψ	im(ψ	X
ejpam-6590	34	7	)	)	PUNCT
ejpam-6590	34	8	=	=	SYM
ejpam-6590	35	1	ψ−ψ∗	ψ−ψ∗	ADJ
ejpam-6590	35	2	2i	2i	NOUN
ejpam-6590	35	3	are	be	AUX
ejpam-6590	35	4	p.s.d	p.s.d	ADJ
ejpam-6590	35	5	.	.	PUNCT
ejpam-6590	36	1	accretive	accretive	ADJ
ejpam-6590	36	2	-	-	PUNCT
ejpam-6590	36	3	dissipative	dissipative	NOUN
ejpam-6590	36	4	matrices	matrix	NOUN
ejpam-6590	36	5	found	find	VERB
ejpam-6590	36	6	many	many	ADJ
ejpam-6590	36	7	applications	application	NOUN
ejpam-6590	36	8	.	.	PUNCT
ejpam-6590	37	1	for	for	ADP
ejpam-6590	37	2	example	example	NOUN
ejpam-6590	37	3	,	,	PUNCT
ejpam-6590	37	4	gunzburger	gunzburger	NOUN
ejpam-6590	37	5	and	and	CCONJ
ejpam-6590	37	6	plemmons	plemmon	NOUN
ejpam-6590	37	7	used	use	VERB
ejpam-6590	37	8	the	the	DET
ejpam-6590	37	9	results	result	NOUN
ejpam-6590	37	10	in	in	ADP
ejpam-6590	37	11	their	their	PRON
ejpam-6590	37	12	study	study	NOUN
ejpam-6590	37	13	of	of	ADP
ejpam-6590	37	14	energy	energy	NOUN
ejpam-6590	37	15	conserving	conserve	VERB
ejpam-6590	37	16	norms	norm	NOUN
ejpam-6590	37	17	for	for	ADP
ejpam-6590	37	18	the	the	DET
ejpam-6590	37	19	solution	solution	NOUN
ejpam-6590	37	20	of	of	ADP
ejpam-6590	37	21	hyperbolic	hyperbolic	ADJ
ejpam-6590	37	22	systems	system	NOUN
ejpam-6590	37	23	of	of	ADP
ejpam-6590	37	24	partial	partial	ADJ
ejpam-6590	37	25	differential	differential	NOUN
ejpam-6590	37	26	equations	equation	NOUN
ejpam-6590	37	27	,	,	PUNCT
ejpam-6590	37	28	see	see	VERB
ejpam-6590	37	29	[	[	X
ejpam-6590	37	30	6	6	NUM
ejpam-6590	37	31	]	]	PUNCT
ejpam-6590	37	32	.	.	PUNCT
ejpam-6590	38	1	many	many	ADJ
ejpam-6590	38	2	researchers	researcher	NOUN
ejpam-6590	38	3	are	be	AUX
ejpam-6590	38	4	interested	interested	ADJ
ejpam-6590	38	5	with	with	ADP
ejpam-6590	38	6	this	this	DET
ejpam-6590	38	7	kind	kind	NOUN
ejpam-6590	38	8	of	of	ADP
ejpam-6590	38	9	matrices	matrix	NOUN
ejpam-6590	38	10	like	like	ADP
ejpam-6590	38	11	,	,	PUNCT
ejpam-6590	38	12	george	george	NOUN
ejpam-6590	38	13	and	and	CCONJ
ejpam-6590	38	14	ikramor	ikramor	NOUN
ejpam-6590	38	15	(	(	PUNCT
ejpam-6590	38	16	2005)[7	2005)[7	NOUN
ejpam-6590	38	17	]	]	X
ejpam-6590	38	18	,	,	PUNCT
ejpam-6590	38	19	also	also	ADV
ejpam-6590	38	20	sakkijha	sakkijha	NOUN
ejpam-6590	38	21	and	and	CCONJ
ejpam-6590	38	22	hasan	hasan	PROPN
ejpam-6590	38	23	(	(	PUNCT
ejpam-6590	38	24	2024)[8	2024)[8	PROPN
ejpam-6590	38	25	]	]	PUNCT
ejpam-6590	38	26	.	.	PUNCT
ejpam-6590	39	1	m.	m.	NOUN
ejpam-6590	39	2	sakkijha	sakkijha	PROPN
ejpam-6590	39	3	,	,	PUNCT
ejpam-6590	39	4	s.	s.	PROPN
ejpam-6590	39	5	hasan	hasan	PROPN
ejpam-6590	39	6	,	,	PUNCT
ejpam-6590	39	7	m.	m.	NOUN
ejpam-6590	39	8	alholi	alholi	PROPN
ejpam-6590	39	9	/	/	SYM
ejpam-6590	39	10	eur	eur	PROPN
ejpam-6590	39	11	.	.	PUNCT
ejpam-6590	40	1	j.	j.	PROPN
ejpam-6590	40	2	pure	pure	PROPN
ejpam-6590	40	3	appl	appl	PROPN
ejpam-6590	40	4	.	.	PROPN
ejpam-6590	40	5	math	math	PROPN
ejpam-6590	40	6	,	,	PUNCT
ejpam-6590	40	7	18	18	NUM
ejpam-6590	40	8	(	(	PUNCT
ejpam-6590	40	9	3	3	NUM
ejpam-6590	40	10	)	)	PUNCT
ejpam-6590	40	11	(	(	PUNCT
ejpam-6590	40	12	2025	2025	NUM
ejpam-6590	40	13	)	)	PUNCT
ejpam-6590	40	14	,	,	PUNCT
ejpam-6590	40	15	6590	6590	NUM
ejpam-6590	40	16	3	3	NUM
ejpam-6590	40	17	of	of	ADP
ejpam-6590	40	18	9	9	NUM
ejpam-6590	40	19	2	2	NUM
ejpam-6590	40	20	.	.	PUNCT
ejpam-6590	40	21	basic	basic	ADJ
ejpam-6590	40	22	lemmas	lemma	NOUN
ejpam-6590	40	23	in	in	ADP
ejpam-6590	40	24	order	order	NOUN
ejpam-6590	40	25	to	to	PART
ejpam-6590	40	26	prove	prove	VERB
ejpam-6590	40	27	our	our	PRON
ejpam-6590	40	28	main	main	ADJ
ejpam-6590	40	29	results	result	NOUN
ejpam-6590	41	1	,	,	PUNCT
ejpam-6590	41	2	we	we	PRON
ejpam-6590	41	3	need	need	VERB
ejpam-6590	41	4	the	the	DET
ejpam-6590	41	5	following	follow	VERB
ejpam-6590	41	6	lemmas	lemmas	NOUN
ejpam-6590	41	7	.	.	PUNCT
ejpam-6590	42	1	lemma	lemma	PROPN
ejpam-6590	42	2	1	1	NUM
ejpam-6590	42	3	.	.	PUNCT
ejpam-6590	43	1	[	[	X
ejpam-6590	43	2	9	9	NUM
ejpam-6590	43	3	]	]	X
ejpam-6590	43	4	if	if	SCONJ
ejpam-6590	43	5	ψ1	ψ1	NOUN
ejpam-6590	43	6	,	,	PUNCT
ejpam-6590	43	7	ψ2	ψ2	NOUN
ejpam-6590	43	8	∈mn(c	∈mn(c	NOUN
ejpam-6590	43	9	)	)	PUNCT
ejpam-6590	43	10	are	be	AUX
ejpam-6590	43	11	p.s.d	p.s.d	ADJ
ejpam-6590	43	12	,	,	PUNCT
ejpam-6590	43	13	then	then	ADV
ejpam-6590	43	14	∥ψ1	∥ψ1	VERB
ejpam-6590	43	15	+	+	CCONJ
ejpam-6590	43	16	iψ2∥	iψ2∥	PROPN
ejpam-6590	43	17	⩽	⩽	PROPN
ejpam-6590	43	18	∥ψ1	∥ψ1	VERB
ejpam-6590	43	19	+	+	CCONJ
ejpam-6590	43	20	ψ2∥.	ψ2∥.	NOUN
ejpam-6590	43	21	lemma	lemma	NOUN
ejpam-6590	43	22	2	2	NUM
ejpam-6590	43	23	.	.	PUNCT
ejpam-6590	44	1	[	[	X
ejpam-6590	44	2	10	10	NUM
ejpam-6590	44	3	]	]	X
ejpam-6590	44	4	if	if	SCONJ
ejpam-6590	44	5	ψ1	ψ1	NOUN
ejpam-6590	44	6	,	,	PUNCT
ejpam-6590	44	7	ψ2	ψ2	NOUN
ejpam-6590	44	8	∈mn(c	∈mn(c	NOUN
ejpam-6590	44	9	)	)	PUNCT
ejpam-6590	44	10	are	be	AUX
ejpam-6590	44	11	p.s.d	p.s.d	ADJ
ejpam-6590	44	12	,	,	PUNCT
ejpam-6590	44	13	then	then	ADV
ejpam-6590	44	14	∥ψ1	∥ψ1	VERB
ejpam-6590	45	1	+	+	CCONJ
ejpam-6590	45	2	ψ2∥	ψ2∥	PROPN
ejpam-6590	45	3	⩽	⩽	PROPN
ejpam-6590	45	4	max(∥ψ1∥	max(∥ψ1∥	PROPN
ejpam-6590	45	5	,	,	PUNCT
ejpam-6590	45	6	∥ψ2∥	∥ψ2∥	PROPN
ejpam-6590	45	7	)	)	PUNCT
ejpam-6590	46	1	+	+	CCONJ
ejpam-6590	46	2	∥∥∥ψ1/2	∥∥∥ψ1/2	PROPN
ejpam-6590	46	3	1	1	NUM
ejpam-6590	46	4	ψ	ψ	SYM
ejpam-6590	46	5	1/2	1/2	NUM
ejpam-6590	46	6	2	2	NUM
ejpam-6590	46	7	∥∥∥	∥∥∥	NOUN
ejpam-6590	46	8	.	.	PUNCT
ejpam-6590	47	1	lemma	lemma	PROPN
ejpam-6590	47	2	3	3	X
ejpam-6590	47	3	.	.	PUNCT
ejpam-6590	48	1	[	[	X
ejpam-6590	48	2	11	11	NUM
ejpam-6590	48	3	]	]	X
ejpam-6590	48	4	if	if	SCONJ
ejpam-6590	48	5	ψ1	ψ1	NOUN
ejpam-6590	48	6	,	,	PUNCT
ejpam-6590	48	7	ψ2	ψ2	NOUN
ejpam-6590	48	8	∈mn(c	∈mn(c	NOUN
ejpam-6590	48	9	)	)	PUNCT
ejpam-6590	48	10	are	be	AUX
ejpam-6590	48	11	p.s.d	p.s.d	ADJ
ejpam-6590	48	12	,	,	PUNCT
ejpam-6590	48	13	then	then	ADV
ejpam-6590	48	14	∥ψ1ψ2	∥ψ1ψ2	PROPN
ejpam-6590	48	15	−	−	PROPN
ejpam-6590	48	16	ψ2ψ1∥	ψ2ψ1∥	NOUN
ejpam-6590	48	17	⩽	⩽	NOUN
ejpam-6590	48	18	1	1	NUM
ejpam-6590	48	19	2	2	NUM
ejpam-6590	48	20	∥ψ1∥∥ψ2∥.	∥ψ1∥∥ψ2∥.	NOUN
ejpam-6590	48	21	lemma	lemma	PROPN
ejpam-6590	48	22	4	4	NUM
ejpam-6590	48	23	.	.	PUNCT
ejpam-6590	49	1	[	[	X
ejpam-6590	49	2	12	12	NUM
ejpam-6590	49	3	]	]	X
ejpam-6590	49	4	if	if	SCONJ
ejpam-6590	49	5	ψ1	ψ1	NOUN
ejpam-6590	49	6	,	,	PUNCT
ejpam-6590	49	7	ψ2	ψ2	NOUN
ejpam-6590	49	8	,	,	PUNCT
ejpam-6590	49	9	ψ3	ψ3	NOUN
ejpam-6590	49	10	,	,	PUNCT
ejpam-6590	49	11	ψ4	ψ4	PROPN
ejpam-6590	49	12	∈mn(c	∈mn(c	PROPN
ejpam-6590	49	13	)	)	PUNCT
ejpam-6590	49	14	,	,	PUNCT
ejpam-6590	50	1	then	then	ADV
ejpam-6590	50	2	r	r	NOUN
ejpam-6590	50	3	(	(	PUNCT
ejpam-6590	50	4	[	[	PUNCT
ejpam-6590	50	5	ψ1	ψ1	ADJ
ejpam-6590	50	6	ψ2	ψ2	NOUN
ejpam-6590	50	7	ψ3	ψ3	ADJ
ejpam-6590	50	8	ψ4	ψ4	PROPN
ejpam-6590	50	9	]	]	PUNCT
ejpam-6590	50	10	)	)	PUNCT
ejpam-6590	50	11	⩽	⩽	ADJ
ejpam-6590	50	12	r	r	NOUN
ejpam-6590	50	13	(	(	PUNCT
ejpam-6590	50	14	[	[	PUNCT
ejpam-6590	50	15	∥ψ1∥	∥ψ1∥	PROPN
ejpam-6590	50	16	∥ψ2∥	∥ψ2∥	PROPN
ejpam-6590	50	17	∥ψ3∥	∥ψ3∥	PROPN
ejpam-6590	50	18	∥ψ4∥	∥ψ4∥	PROPN
ejpam-6590	50	19	]	]	PUNCT
ejpam-6590	50	20	)	)	PUNCT
ejpam-6590	50	21	.	.	PUNCT
ejpam-6590	51	1	lemma	lemma	PROPN
ejpam-6590	51	2	5	5	NUM
ejpam-6590	51	3	.	.	PUNCT
ejpam-6590	52	1	[	[	X
ejpam-6590	52	2	13	13	NUM
ejpam-6590	52	3	]	]	X
ejpam-6590	52	4	if	if	SCONJ
ejpam-6590	52	5	ψ1	ψ1	NOUN
ejpam-6590	52	6	,	,	PUNCT
ejpam-6590	52	7	ψ2	ψ2	NOUN
ejpam-6590	52	8	∈mn(c	∈mn(c	NOUN
ejpam-6590	52	9	)	)	PUNCT
ejpam-6590	52	10	,	,	PUNCT
ejpam-6590	52	11	then∥∥∥∥	then∥∥∥∥	PROPN
ejpam-6590	52	12	[	[	PUNCT
ejpam-6590	52	13	ψ1	ψ1	NOUN
ejpam-6590	52	14	0	0	NUM
ejpam-6590	52	15	0	0	NUM
ejpam-6590	52	16	ψ2	ψ2	NOUN
ejpam-6590	52	17	]	]	PUNCT
ejpam-6590	52	18	∥∥∥∥	∥∥∥∥	NUM
ejpam-6590	52	19	=	=	SYM
ejpam-6590	52	20	max(∥ψ1∥	max(∥ψ1∥	NOUN
ejpam-6590	52	21	,	,	PUNCT
ejpam-6590	52	22	∥ψ2∥	∥ψ2∥	PROPN
ejpam-6590	52	23	)	)	PUNCT
ejpam-6590	52	24	.	.	PUNCT
ejpam-6590	53	1	lemma	lemma	PROPN
ejpam-6590	53	2	6	6	NUM
ejpam-6590	53	3	.	.	PUNCT
ejpam-6590	54	1	[	[	X
ejpam-6590	54	2	14	14	NUM
ejpam-6590	54	3	]	]	X
ejpam-6590	54	4	if	if	SCONJ
ejpam-6590	54	5	ψ1	ψ1	NOUN
ejpam-6590	54	6	,	,	PUNCT
ejpam-6590	54	7	ψ2	ψ2	NOUN
ejpam-6590	54	8	∈mn(c	∈mn(c	NOUN
ejpam-6590	54	9	)	)	PUNCT
ejpam-6590	54	10	are	be	AUX
ejpam-6590	54	11	p.s.d	p.s.d	ADJ
ejpam-6590	54	12	,	,	PUNCT
ejpam-6590	54	13	then∥∥∥ψ1/2	then∥∥∥ψ1/2	NOUN
ejpam-6590	54	14	1	1	NUM
ejpam-6590	54	15	ψ	ψ	SYM
ejpam-6590	54	16	1/2	1/2	NUM
ejpam-6590	54	17	2	2	NUM
ejpam-6590	54	18	∥∥∥	∥∥∥	NOUN
ejpam-6590	54	19	⩽	⩽	NOUN
ejpam-6590	54	20	∥ψ1ψ2∥1/2	∥ψ1ψ2∥1/2	PROPN
ejpam-6590	54	21	.	.	PUNCT
ejpam-6590	55	1	lemma	lemma	PROPN
ejpam-6590	55	2	7	7	NUM
ejpam-6590	55	3	.	.	PUNCT
ejpam-6590	56	1	[	[	X
ejpam-6590	56	2	10	10	NUM
ejpam-6590	56	3	]	]	X
ejpam-6590	56	4	if	if	SCONJ
ejpam-6590	56	5	ψ1	ψ1	NOUN
ejpam-6590	56	6	,	,	PUNCT
ejpam-6590	56	7	ψ2	ψ2	NOUN
ejpam-6590	56	8	∈mn(c	∈mn(c	NOUN
ejpam-6590	56	9	)	)	PUNCT
ejpam-6590	56	10	are	be	AUX
ejpam-6590	56	11	p.s.d	p.s.d	ADJ
ejpam-6590	56	12	,	,	PUNCT
ejpam-6590	56	13	then	then	ADV
ejpam-6590	56	14	∥ψ1	∥ψ1	VERB
ejpam-6590	56	15	−	−	PROPN
ejpam-6590	56	16	ψ2∥	ψ2∥	PROPN
ejpam-6590	56	17	≤	≤	PROPN
ejpam-6590	56	18	max(∥ψ1∥	max(∥ψ1∥	PROPN
ejpam-6590	56	19	,	,	PUNCT
ejpam-6590	56	20	∥ψ2∥	∥ψ2∥	PROPN
ejpam-6590	56	21	)	)	PUNCT
ejpam-6590	56	22	.	.	PUNCT
ejpam-6590	57	1	3	3	X
ejpam-6590	57	2	.	.	X
ejpam-6590	57	3	main	main	ADJ
ejpam-6590	57	4	results	result	NOUN
ejpam-6590	57	5	in	in	ADP
ejpam-6590	57	6	this	this	DET
ejpam-6590	57	7	section	section	NOUN
ejpam-6590	57	8	,	,	PUNCT
ejpam-6590	57	9	we	we	PRON
ejpam-6590	57	10	will	will	AUX
ejpam-6590	57	11	present	present	VERB
ejpam-6590	57	12	some	some	DET
ejpam-6590	57	13	spectral	spectral	ADJ
ejpam-6590	57	14	radius	radius	NOUN
ejpam-6590	57	15	inequalities	inequality	NOUN
ejpam-6590	57	16	for	for	ADP
ejpam-6590	57	17	2×2	2×2	NUM
ejpam-6590	57	18	block	block	NOUN
ejpam-6590	57	19	accretivedissipative	accretivedissipative	ADJ
ejpam-6590	57	20	matrices	matrix	NOUN
ejpam-6590	57	21	.	.	PUNCT
ejpam-6590	58	1	theorem	theorem	NOUN
ejpam-6590	58	2	1	1	NUM
ejpam-6590	58	3	.	.	PUNCT
ejpam-6590	59	1	let	let	VERB
ejpam-6590	59	2	ψ	ψ	X
ejpam-6590	59	3	,	,	PUNCT
ejpam-6590	59	4	φ	φ	PROPN
ejpam-6590	59	5	∈	∈	PROPN
ejpam-6590	59	6	mn(c	mn(c	X
ejpam-6590	59	7	)	)	PUNCT
ejpam-6590	59	8	be	be	AUX
ejpam-6590	59	9	acc	acc	PROPN
ejpam-6590	59	10	-	-	PUNCT
ejpam-6590	59	11	dis	dis	PROPN
ejpam-6590	59	12	matrices	matrix	NOUN
ejpam-6590	59	13	with	with	ADP
ejpam-6590	59	14	cd	cd	PROPN
ejpam-6590	59	15	ψ	ψ	NOUN
ejpam-6590	60	1	=	=	SYM
ejpam-6590	60	2	ψ1	ψ1	NOUN
ejpam-6590	60	3	+	+	CCONJ
ejpam-6590	60	4	iψ2	iψ2	NOUN
ejpam-6590	60	5	and	and	CCONJ
ejpam-6590	60	6	φ	φ	NOUN
ejpam-6590	60	7	=	=	SYM
ejpam-6590	60	8	ϕ1	ϕ1	PROPN
ejpam-6590	60	9	+	+	CCONJ
ejpam-6590	60	10	iϕ2	iϕ2	NOUN
ejpam-6590	60	11	.	.	PUNCT
ejpam-6590	61	1	then	then	ADV
ejpam-6590	61	2	r	r	X
ejpam-6590	61	3	(	(	PUNCT
ejpam-6590	61	4	[	[	PUNCT
ejpam-6590	61	5	ψ	ψ	X
ejpam-6590	61	6	0	0	NUM
ejpam-6590	61	7	φ	φ	NOUN
ejpam-6590	61	8	0	0	NUM
ejpam-6590	61	9	]	]	SYM
ejpam-6590	61	10	)	)	PUNCT
ejpam-6590	61	11	⩽	⩽	ADJ
ejpam-6590	61	12	√	√	PUNCT
ejpam-6590	61	13	max	max	PROPN
ejpam-6590	61	14	(	(	PUNCT
ejpam-6590	61	15	r2(ψ1	r2(ψ1	NUM
ejpam-6590	61	16	)	)	PUNCT
ejpam-6590	61	17	,	,	PUNCT
ejpam-6590	61	18	r2(ψ2	r2(ψ2	NOUN
ejpam-6590	61	19	)	)	PUNCT
ejpam-6590	61	20	)	)	PUNCT
ejpam-6590	62	1	+	+	CCONJ
ejpam-6590	62	2	2r(ψ1)r(ψ2	2r(ψ1)r(ψ2	NUM
ejpam-6590	62	3	)	)	PUNCT
ejpam-6590	62	4	=	=	SYM
ejpam-6590	62	5	α	α	X
ejpam-6590	62	6	.	.	PUNCT
ejpam-6590	62	7	m.	m.	NOUN
ejpam-6590	62	8	sakkijha	sakkijha	PROPN
ejpam-6590	62	9	,	,	PUNCT
ejpam-6590	62	10	s.	s.	PROPN
ejpam-6590	62	11	hasan	hasan	PROPN
ejpam-6590	62	12	,	,	PUNCT
ejpam-6590	62	13	m.	m.	NOUN
ejpam-6590	62	14	alholi	alholi	PROPN
ejpam-6590	62	15	/	/	SYM
ejpam-6590	62	16	eur	eur	PROPN
ejpam-6590	62	17	.	.	PUNCT
ejpam-6590	63	1	j.	j.	PROPN
ejpam-6590	63	2	pure	pure	PROPN
ejpam-6590	63	3	appl	appl	PROPN
ejpam-6590	63	4	.	.	PROPN
ejpam-6590	63	5	math	math	PROPN
ejpam-6590	63	6	,	,	PUNCT
ejpam-6590	63	7	18	18	NUM
ejpam-6590	63	8	(	(	PUNCT
ejpam-6590	63	9	3	3	NUM
ejpam-6590	63	10	)	)	PUNCT
ejpam-6590	63	11	(	(	PUNCT
ejpam-6590	63	12	2025	2025	NUM
ejpam-6590	63	13	)	)	PUNCT
ejpam-6590	63	14	,	,	PUNCT
ejpam-6590	63	15	6590	6590	NUM
ejpam-6590	63	16	4	4	NUM
ejpam-6590	63	17	of	of	ADP
ejpam-6590	63	18	9	9	NUM
ejpam-6590	63	19	proof	proof	NOUN
ejpam-6590	63	20	.	.	PUNCT
ejpam-6590	64	1	consider	consider	VERB
ejpam-6590	64	2	r2	r2	PROPN
ejpam-6590	64	3	(	(	PUNCT
ejpam-6590	64	4	[	[	PUNCT
ejpam-6590	64	5	ψ	ψ	X
ejpam-6590	64	6	0	0	NUM
ejpam-6590	64	7	φ	φ	NOUN
ejpam-6590	64	8	0	0	NUM
ejpam-6590	64	9	]	]	PUNCT
ejpam-6590	64	10	)	)	PUNCT
ejpam-6590	65	1	=	=	SYM
ejpam-6590	65	2	r	r	NOUN
ejpam-6590	65	3	(	(	PUNCT
ejpam-6590	65	4	[	[	PUNCT
ejpam-6590	65	5	ψ	ψ	X
ejpam-6590	65	6	0	0	NUM
ejpam-6590	65	7	φ	φ	NOUN
ejpam-6590	65	8	0	0	NUM
ejpam-6590	65	9	]	]	SYM
ejpam-6590	65	10	)	)	PUNCT
ejpam-6590	65	11	2	2	NUM
ejpam-6590	65	12	(	(	PUNCT
ejpam-6590	65	13	by(6	by(6	PROPN
ejpam-6590	65	14	)	)	PUNCT
ejpam-6590	65	15	)	)	PUNCT
ejpam-6590	66	1	=	=	SYM
ejpam-6590	66	2	r	r	NOUN
ejpam-6590	66	3	(	(	PUNCT
ejpam-6590	66	4	[	[	PUNCT
ejpam-6590	66	5	ψ2	ψ2	NOUN
ejpam-6590	66	6	0	0	NUM
ejpam-6590	66	7	φψ	φψ	VERB
ejpam-6590	66	8	0	0	NUM
ejpam-6590	66	9	]	]	PUNCT
ejpam-6590	66	10	)	)	PUNCT
ejpam-6590	67	1	=	=	SYM
ejpam-6590	67	2	r	r	NOUN
ejpam-6590	67	3	(	(	PUNCT
ejpam-6590	67	4	[	[	PUNCT
ejpam-6590	67	5	ψ	ψ	X
ejpam-6590	67	6	0	0	NUM
ejpam-6590	67	7	φ	φ	NOUN
ejpam-6590	67	8	0	0	NUM
ejpam-6590	67	9	]	]	PUNCT
ejpam-6590	67	10	[	[	PUNCT
ejpam-6590	67	11	ψ	ψ	X
ejpam-6590	67	12	0	0	NUM
ejpam-6590	67	13	0	0	NUM
ejpam-6590	67	14	0	0	NUM
ejpam-6590	67	15	]	]	PUNCT
ejpam-6590	67	16	)	)	PUNCT
ejpam-6590	68	1	=	=	SYM
ejpam-6590	68	2	r	r	NOUN
ejpam-6590	68	3	(	(	PUNCT
ejpam-6590	68	4	[	[	PUNCT
ejpam-6590	68	5	ψ	ψ	X
ejpam-6590	68	6	0	0	NUM
ejpam-6590	68	7	0	0	NUM
ejpam-6590	68	8	0	0	NUM
ejpam-6590	68	9	]	]	PUNCT
ejpam-6590	68	10	[	[	PUNCT
ejpam-6590	68	11	ψ	ψ	X
ejpam-6590	68	12	0	0	NUM
ejpam-6590	68	13	φ	φ	NOUN
ejpam-6590	68	14	0	0	NUM
ejpam-6590	68	15	]	]	PUNCT
ejpam-6590	68	16	)	)	PUNCT
ejpam-6590	68	17	(	(	PUNCT
ejpam-6590	68	18	by(9	by(9	NOUN
ejpam-6590	68	19	)	)	PUNCT
ejpam-6590	68	20	)	)	PUNCT
ejpam-6590	69	1	=	=	SYM
ejpam-6590	69	2	r	r	NOUN
ejpam-6590	69	3	(	(	PUNCT
ejpam-6590	69	4	[	[	PUNCT
ejpam-6590	69	5	ψ2	ψ2	NOUN
ejpam-6590	69	6	0	0	NUM
ejpam-6590	69	7	0	0	NUM
ejpam-6590	69	8	0	0	NUM
ejpam-6590	69	9	]	]	SYM
ejpam-6590	69	10	)	)	PUNCT
ejpam-6590	69	11	⩽	⩽	ADJ
ejpam-6590	69	12	r	r	NOUN
ejpam-6590	69	13	(	(	PUNCT
ejpam-6590	69	14	[	[	PUNCT
ejpam-6590	69	15	∥∥ψ2	∥∥ψ2	X
ejpam-6590	69	16	∥∥	∥∥	X
ejpam-6590	69	17	0	0	NUM
ejpam-6590	69	18	0	0	NUM
ejpam-6590	69	19	0	0	NUM
ejpam-6590	69	20	]	]	PUNCT
ejpam-6590	69	21	)	)	PUNCT
ejpam-6590	69	22	(	(	PUNCT
ejpam-6590	69	23	by	by	ADP
ejpam-6590	69	24	lemma	lemma	PROPN
ejpam-6590	69	25	4	4	NUM
ejpam-6590	69	26	)	)	PUNCT
ejpam-6590	69	27	=	=	SYM
ejpam-6590	69	28	r	r	NOUN
ejpam-6590	69	29	(	(	PUNCT
ejpam-6590	69	30	[	[	PUNCT
ejpam-6590	69	31	∥∥(ψ2	∥∥(ψ2	NOUN
ejpam-6590	69	32	1	1	NUM
ejpam-6590	69	33	−	−	PROPN
ejpam-6590	69	34	ψ2	ψ2	NOUN
ejpam-6590	69	35	2	2	NUM
ejpam-6590	69	36	)	)	PUNCT
ejpam-6590	69	37	+	+	CCONJ
ejpam-6590	69	38	i(ψ1ψ2	i(ψ1ψ2	NOUN
ejpam-6590	69	39	+	+	CCONJ
ejpam-6590	69	40	ψ2ψ1	ψ2ψ1	NOUN
ejpam-6590	69	41	)	)	PUNCT
ejpam-6590	69	42	∥∥	∥∥	X
ejpam-6590	69	43	0	0	NUM
ejpam-6590	69	44	0	0	NUM
ejpam-6590	69	45	0	0	NUM
ejpam-6590	69	46	]	]	PUNCT
ejpam-6590	69	47	)	)	PUNCT
ejpam-6590	69	48	=	=	SYM
ejpam-6590	69	49	∥∥(ψ2	∥∥(ψ2	NOUN
ejpam-6590	69	50	1	1	NUM
ejpam-6590	69	51	−	−	PROPN
ejpam-6590	69	52	ψ2	ψ2	NOUN
ejpam-6590	69	53	2	2	NUM
ejpam-6590	69	54	)	)	PUNCT
ejpam-6590	69	55	+	+	CCONJ
ejpam-6590	69	56	i(ψ1ψ2	i(ψ1ψ2	NOUN
ejpam-6590	69	57	+	+	CCONJ
ejpam-6590	69	58	ψ2ψ1	ψ2ψ1	NOUN
ejpam-6590	69	59	)	)	PUNCT
ejpam-6590	69	60	∥∥	∥∥	PROPN
ejpam-6590	69	61	⩽	⩽	NOUN
ejpam-6590	69	62	∥∥ψ2	∥∥ψ2	PROPN
ejpam-6590	69	63	1	1	NUM
ejpam-6590	69	64	−	−	NOUN
ejpam-6590	69	65	ψ2	ψ2	NOUN
ejpam-6590	69	66	2	2	NUM
ejpam-6590	69	67	∥∥+	∥∥+	SYM
ejpam-6590	69	68	∥ψ1ψ2	∥ψ1ψ2	PROPN
ejpam-6590	69	69	+	+	NUM
ejpam-6590	69	70	ψ2ψ1∥	ψ2ψ1∥	NOUN
ejpam-6590	69	71	⩽	⩽	NOUN
ejpam-6590	69	72	∥∥ψ2	∥∥ψ2	PROPN
ejpam-6590	69	73	1	1	NUM
ejpam-6590	69	74	−	−	NOUN
ejpam-6590	69	75	ψ2	ψ2	NOUN
ejpam-6590	69	76	2	2	NUM
ejpam-6590	69	77	∥∥+	∥∥+	SYM
ejpam-6590	69	78	∥ψ1ψ2∥+	∥ψ1ψ2∥+	PROPN
ejpam-6590	69	79	∥ψ2ψ1∥	∥ψ2ψ1∥	PROPN
ejpam-6590	69	80	⩽	⩽	PROPN
ejpam-6590	69	81	max	max	PROPN
ejpam-6590	69	82	(	(	PUNCT
ejpam-6590	69	83	∥∥ψ2	∥∥ψ2	PROPN
ejpam-6590	69	84	1	1	NUM
ejpam-6590	69	85	∥∥	∥∥	X
ejpam-6590	69	86	,	,	PUNCT
ejpam-6590	69	87	∥∥ψ2	∥∥ψ2	PROPN
ejpam-6590	69	88	2	2	NUM
ejpam-6590	69	89	∥∥)+	∥∥)+	NOUN
ejpam-6590	69	90	∥ψ1ψ2∥+	∥ψ1ψ2∥+	NOUN
ejpam-6590	69	91	∥ψ2ψ1∥	∥ψ2ψ1∥	NOUN
ejpam-6590	69	92	(	(	PUNCT
ejpam-6590	69	93	by	by	ADP
ejpam-6590	69	94	lemma	lemma	PROPN
ejpam-6590	69	95	7	7	NUM
ejpam-6590	69	96	)	)	PUNCT
ejpam-6590	69	97	≤	≤	NUM
ejpam-6590	69	98	max	max	NOUN
ejpam-6590	69	99	(	(	PUNCT
ejpam-6590	69	100	r2(ψ1	r2(ψ1	NUM
ejpam-6590	69	101	)	)	PUNCT
ejpam-6590	69	102	,	,	PUNCT
ejpam-6590	69	103	r	r	NOUN
ejpam-6590	69	104	2(ψ2	2(ψ2	NUM
ejpam-6590	69	105	)	)	PUNCT
ejpam-6590	69	106	)	)	PUNCT
ejpam-6590	70	1	+	+	CCONJ
ejpam-6590	70	2	2r(ψ1)r(ψ2	2r(ψ1)r(ψ2	NUM
ejpam-6590	70	3	)	)	PUNCT
ejpam-6590	70	4	(	(	PUNCT
ejpam-6590	70	5	by	by	ADP
ejpam-6590	70	6	(	(	PUNCT
ejpam-6590	70	7	6	6	NUM
ejpam-6590	70	8	)	)	PUNCT
ejpam-6590	70	9	and	and	CCONJ
ejpam-6590	70	10	(	(	PUNCT
ejpam-6590	70	11	9	9	NUM
ejpam-6590	70	12	)	)	PUNCT
ejpam-6590	70	13	)	)	PUNCT
ejpam-6590	70	14	.	.	PUNCT
ejpam-6590	71	1	the	the	DET
ejpam-6590	71	2	proof	proof	NOUN
ejpam-6590	71	3	is	be	AUX
ejpam-6590	71	4	obvious	obvious	ADJ
ejpam-6590	71	5	by	by	ADP
ejpam-6590	71	6	taking	take	VERB
ejpam-6590	71	7	the	the	DET
ejpam-6590	71	8	square	square	ADJ
ejpam-6590	71	9	root	root	NOUN
ejpam-6590	71	10	.	.	PUNCT
ejpam-6590	72	1	theorem	theorem	NOUN
ejpam-6590	72	2	2	2	NUM
ejpam-6590	72	3	.	.	PUNCT
ejpam-6590	73	1	let	let	VERB
ejpam-6590	73	2	ψ	ψ	X
ejpam-6590	73	3	,	,	PUNCT
ejpam-6590	73	4	φ	φ	PROPN
ejpam-6590	73	5	∈mn(c	∈mn(c	NOUN
ejpam-6590	73	6	)	)	PUNCT
ejpam-6590	73	7	be	be	AUX
ejpam-6590	73	8	acc	acc	PROPN
ejpam-6590	73	9	-	-	PUNCT
ejpam-6590	73	10	dis	dis	PROPN
ejpam-6590	73	11	matrices	matrix	NOUN
ejpam-6590	73	12	with	with	ADP
ejpam-6590	73	13	cd	cd	PROPN
ejpam-6590	73	14	ψ	ψ	NOUN
ejpam-6590	73	15	=	=	SYM
ejpam-6590	73	16	ψ1	ψ1	NOUN
ejpam-6590	73	17	+	+	CCONJ
ejpam-6590	73	18	iψ2,φ	iψ2,φ	NOUN
ejpam-6590	73	19	=	=	SYM
ejpam-6590	73	20	ϕ1	ϕ1	NOUN
ejpam-6590	73	21	+	+	CCONJ
ejpam-6590	73	22	iϕ2	iϕ2	NOUN
ejpam-6590	73	23	.	.	PUNCT
ejpam-6590	74	1	then	then	ADV
ejpam-6590	74	2	r	r	X
ejpam-6590	74	3	(	(	PUNCT
ejpam-6590	74	4	[	[	PUNCT
ejpam-6590	74	5	ψ	ψ	X
ejpam-6590	74	6	0	0	NUM
ejpam-6590	74	7	φ	φ	NOUN
ejpam-6590	74	8	0	0	NUM
ejpam-6590	74	9	]	]	SYM
ejpam-6590	74	10	)	)	PUNCT
ejpam-6590	74	11	⩽	⩽	ADJ
ejpam-6590	74	12	√	√	PUNCT
ejpam-6590	74	13	max	max	PROPN
ejpam-6590	74	14	(	(	PUNCT
ejpam-6590	74	15	r2(ψ1	r2(ψ1	NUM
ejpam-6590	74	16	)	)	PUNCT
ejpam-6590	74	17	,	,	PUNCT
ejpam-6590	74	18	r2(ψ2	r2(ψ2	NOUN
ejpam-6590	74	19	)	)	PUNCT
ejpam-6590	74	20	)	)	PUNCT
ejpam-6590	75	1	+	+	CCONJ
ejpam-6590	75	2	max	max	PROPN
ejpam-6590	75	3	(	(	PUNCT
ejpam-6590	75	4	r2(ϕ1	r2(ϕ1	NOUN
ejpam-6590	75	5	)	)	PUNCT
ejpam-6590	75	6	,	,	PUNCT
ejpam-6590	75	7	r2(ϕ2	r2(ϕ2	NOUN
ejpam-6590	75	8	)	)	PUNCT
ejpam-6590	75	9	)	)	PUNCT
ejpam-6590	76	1	+	+	CCONJ
ejpam-6590	76	2	3	3	NUM
ejpam-6590	76	3	2	2	NUM
ejpam-6590	76	4	r(ψ1)r(ψ2	r(ψ1)r(ψ2	PROPN
ejpam-6590	76	5	)	)	PUNCT
ejpam-6590	76	6	+	+	CCONJ
ejpam-6590	76	7	3	3	NUM
ejpam-6590	76	8	2	2	NUM
ejpam-6590	76	9	r(ϕ1)r(ϕ2	r(ϕ1)r(ϕ2	NOUN
ejpam-6590	76	10	)	)	PUNCT
ejpam-6590	76	11	=	=	PUNCT
ejpam-6590	77	1	β	β	NOUN
ejpam-6590	77	2	proof	proof	NOUN
ejpam-6590	77	3	.	.	PUNCT
ejpam-6590	78	1	consider	consider	VERB
ejpam-6590	78	2	r	r	NOUN
ejpam-6590	78	3	(	(	PUNCT
ejpam-6590	78	4	[	[	PUNCT
ejpam-6590	78	5	ψ	ψ	X
ejpam-6590	78	6	0	0	NUM
ejpam-6590	78	7	φ	φ	NOUN
ejpam-6590	78	8	0	0	NUM
ejpam-6590	78	9	]	]	SYM
ejpam-6590	78	10	)	)	PUNCT
ejpam-6590	79	1	⩽	⩽	ADJ
ejpam-6590	79	2	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6590	79	3	[	[	PUNCT
ejpam-6590	79	4	ψ	ψ	X
ejpam-6590	79	5	0	0	NUM
ejpam-6590	79	6	φ	φ	NOUN
ejpam-6590	79	7	0	0	NUM
ejpam-6590	79	8	]	]	PUNCT
ejpam-6590	79	9	∥∥∥∥	∥∥∥∥	NUM
ejpam-6590	79	10	(	(	PUNCT
ejpam-6590	79	11	by	by	ADP
ejpam-6590	79	12	(	(	PUNCT
ejpam-6590	79	13	3	3	NUM
ejpam-6590	79	14	)	)	PUNCT
ejpam-6590	79	15	)	)	PUNCT
ejpam-6590	79	16	m.	m.	NOUN
ejpam-6590	79	17	sakkijha	sakkijha	PROPN
ejpam-6590	79	18	,	,	PUNCT
ejpam-6590	79	19	s.	s.	PROPN
ejpam-6590	79	20	hasan	hasan	PROPN
ejpam-6590	79	21	,	,	PUNCT
ejpam-6590	79	22	m.	m.	NOUN
ejpam-6590	79	23	alholi	alholi	PROPN
ejpam-6590	79	24	/	/	SYM
ejpam-6590	79	25	eur	eur	PROPN
ejpam-6590	79	26	.	.	PUNCT
ejpam-6590	80	1	j.	j.	PROPN
ejpam-6590	80	2	pure	pure	PROPN
ejpam-6590	80	3	appl	appl	PROPN
ejpam-6590	80	4	.	.	PROPN
ejpam-6590	80	5	math	math	PROPN
ejpam-6590	80	6	,	,	PUNCT
ejpam-6590	80	7	18	18	NUM
ejpam-6590	80	8	(	(	PUNCT
ejpam-6590	80	9	3	3	NUM
ejpam-6590	80	10	)	)	PUNCT
ejpam-6590	80	11	(	(	PUNCT
ejpam-6590	80	12	2025	2025	NUM
ejpam-6590	80	13	)	)	PUNCT
ejpam-6590	80	14	,	,	PUNCT
ejpam-6590	80	15	6590	6590	NUM
ejpam-6590	80	16	5	5	NUM
ejpam-6590	80	17	of	of	ADP
ejpam-6590	80	18	9	9	NUM
ejpam-6590	80	19	=	=	SYM
ejpam-6590	80	20	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6590	80	21	[	[	PUNCT
ejpam-6590	80	22	ψ∗	ψ∗	NOUN
ejpam-6590	80	23	φ∗	φ∗	NOUN
ejpam-6590	80	24	0	0	NUM
ejpam-6590	80	25	0	0	NUM
ejpam-6590	80	26	]	]	PUNCT
ejpam-6590	81	1	[	[	PUNCT
ejpam-6590	81	2	ψ	ψ	X
ejpam-6590	81	3	0	0	NUM
ejpam-6590	81	4	φ	φ	NOUN
ejpam-6590	81	5	0	0	NUM
ejpam-6590	82	1	]	]	X
ejpam-6590	82	2	∥∥∥∥1/2	∥∥∥∥1/2	NOUN
ejpam-6590	82	3	(	(	PUNCT
ejpam-6590	82	4	by	by	ADP
ejpam-6590	82	5	(	(	PUNCT
ejpam-6590	82	6	4	4	NUM
ejpam-6590	82	7	)	)	PUNCT
ejpam-6590	82	8	)	)	PUNCT
ejpam-6590	82	9	=	=	SYM
ejpam-6590	83	1	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6590	83	2	[	[	PUNCT
ejpam-6590	83	3	ψ∗ψ+φ∗φ	ψ∗ψ+φ∗φ	ADP
ejpam-6590	83	4	0	0	NUM
ejpam-6590	83	5	0	0	NUM
ejpam-6590	83	6	0	0	NUM
ejpam-6590	83	7	]	]	X
ejpam-6590	83	8	∥∥∥∥1/2	∥∥∥∥1/2	NOUN
ejpam-6590	83	9	=	=	PUNCT
ejpam-6590	83	10	∥ψ∗ψ+φ∗φ∥1/2	∥ψ∗ψ+φ∗φ∥1/2	PROPN
ejpam-6590	84	1	=	=	NOUN
ejpam-6590	84	2	∥(ψ1	∥(ψ1	NOUN
ejpam-6590	84	3	−	−	NOUN
ejpam-6590	84	4	iψ2)(ψ1	iψ2)(ψ1	NOUN
ejpam-6590	84	5	+	+	CCONJ
ejpam-6590	84	6	iψ2	iψ2	NOUN
ejpam-6590	84	7	)	)	PUNCT
ejpam-6590	84	8	+	+	CCONJ
ejpam-6590	84	9	(	(	PUNCT
ejpam-6590	84	10	ϕ1	ϕ1	NOUN
ejpam-6590	84	11	−	−	NOUN
ejpam-6590	84	12	iϕ2)(ϕ1	iϕ2)(ϕ1	VERB
ejpam-6590	84	13	+	+	NUM
ejpam-6590	84	14	iϕ2)∥1/2	iϕ2)∥1/2	NUM
ejpam-6590	84	15	=	=	NOUN
ejpam-6590	84	16	∥∥(ψ2	∥∥(ψ2	NOUN
ejpam-6590	84	17	1	1	NUM
ejpam-6590	85	1	+	+	NUM
ejpam-6590	85	2	ψ2	ψ2	NOUN
ejpam-6590	85	3	2	2	NUM
ejpam-6590	85	4	)	)	PUNCT
ejpam-6590	85	5	+	+	CCONJ
ejpam-6590	85	6	(	(	PUNCT
ejpam-6590	85	7	ϕ21	ϕ21	NOUN
ejpam-6590	85	8	+	+	CCONJ
ejpam-6590	85	9	ϕ22	ϕ22	NOUN
ejpam-6590	85	10	)	)	PUNCT
ejpam-6590	86	1	+	+	CCONJ
ejpam-6590	86	2	i(ψ1ψ2	i(ψ1ψ2	NOUN
ejpam-6590	86	3	−	−	PROPN
ejpam-6590	86	4	ψ2ψ1	ψ2ψ1	NOUN
ejpam-6590	86	5	)	)	PUNCT
ejpam-6590	87	1	+	+	CCONJ
ejpam-6590	87	2	i(ϕ1ϕ2	i(ϕ1ϕ2	ADV
ejpam-6590	87	3	−	−	NOUN
ejpam-6590	87	4	ϕ2ϕ1	ϕ2ϕ1	NOUN
ejpam-6590	87	5	)	)	PUNCT
ejpam-6590	87	6	∥∥1/2	∥∥1/2	ADJ
ejpam-6590	87	7	⩽	⩽	NOUN
ejpam-6590	87	8	(	(	PUNCT
ejpam-6590	87	9	∥∥ψ2	∥∥ψ2	PROPN
ejpam-6590	87	10	1	1	NUM
ejpam-6590	87	11	+	+	NUM
ejpam-6590	87	12	ψ2	ψ2	NOUN
ejpam-6590	87	13	2	2	NUM
ejpam-6590	87	14	∥∥+	∥∥+	NOUN
ejpam-6590	87	15	∥∥ϕ21	∥∥ϕ21	PROPN
ejpam-6590	88	1	+	+	CCONJ
ejpam-6590	88	2	ϕ22	ϕ22	PROPN
ejpam-6590	88	3	∥∥+	∥∥+	NUM
ejpam-6590	88	4	∥ψ1ψ2	∥ψ1ψ2	PROPN
ejpam-6590	88	5	−	−	PROPN
ejpam-6590	88	6	ψ2ψ1∥+	ψ2ψ1∥+	PROPN
ejpam-6590	88	7	∥ϕ1ϕ2	∥ϕ1ϕ2	NOUN
ejpam-6590	88	8	−	−	NOUN
ejpam-6590	88	9	ϕ2ϕ1∥	ϕ2ϕ1∥	VERB
ejpam-6590	88	10	)	)	PUNCT
ejpam-6590	88	11	1/2	1/2	NUM
ejpam-6590	88	12	⩽(max(∥ψ2	⩽(max(∥ψ2	PROPN
ejpam-6590	88	13	1∥	1∥	NUM
ejpam-6590	88	14	,	,	PUNCT
ejpam-6590	88	15	∥ψ2	∥ψ2	X
ejpam-6590	88	16	2∥	2∥	NUM
ejpam-6590	88	17	)	)	PUNCT
ejpam-6590	88	18	+	+	CCONJ
ejpam-6590	88	19	∥ψ1ψ2∥+max(∥ϕ21∥	∥ψ1ψ2∥+max(∥ϕ21∥	PROPN
ejpam-6590	88	20	,	,	PUNCT
ejpam-6590	88	21	∥ϕ22∥	∥ϕ22∥	PROPN
ejpam-6590	88	22	)	)	PUNCT
ejpam-6590	88	23	+	+	CCONJ
ejpam-6590	88	24	∥ϕ1ϕ2∥	∥ϕ1ϕ2∥	NUM
ejpam-6590	88	25	+	+	CCONJ
ejpam-6590	88	26	1	1	NUM
ejpam-6590	88	27	2	2	NUM
ejpam-6590	88	28	∥ψ1∥∥ψ2∥+	∥ψ1∥∥ψ2∥+	NOUN
ejpam-6590	88	29	1	1	NUM
ejpam-6590	88	30	2	2	NUM
ejpam-6590	88	31	∥ϕ1∥∥ϕ2∥	∥ϕ1∥∥ϕ2∥	NUM
ejpam-6590	88	32	)	)	PUNCT
ejpam-6590	88	33	1	1	NUM
ejpam-6590	88	34	2	2	NUM
ejpam-6590	88	35	(	(	PUNCT
ejpam-6590	88	36	by	by	ADP
ejpam-6590	88	37	lemma	lemma	PROPN
ejpam-6590	88	38	2	2	PROPN
ejpam-6590	88	39	and	and	CCONJ
ejpam-6590	88	40	lemma	lemma	PROPN
ejpam-6590	88	41	3	3	X
ejpam-6590	88	42	)	)	PUNCT
ejpam-6590	88	43	⩽(max(∥ψ2	⩽(max(∥ψ2	NOUN
ejpam-6590	88	44	1∥	1∥	NUM
ejpam-6590	88	45	,	,	PUNCT
ejpam-6590	88	46	∥ψ2	∥ψ2	X
ejpam-6590	88	47	2∥	2∥	NUM
ejpam-6590	88	48	)	)	PUNCT
ejpam-6590	89	1	+	+	CCONJ
ejpam-6590	89	2	∥ψ1∥∥ψ2∥+max(∥ϕ21∥	∥ψ1∥∥ψ2∥+max(∥ϕ21∥	PROPN
ejpam-6590	89	3	,	,	PUNCT
ejpam-6590	89	4	∥ϕ22∥	∥ϕ22∥	PROPN
ejpam-6590	89	5	)	)	PUNCT
ejpam-6590	90	1	+	+	CCONJ
ejpam-6590	90	2	∥ϕ1∥∥ϕ2∥	∥ϕ1∥∥ϕ2∥	ADJ
ejpam-6590	90	3	+	+	CCONJ
ejpam-6590	90	4	1	1	NUM
ejpam-6590	90	5	2	2	NUM
ejpam-6590	90	6	∥ψ1∥∥ψ2∥+	∥ψ1∥∥ψ2∥+	NOUN
ejpam-6590	90	7	1	1	NUM
ejpam-6590	90	8	2	2	NUM
ejpam-6590	90	9	∥ϕ1∥∥ϕ2∥	∥ϕ1∥∥ϕ2∥	NUM
ejpam-6590	90	10	)	)	PUNCT
ejpam-6590	90	11	1	1	NUM
ejpam-6590	90	12	2	2	NUM
ejpam-6590	90	13	=	=	SYM
ejpam-6590	90	14	√	√	NUM
ejpam-6590	90	15	max	max	PROPN
ejpam-6590	90	16	(	(	PUNCT
ejpam-6590	90	17	r2(ψ1	r2(ψ1	NUM
ejpam-6590	90	18	)	)	PUNCT
ejpam-6590	90	19	,	,	PUNCT
ejpam-6590	90	20	r2(ψ2	r2(ψ2	NOUN
ejpam-6590	90	21	)	)	PUNCT
ejpam-6590	90	22	)	)	PUNCT
ejpam-6590	91	1	+	+	CCONJ
ejpam-6590	91	2	max	max	PROPN
ejpam-6590	91	3	(	(	PUNCT
ejpam-6590	91	4	r2(ϕ1	r2(ϕ1	NOUN
ejpam-6590	91	5	)	)	PUNCT
ejpam-6590	91	6	,	,	PUNCT
ejpam-6590	91	7	r2(ϕ2	r2(ϕ2	NOUN
ejpam-6590	91	8	)	)	PUNCT
ejpam-6590	91	9	)	)	PUNCT
ejpam-6590	92	1	+	+	CCONJ
ejpam-6590	92	2	3	3	NUM
ejpam-6590	92	3	2	2	NUM
ejpam-6590	92	4	r(ψ1)r(ψ2	r(ψ1)r(ψ2	PROPN
ejpam-6590	92	5	)	)	PUNCT
ejpam-6590	92	6	+	+	CCONJ
ejpam-6590	92	7	3	3	NUM
ejpam-6590	92	8	2	2	NUM
ejpam-6590	92	9	r(ϕ1)r(ϕ2	r(ϕ1)r(ϕ2	NOUN
ejpam-6590	92	10	)	)	PUNCT
ejpam-6590	92	11	by	by	ADP
ejpam-6590	92	12	theorem	theorem	NOUN
ejpam-6590	92	13	1	1	NUM
ejpam-6590	92	14	and	and	CCONJ
ejpam-6590	92	15	2	2	NUM
ejpam-6590	92	16	,	,	PUNCT
ejpam-6590	92	17	we	we	PRON
ejpam-6590	92	18	conclude	conclude	VERB
ejpam-6590	92	19	that	that	SCONJ
ejpam-6590	92	20	r	r	NOUN
ejpam-6590	92	21	(	(	PUNCT
ejpam-6590	92	22	[	[	PUNCT
ejpam-6590	92	23	ψ	ψ	X
ejpam-6590	92	24	0	0	NUM
ejpam-6590	92	25	φ	φ	NOUN
ejpam-6590	92	26	0	0	NUM
ejpam-6590	92	27	]	]	PUNCT
ejpam-6590	92	28	)	)	PUNCT
ejpam-6590	92	29	≤	≤	PUNCT
ejpam-6590	93	1	min(α	min(α	PROPN
ejpam-6590	93	2	,	,	PUNCT
ejpam-6590	93	3	β	β	NOUN
ejpam-6590	93	4	)	)	PUNCT
ejpam-6590	93	5	.	.	PUNCT
ejpam-6590	94	1	corollary	corollary	ADJ
ejpam-6590	94	2	1	1	NUM
ejpam-6590	94	3	.	.	PUNCT
ejpam-6590	95	1	let	let	VERB
ejpam-6590	95	2	ψ	ψ	X
ejpam-6590	95	3	,	,	PUNCT
ejpam-6590	95	4	φ	φ	PROPN
ejpam-6590	95	5	∈	∈	PROPN
ejpam-6590	95	6	mn(c	mn(c	X
ejpam-6590	95	7	)	)	PUNCT
ejpam-6590	95	8	be	be	AUX
ejpam-6590	95	9	acc	acc	PROPN
ejpam-6590	95	10	-	-	PUNCT
ejpam-6590	95	11	dis	dis	PROPN
ejpam-6590	95	12	matrices	matrix	NOUN
ejpam-6590	95	13	with	with	ADP
ejpam-6590	95	14	cd	cd	PROPN
ejpam-6590	95	15	ψ	ψ	NOUN
ejpam-6590	96	1	=	=	X
ejpam-6590	96	2	ψ1	ψ1	NOUN
ejpam-6590	96	3	+	+	CCONJ
ejpam-6590	96	4	iψ2	iψ2	PROPN
ejpam-6590	96	5	,	,	PUNCT
ejpam-6590	96	6	φ	φ	NOUN
ejpam-6590	96	7	=	=	SYM
ejpam-6590	96	8	ϕ1	ϕ1	PROPN
ejpam-6590	96	9	+	+	CCONJ
ejpam-6590	96	10	iϕ2	iϕ2	NOUN
ejpam-6590	96	11	.	.	PUNCT
ejpam-6590	97	1	then	then	ADV
ejpam-6590	97	2	r	r	X
ejpam-6590	97	3	(	(	PUNCT
ejpam-6590	97	4	[	[	PUNCT
ejpam-6590	97	5	0	0	NUM
ejpam-6590	97	6	φ	φ	NUM
ejpam-6590	97	7	0	0	NUM
ejpam-6590	97	8	ψ	ψ	X
ejpam-6590	97	9	]	]	X
ejpam-6590	97	10	)	)	PUNCT
ejpam-6590	97	11	⩽	⩽	PROPN
ejpam-6590	98	1	min(α	min(α	PROPN
ejpam-6590	98	2	,	,	PUNCT
ejpam-6590	98	3	β	β	NOUN
ejpam-6590	98	4	)	)	PUNCT
ejpam-6590	98	5	.	.	PUNCT
ejpam-6590	99	1	proof	proof	NOUN
ejpam-6590	99	2	.	.	PUNCT
ejpam-6590	100	1	the	the	DET
ejpam-6590	100	2	proof	proof	NOUN
ejpam-6590	100	3	is	be	AUX
ejpam-6590	100	4	observed	observe	VERB
ejpam-6590	100	5	by	by	ADP
ejpam-6590	100	6	using	use	VERB
ejpam-6590	100	7	(	(	PUNCT
ejpam-6590	100	8	8)	8)	NUM
ejpam-6590	100	9	as	as	SCONJ
ejpam-6590	100	10	follows	follow	VERB
ejpam-6590	100	11	:	:	PUNCT
ejpam-6590	100	12	r	r	NOUN
ejpam-6590	100	13	(	(	PUNCT
ejpam-6590	100	14	[	[	PUNCT
ejpam-6590	100	15	0	0	NUM
ejpam-6590	100	16	φ	φ	NUM
ejpam-6590	100	17	0	0	NUM
ejpam-6590	100	18	ψ	ψ	X
ejpam-6590	100	19	]	]	X
ejpam-6590	100	20	)	)	PUNCT
ejpam-6590	101	1	=	=	SYM
ejpam-6590	101	2	r	r	NOUN
ejpam-6590	101	3	(	(	PUNCT
ejpam-6590	101	4	u∗	u∗	PROPN
ejpam-6590	101	5	[	[	PUNCT
ejpam-6590	101	6	ψ	ψ	X
ejpam-6590	101	7	0	0	NUM
ejpam-6590	101	8	φ	φ	NOUN
ejpam-6590	101	9	0	0	NUM
ejpam-6590	101	10	]	]	SYM
ejpam-6590	101	11	u	u	NOUN
ejpam-6590	101	12	)	)	PUNCT
ejpam-6590	101	13	=	=	SYM
ejpam-6590	102	1	r	r	NOUN
ejpam-6590	102	2	(	(	PUNCT
ejpam-6590	102	3	[	[	PUNCT
ejpam-6590	102	4	ψ	ψ	X
ejpam-6590	102	5	0	0	NUM
ejpam-6590	102	6	φ	φ	NOUN
ejpam-6590	102	7	0	0	NUM
ejpam-6590	102	8	]	]	PUNCT
ejpam-6590	102	9	)	)	PUNCT
ejpam-6590	102	10	,	,	PUNCT
ejpam-6590	102	11	where	where	SCONJ
ejpam-6590	102	12	u	u	NOUN
ejpam-6590	102	13	=	=	X
ejpam-6590	102	14	[	[	PUNCT
ejpam-6590	102	15	0	0	NUM
ejpam-6590	102	16	i	i	PRON
ejpam-6590	102	17	i	i	VERB
ejpam-6590	102	18	0	0	NUM
ejpam-6590	102	19	]	]	PUNCT
ejpam-6590	102	20	.	.	PUNCT
ejpam-6590	103	1	corollary	corollary	ADJ
ejpam-6590	103	2	2	2	NUM
ejpam-6590	103	3	.	.	PUNCT
ejpam-6590	104	1	let	let	VERB
ejpam-6590	104	2	ψ	ψ	X
ejpam-6590	104	3	,	,	PUNCT
ejpam-6590	104	4	φ	φ	PROPN
ejpam-6590	104	5	∈mn(c	∈mn(c	NOUN
ejpam-6590	104	6	)	)	PUNCT
ejpam-6590	104	7	be	be	AUX
ejpam-6590	104	8	acc	acc	PROPN
ejpam-6590	104	9	-	-	PUNCT
ejpam-6590	104	10	dis	dis	PROPN
ejpam-6590	104	11	matrices	matrix	NOUN
ejpam-6590	104	12	with	with	ADP
ejpam-6590	104	13	cd	cd	PROPN
ejpam-6590	104	14	ψ	ψ	NOUN
ejpam-6590	104	15	=	=	SYM
ejpam-6590	104	16	ψ1+iψ2	ψ1+iψ2	PROPN
ejpam-6590	105	1	,	,	PUNCT
ejpam-6590	105	2	φ	φ	NOUN
ejpam-6590	105	3	=	=	SYM
ejpam-6590	105	4	ϕ1+iϕ2	ϕ1+iϕ2	PROPN
ejpam-6590	105	5	.	.	PUNCT
ejpam-6590	106	1	then	then	ADV
ejpam-6590	106	2	r	r	X
ejpam-6590	106	3	(	(	PUNCT
ejpam-6590	106	4	[	[	PUNCT
ejpam-6590	106	5	ψ	ψ	X
ejpam-6590	106	6	0	0	NUM
ejpam-6590	106	7	−φ	−φ	NOUN
ejpam-6590	106	8	0	0	NUM
ejpam-6590	106	9	]	]	PUNCT
ejpam-6590	106	10	)	)	PUNCT
ejpam-6590	106	11	≤	≤	PUNCT
ejpam-6590	107	1	min(α	min(α	PROPN
ejpam-6590	107	2	,	,	PUNCT
ejpam-6590	107	3	β	β	NOUN
ejpam-6590	107	4	)	)	PUNCT
ejpam-6590	107	5	.	.	PUNCT
ejpam-6590	108	1	m.	m.	NOUN
ejpam-6590	108	2	sakkijha	sakkijha	PROPN
ejpam-6590	108	3	,	,	PUNCT
ejpam-6590	108	4	s.	s.	PROPN
ejpam-6590	108	5	hasan	hasan	PROPN
ejpam-6590	108	6	,	,	PUNCT
ejpam-6590	108	7	m.	m.	NOUN
ejpam-6590	108	8	alholi	alholi	PROPN
ejpam-6590	108	9	/	/	SYM
ejpam-6590	108	10	eur	eur	PROPN
ejpam-6590	108	11	.	.	PUNCT
ejpam-6590	109	1	j.	j.	PROPN
ejpam-6590	109	2	pure	pure	PROPN
ejpam-6590	109	3	appl	appl	PROPN
ejpam-6590	109	4	.	.	PROPN
ejpam-6590	109	5	math	math	PROPN
ejpam-6590	109	6	,	,	PUNCT
ejpam-6590	109	7	18	18	NUM
ejpam-6590	109	8	(	(	PUNCT
ejpam-6590	109	9	3	3	NUM
ejpam-6590	109	10	)	)	PUNCT
ejpam-6590	109	11	(	(	PUNCT
ejpam-6590	109	12	2025	2025	NUM
ejpam-6590	109	13	)	)	PUNCT
ejpam-6590	109	14	,	,	PUNCT
ejpam-6590	109	15	6590	6590	NUM
ejpam-6590	109	16	6	6	NUM
ejpam-6590	109	17	of	of	ADP
ejpam-6590	109	18	9	9	NUM
ejpam-6590	109	19	proof	proof	NOUN
ejpam-6590	109	20	.	.	PUNCT
ejpam-6590	110	1	the	the	DET
ejpam-6590	110	2	proof	proof	NOUN
ejpam-6590	110	3	is	be	AUX
ejpam-6590	110	4	due	due	ADJ
ejpam-6590	110	5	to	to	ADP
ejpam-6590	110	6	using	use	VERB
ejpam-6590	110	7	(	(	PUNCT
ejpam-6590	110	8	8)	8)	NUM
ejpam-6590	110	9	,	,	PUNCT
ejpam-6590	110	10	since	since	SCONJ
ejpam-6590	110	11	r	r	NOUN
ejpam-6590	110	12	(	(	PUNCT
ejpam-6590	110	13	[	[	PUNCT
ejpam-6590	110	14	ψ	ψ	X
ejpam-6590	110	15	0	0	NUM
ejpam-6590	110	16	−φ	−φ	NOUN
ejpam-6590	110	17	0	0	NUM
ejpam-6590	110	18	]	]	PUNCT
ejpam-6590	110	19	)	)	PUNCT
ejpam-6590	111	1	=	=	SYM
ejpam-6590	111	2	r	r	NOUN
ejpam-6590	111	3	(	(	PUNCT
ejpam-6590	111	4	u∗	u∗	PROPN
ejpam-6590	111	5	[	[	PUNCT
ejpam-6590	111	6	ψ	ψ	X
ejpam-6590	111	7	0	0	NUM
ejpam-6590	111	8	φ	φ	NOUN
ejpam-6590	111	9	0	0	NUM
ejpam-6590	111	10	]	]	SYM
ejpam-6590	111	11	u	u	NOUN
ejpam-6590	111	12	)	)	PUNCT
ejpam-6590	111	13	=	=	SYM
ejpam-6590	112	1	r	r	NOUN
ejpam-6590	112	2	(	(	PUNCT
ejpam-6590	112	3	[	[	PUNCT
ejpam-6590	112	4	ψ	ψ	X
ejpam-6590	112	5	0	0	NUM
ejpam-6590	112	6	φ	φ	NOUN
ejpam-6590	112	7	0	0	NUM
ejpam-6590	112	8	]	]	PUNCT
ejpam-6590	112	9	)	)	PUNCT
ejpam-6590	112	10	,	,	PUNCT
ejpam-6590	112	11	where	where	SCONJ
ejpam-6590	112	12	u	u	NOUN
ejpam-6590	112	13	=	=	X
ejpam-6590	112	14	[	[	PUNCT
ejpam-6590	112	15	i	i	NOUN
ejpam-6590	112	16	0	0	NUM
ejpam-6590	112	17	0	0	NUM
ejpam-6590	112	18	−i	−i	NOUN
ejpam-6590	112	19	]	]	PUNCT
ejpam-6590	112	20	.	.	PUNCT
ejpam-6590	113	1	corollary	corollary	ADJ
ejpam-6590	113	2	3	3	X
ejpam-6590	113	3	.	.	PUNCT
ejpam-6590	114	1	let	let	VERB
ejpam-6590	114	2	φ	φ	NUM
ejpam-6590	114	3	,	,	PUNCT
ejpam-6590	114	4	ψ	ψ	X
ejpam-6590	114	5	∈mn(c	∈mn(c	NOUN
ejpam-6590	114	6	)	)	PUNCT
ejpam-6590	114	7	be	be	VERB
ejpam-6590	114	8	acc	acc	PROPN
ejpam-6590	114	9	-	-	PUNCT
ejpam-6590	114	10	dis	dis	PROPN
ejpam-6590	114	11	matrices	matrix	NOUN
ejpam-6590	114	12	with	with	ADP
ejpam-6590	114	13	cd	cd	PROPN
ejpam-6590	114	14	ψ	ψ	NOUN
ejpam-6590	114	15	=	=	PUNCT
ejpam-6590	114	16	ψ1+iψ2,φ	ψ1+iψ2,φ	NUM
ejpam-6590	114	17	=	=	SYM
ejpam-6590	114	18	ϕ1+iϕ2	ϕ1+iϕ2	NOUN
ejpam-6590	114	19	.	.	PUNCT
ejpam-6590	115	1	then	then	ADV
ejpam-6590	115	2	r	r	X
ejpam-6590	115	3	(	(	PUNCT
ejpam-6590	115	4	[	[	PUNCT
ejpam-6590	115	5	ψ	ψ	X
ejpam-6590	115	6	φ	φ	X
ejpam-6590	115	7	0	0	NUM
ejpam-6590	115	8	0	0	NUM
ejpam-6590	115	9	]	]	PUNCT
ejpam-6590	115	10	)	)	PUNCT
ejpam-6590	115	11	≤	≤	PUNCT
ejpam-6590	116	1	min(α	min(α	PROPN
ejpam-6590	116	2	,	,	PUNCT
ejpam-6590	116	3	β	β	NOUN
ejpam-6590	116	4	)	)	PUNCT
ejpam-6590	116	5	.	.	PUNCT
ejpam-6590	117	1	proof	proof	NOUN
ejpam-6590	117	2	.	.	PUNCT
ejpam-6590	118	1	consider	consider	VERB
ejpam-6590	118	2	r	r	NOUN
ejpam-6590	118	3	(	(	PUNCT
ejpam-6590	118	4	[	[	PUNCT
ejpam-6590	118	5	ψ	ψ	X
ejpam-6590	118	6	φ	φ	X
ejpam-6590	118	7	0	0	NUM
ejpam-6590	118	8	0	0	NUM
ejpam-6590	118	9	]	]	PUNCT
ejpam-6590	118	10	)	)	PUNCT
ejpam-6590	119	1	=	=	SYM
ejpam-6590	119	2	r	r	NOUN
ejpam-6590	119	3	(	(	PUNCT
ejpam-6590	119	4	[	[	PUNCT
ejpam-6590	119	5	ψ∗	ψ∗	NOUN
ejpam-6590	119	6	0	0	NUM
ejpam-6590	119	7	φ∗	φ∗	NOUN
ejpam-6590	119	8	0	0	NUM
ejpam-6590	119	9	]	]	PUNCT
ejpam-6590	119	10	)	)	PUNCT
ejpam-6590	119	11	(	(	PUNCT
ejpam-6590	119	12	by	by	ADP
ejpam-6590	119	13	(	(	PUNCT
ejpam-6590	119	14	7	7	NUM
ejpam-6590	119	15	)	)	PUNCT
ejpam-6590	119	16	)	)	PUNCT
ejpam-6590	119	17	now	now	ADV
ejpam-6590	119	18	,	,	PUNCT
ejpam-6590	119	19	using	use	VERB
ejpam-6590	119	20	the	the	DET
ejpam-6590	119	21	same	same	ADJ
ejpam-6590	119	22	procedure	procedure	NOUN
ejpam-6590	119	23	in	in	ADP
ejpam-6590	119	24	theorem	theorem	NOUN
ejpam-6590	119	25	1	1	NUM
ejpam-6590	119	26	,	,	PUNCT
ejpam-6590	119	27	we	we	PRON
ejpam-6590	119	28	get	get	VERB
ejpam-6590	119	29	r	r	NOUN
ejpam-6590	119	30	(	(	PUNCT
ejpam-6590	119	31	[	[	PUNCT
ejpam-6590	119	32	ψ	ψ	X
ejpam-6590	119	33	φ	φ	X
ejpam-6590	119	34	0	0	NUM
ejpam-6590	119	35	0	0	NUM
ejpam-6590	119	36	]	]	PUNCT
ejpam-6590	119	37	)	)	PUNCT
ejpam-6590	119	38	⩽	⩽	NOUN
ejpam-6590	119	39	(	(	PUNCT
ejpam-6590	119	40	∥∥∥(ψ∗)2	∥∥∥(ψ∗)2	PROPN
ejpam-6590	119	41	∥∥∥)1/2	∥∥∥)1/2	NUM
ejpam-6590	120	1	=	=	SYM
ejpam-6590	120	2	(	(	PUNCT
ejpam-6590	120	3	∥∥∥(ψ2	∥∥∥(ψ2	PROPN
ejpam-6590	120	4	)	)	PUNCT
ejpam-6590	120	5	∗∥∥∥)1/2	∗∥∥∥)1/2	PROPN
ejpam-6590	121	1	=	=	SYM
ejpam-6590	121	2	(	(	PUNCT
ejpam-6590	121	3	∥∥ψ2	∥∥ψ2	PROPN
ejpam-6590	121	4	∥∥)1/2	∥∥)1/2	PROPN
ejpam-6590	121	5	⩽	⩽	NOUN
ejpam-6590	121	6	α	α	X
ejpam-6590	121	7	.	.	PUNCT
ejpam-6590	122	1	also	also	ADV
ejpam-6590	122	2	,	,	PUNCT
ejpam-6590	122	3	r	r	NOUN
ejpam-6590	122	4	(	(	PUNCT
ejpam-6590	122	5	[	[	PUNCT
ejpam-6590	122	6	ψ	ψ	X
ejpam-6590	122	7	φ	φ	X
ejpam-6590	122	8	0	0	NUM
ejpam-6590	122	9	0	0	NUM
ejpam-6590	122	10	]	]	PUNCT
ejpam-6590	122	11	)	)	PUNCT
ejpam-6590	122	12	⩽	⩽	ADJ
ejpam-6590	122	13	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6590	122	14	[	[	PUNCT
ejpam-6590	122	15	ψ	ψ	X
ejpam-6590	122	16	φ	φ	X
ejpam-6590	122	17	0	0	NUM
ejpam-6590	122	18	0	0	NUM
ejpam-6590	122	19	]	]	SYM
ejpam-6590	122	20	∥∥∥∥	∥∥∥∥	NUM
ejpam-6590	122	21	=	=	SYM
ejpam-6590	122	22	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6590	122	23	[	[	PUNCT
ejpam-6590	122	24	ψ	ψ	X
ejpam-6590	122	25	φ	φ	X
ejpam-6590	122	26	0	0	NUM
ejpam-6590	122	27	0	0	NUM
ejpam-6590	122	28	]	]	PUNCT
ejpam-6590	122	29	[	[	PUNCT
ejpam-6590	122	30	ψ∗	ψ∗	NOUN
ejpam-6590	122	31	0	0	NUM
ejpam-6590	122	32	φ∗	φ∗	NOUN
ejpam-6590	122	33	0	0	NUM
ejpam-6590	122	34	]	]	X
ejpam-6590	122	35	∥∥∥∥1/2	∥∥∥∥1/2	ADJ
ejpam-6590	122	36	⩽	⩽	NOUN
ejpam-6590	122	37	β	β	PROPN
ejpam-6590	122	38	,	,	PUNCT
ejpam-6590	122	39	which	which	PRON
ejpam-6590	122	40	completes	complete	VERB
ejpam-6590	122	41	the	the	DET
ejpam-6590	122	42	proof	proof	NOUN
ejpam-6590	122	43	.	.	PUNCT
ejpam-6590	123	1	theorem	theorem	NOUN
ejpam-6590	123	2	3	3	X
ejpam-6590	123	3	.	.	PUNCT
ejpam-6590	124	1	let	let	VERB
ejpam-6590	124	2	ψ	ψ	X
ejpam-6590	124	3	,	,	PUNCT
ejpam-6590	124	4	φ	φ	PROPN
ejpam-6590	124	5	∈mn(c	∈mn(c	NOUN
ejpam-6590	124	6	)	)	PUNCT
ejpam-6590	124	7	be	be	AUX
ejpam-6590	124	8	acc	acc	PROPN
ejpam-6590	124	9	-	-	PUNCT
ejpam-6590	124	10	dis	dis	PROPN
ejpam-6590	124	11	matrices	matrix	NOUN
ejpam-6590	124	12	with	with	ADP
ejpam-6590	124	13	cd	cd	PROPN
ejpam-6590	124	14	ψ	ψ	NOUN
ejpam-6590	124	15	=	=	SYM
ejpam-6590	124	16	ψ1	ψ1	NOUN
ejpam-6590	124	17	+	+	CCONJ
ejpam-6590	124	18	iψ2,φ	iψ2,φ	NOUN
ejpam-6590	124	19	=	=	SYM
ejpam-6590	124	20	ϕ1	ϕ1	NOUN
ejpam-6590	124	21	+	+	CCONJ
ejpam-6590	124	22	iϕ2	iϕ2	NOUN
ejpam-6590	124	23	.	.	PUNCT
ejpam-6590	125	1	then	then	ADV
ejpam-6590	125	2	r	r	X
ejpam-6590	125	3	(	(	PUNCT
ejpam-6590	125	4	[	[	PUNCT
ejpam-6590	125	5	ψ	ψ	X
ejpam-6590	125	6	φ	φ	X
ejpam-6590	125	7	φ	φ	X
ejpam-6590	125	8	ψ	ψ	X
ejpam-6590	125	9	]	]	X
ejpam-6590	125	10	)	)	PUNCT
ejpam-6590	125	11	≤	≤	NUM
ejpam-6590	125	12	r(ψ1	r(ψ1	NOUN
ejpam-6590	125	13	+	+	CCONJ
ejpam-6590	125	14	ϕ1	ϕ1	NOUN
ejpam-6590	125	15	)	)	PUNCT
ejpam-6590	125	16	+	+	CCONJ
ejpam-6590	125	17	r(ψ2	r(ψ2	NOUN
ejpam-6590	125	18	+	+	CCONJ
ejpam-6590	125	19	ϕ2	ϕ2	ADV
ejpam-6590	125	20	)	)	PUNCT
ejpam-6590	125	21	.	.	PUNCT
ejpam-6590	126	1	proof	proof	NOUN
ejpam-6590	126	2	.	.	PUNCT
ejpam-6590	127	1	consider	consider	VERB
ejpam-6590	127	2	r	r	NOUN
ejpam-6590	127	3	(	(	PUNCT
ejpam-6590	127	4	u∗	u∗	PROPN
ejpam-6590	127	5	[	[	PUNCT
ejpam-6590	127	6	ψ	ψ	X
ejpam-6590	127	7	φ	φ	X
ejpam-6590	127	8	φ	φ	X
ejpam-6590	127	9	ψ	ψ	X
ejpam-6590	127	10	]	]	X
ejpam-6590	127	11	u	u	NOUN
ejpam-6590	127	12	)	)	PUNCT
ejpam-6590	128	1	=	=	SYM
ejpam-6590	128	2	r	r	NOUN
ejpam-6590	128	3	(	(	PUNCT
ejpam-6590	128	4	[	[	PUNCT
ejpam-6590	128	5	ψ	ψ	X
ejpam-6590	128	6	φ	φ	X
ejpam-6590	128	7	φ	φ	X
ejpam-6590	128	8	ψ	ψ	X
ejpam-6590	128	9	]	]	X
ejpam-6590	128	10	)	)	PUNCT
ejpam-6590	128	11	,	,	PUNCT
ejpam-6590	128	12	(	(	PUNCT
ejpam-6590	128	13	by	by	ADP
ejpam-6590	128	14	(	(	PUNCT
ejpam-6590	128	15	8)	8)	NUM
ejpam-6590	128	16	)	)	PUNCT
ejpam-6590	128	17	where	where	SCONJ
ejpam-6590	128	18	u	u	NOUN
ejpam-6590	128	19	=	=	PROPN
ejpam-6590	128	20	1√	1√	PROPN
ejpam-6590	128	21	2	2	NUM
ejpam-6590	128	22	[	[	PUNCT
ejpam-6590	128	23	i	i	PRON
ejpam-6590	128	24	i	i	PRON
ejpam-6590	128	25	−i	−i	VERB
ejpam-6590	128	26	i	i	PRON
ejpam-6590	128	27	]	]	PUNCT
ejpam-6590	128	28	.	.	PUNCT
ejpam-6590	129	1	m.	m.	NOUN
ejpam-6590	129	2	sakkijha	sakkijha	PROPN
ejpam-6590	129	3	,	,	PUNCT
ejpam-6590	129	4	s.	s.	PROPN
ejpam-6590	129	5	hasan	hasan	PROPN
ejpam-6590	129	6	,	,	PUNCT
ejpam-6590	129	7	m.	m.	NOUN
ejpam-6590	129	8	alholi	alholi	PROPN
ejpam-6590	129	9	/	/	SYM
ejpam-6590	129	10	eur	eur	PROPN
ejpam-6590	129	11	.	.	PUNCT
ejpam-6590	130	1	j.	j.	PROPN
ejpam-6590	130	2	pure	pure	PROPN
ejpam-6590	130	3	appl	appl	PROPN
ejpam-6590	130	4	.	.	PROPN
ejpam-6590	130	5	math	math	PROPN
ejpam-6590	130	6	,	,	PUNCT
ejpam-6590	130	7	18	18	NUM
ejpam-6590	130	8	(	(	PUNCT
ejpam-6590	130	9	3	3	NUM
ejpam-6590	130	10	)	)	PUNCT
ejpam-6590	130	11	(	(	PUNCT
ejpam-6590	130	12	2025	2025	NUM
ejpam-6590	130	13	)	)	PUNCT
ejpam-6590	130	14	,	,	PUNCT
ejpam-6590	130	15	6590	6590	NUM
ejpam-6590	130	16	7	7	NUM
ejpam-6590	130	17	of	of	ADP
ejpam-6590	130	18	9	9	NUM
ejpam-6590	130	19	now	now	ADV
ejpam-6590	130	20	,	,	PUNCT
ejpam-6590	130	21	r	r	NOUN
ejpam-6590	130	22	(	(	PUNCT
ejpam-6590	130	23	[	[	PUNCT
ejpam-6590	130	24	ψ	ψ	X
ejpam-6590	130	25	φ	φ	X
ejpam-6590	130	26	φ	φ	X
ejpam-6590	130	27	ψ	ψ	X
ejpam-6590	130	28	]	]	X
ejpam-6590	130	29	)	)	PUNCT
ejpam-6590	130	30	=	=	SYM
ejpam-6590	130	31	1	1	NUM
ejpam-6590	130	32	2	2	NUM
ejpam-6590	130	33	r	r	NOUN
ejpam-6590	130	34	(	(	PUNCT
ejpam-6590	130	35	[	[	PUNCT
ejpam-6590	130	36	i	i	PRON
ejpam-6590	130	37	i	i	PRON
ejpam-6590	130	38	−i	−i	VERB
ejpam-6590	131	1	i	i	PRON
ejpam-6590	131	2	]	]	PUNCT
ejpam-6590	132	1	[	[	PUNCT
ejpam-6590	132	2	ψ	ψ	X
ejpam-6590	132	3	φ	φ	X
ejpam-6590	132	4	φ	φ	X
ejpam-6590	132	5	ψ	ψ	X
ejpam-6590	132	6	]	]	X
ejpam-6590	133	1	[	[	PUNCT
ejpam-6590	133	2	i	i	PRON
ejpam-6590	133	3	−i	−i	PROPN
ejpam-6590	133	4	i	i	PRON
ejpam-6590	133	5	i	i	PRON
ejpam-6590	133	6	]	]	X
ejpam-6590	133	7	)	)	PUNCT
ejpam-6590	133	8	=	=	SYM
ejpam-6590	133	9	1	1	NUM
ejpam-6590	133	10	2	2	NUM
ejpam-6590	133	11	r	r	NOUN
ejpam-6590	133	12	(	(	PUNCT
ejpam-6590	133	13	[	[	PUNCT
ejpam-6590	133	14	2(ψ	2(ψ	NUM
ejpam-6590	133	15	+	+	CCONJ
ejpam-6590	133	16	φ	φ	NUM
ejpam-6590	133	17	)	)	PUNCT
ejpam-6590	133	18	0	0	NUM
ejpam-6590	133	19	0	0	NUM
ejpam-6590	133	20	2(ψ−	2(ψ−	NUM
ejpam-6590	133	21	φ	φ	NUM
ejpam-6590	133	22	)	)	PUNCT
ejpam-6590	133	23	]	]	PUNCT
ejpam-6590	133	24	)	)	PUNCT
ejpam-6590	134	1	=	=	SYM
ejpam-6590	134	2	r	r	NOUN
ejpam-6590	134	3	(	(	PUNCT
ejpam-6590	134	4	[	[	PUNCT
ejpam-6590	134	5	ψ+φ	ψ+φ	X
ejpam-6590	134	6	0	0	NUM
ejpam-6590	134	7	0	0	NUM
ejpam-6590	134	8	ψ−	ψ−	VERB
ejpam-6590	134	9	φ	φ	PROPN
ejpam-6590	134	10	]	]	PUNCT
ejpam-6590	134	11	)	)	PUNCT
ejpam-6590	134	12	(	(	PUNCT
ejpam-6590	134	13	by	by	ADP
ejpam-6590	134	14	(	(	PUNCT
ejpam-6590	134	15	5	5	NUM
ejpam-6590	134	16	)	)	PUNCT
ejpam-6590	134	17	)	)	PUNCT
ejpam-6590	134	18	⩽	⩽	ADP
ejpam-6590	134	19	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6590	134	20	[	[	PUNCT
ejpam-6590	134	21	ψ+φ	ψ+φ	X
ejpam-6590	134	22	0	0	NUM
ejpam-6590	134	23	0	0	NUM
ejpam-6590	134	24	ψ−	ψ−	VERB
ejpam-6590	134	25	φ	φ	PROPN
ejpam-6590	134	26	]	]	X
ejpam-6590	134	27	∥∥∥∥	∥∥∥∥	NUM
ejpam-6590	134	28	(	(	PUNCT
ejpam-6590	134	29	by	by	ADP
ejpam-6590	134	30	(	(	PUNCT
ejpam-6590	134	31	3	3	NUM
ejpam-6590	134	32	)	)	PUNCT
ejpam-6590	134	33	)	)	PUNCT
ejpam-6590	134	34	=	=	SYM
ejpam-6590	135	1	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6590	135	2	[	[	PUNCT
ejpam-6590	135	3	(	(	PUNCT
ejpam-6590	135	4	ψ1	ψ1	ADJ
ejpam-6590	135	5	+	+	CCONJ
ejpam-6590	135	6	ϕ1	ϕ1	NOUN
ejpam-6590	135	7	)	)	PUNCT
ejpam-6590	135	8	+	+	CCONJ
ejpam-6590	135	9	i(ψ2	i(ψ2	NOUN
ejpam-6590	135	10	+	+	CCONJ
ejpam-6590	135	11	ϕ2	ϕ2	ADV
ejpam-6590	135	12	)	)	PUNCT
ejpam-6590	135	13	0	0	NUM
ejpam-6590	135	14	0	0	NUM
ejpam-6590	135	15	(	(	PUNCT
ejpam-6590	135	16	ψ1	ψ1	ADJ
ejpam-6590	135	17	−	−	NOUN
ejpam-6590	135	18	ϕ1	ϕ1	NOUN
ejpam-6590	135	19	)	)	PUNCT
ejpam-6590	135	20	+	+	CCONJ
ejpam-6590	135	21	i(ψ2	i(ψ2	NOUN
ejpam-6590	135	22	−	−	NOUN
ejpam-6590	135	23	ϕ2	ϕ2	ADV
ejpam-6590	135	24	)	)	PUNCT
ejpam-6590	135	25	]	]	PUNCT
ejpam-6590	135	26	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6590	135	27	=	=	SYM
ejpam-6590	135	28	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6590	135	29	[	[	PUNCT
ejpam-6590	135	30	(	(	PUNCT
ejpam-6590	135	31	ψ1	ψ1	ADJ
ejpam-6590	135	32	+	+	CCONJ
ejpam-6590	135	33	ϕ1	ϕ1	NOUN
ejpam-6590	135	34	)	)	PUNCT
ejpam-6590	135	35	0	0	NUM
ejpam-6590	135	36	0	0	NUM
ejpam-6590	135	37	(	(	PUNCT
ejpam-6590	135	38	ψ1	ψ1	ADJ
ejpam-6590	135	39	−	−	PROPN
ejpam-6590	135	40	ϕ1	ϕ1	NOUN
ejpam-6590	135	41	)	)	PUNCT
ejpam-6590	135	42	]	]	PUNCT
ejpam-6590	136	1	+	+	CCONJ
ejpam-6590	136	2	i	i	PRON
ejpam-6590	136	3	[	[	PUNCT
ejpam-6590	136	4	(	(	PUNCT
ejpam-6590	136	5	ψ2	ψ2	NOUN
ejpam-6590	136	6	+	+	CCONJ
ejpam-6590	136	7	ϕ2	ϕ2	ADV
ejpam-6590	136	8	)	)	PUNCT
ejpam-6590	136	9	0	0	NUM
ejpam-6590	136	10	0	0	NUM
ejpam-6590	136	11	(	(	PUNCT
ejpam-6590	136	12	ψ2	ψ2	NOUN
ejpam-6590	136	13	−	−	NOUN
ejpam-6590	136	14	ϕ2	ϕ2	ADV
ejpam-6590	136	15	)	)	PUNCT
ejpam-6590	136	16	]	]	PUNCT
ejpam-6590	136	17	∥∥∥∥	∥∥∥∥	NUM
ejpam-6590	136	18	⩽	⩽	NOUN
ejpam-6590	136	19	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6590	136	20	[	[	PUNCT
ejpam-6590	136	21	(	(	PUNCT
ejpam-6590	136	22	ψ1	ψ1	ADJ
ejpam-6590	136	23	+	+	CCONJ
ejpam-6590	136	24	ϕ1	ϕ1	NOUN
ejpam-6590	136	25	)	)	PUNCT
ejpam-6590	136	26	0	0	NUM
ejpam-6590	136	27	0	0	NUM
ejpam-6590	136	28	(	(	PUNCT
ejpam-6590	136	29	ψ1	ψ1	ADJ
ejpam-6590	136	30	−	−	PROPN
ejpam-6590	136	31	ϕ1	ϕ1	NOUN
ejpam-6590	136	32	)	)	PUNCT
ejpam-6590	136	33	]	]	PUNCT
ejpam-6590	136	34	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-6590	136	35	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6590	136	36	[	[	PUNCT
ejpam-6590	136	37	(	(	PUNCT
ejpam-6590	136	38	ψ2	ψ2	NOUN
ejpam-6590	136	39	+	+	CCONJ
ejpam-6590	136	40	ϕ2	ϕ2	ADV
ejpam-6590	136	41	)	)	PUNCT
ejpam-6590	136	42	0	0	NUM
ejpam-6590	136	43	0	0	NUM
ejpam-6590	136	44	(	(	PUNCT
ejpam-6590	136	45	ψ2	ψ2	NOUN
ejpam-6590	136	46	−	−	NOUN
ejpam-6590	136	47	ϕ2	ϕ2	ADV
ejpam-6590	136	48	)	)	PUNCT
ejpam-6590	136	49	]	]	PUNCT
ejpam-6590	136	50	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6590	136	51	=	=	SYM
ejpam-6590	136	52	max	max	PROPN
ejpam-6590	136	53	(	(	PUNCT
ejpam-6590	136	54	∥ψ1	∥ψ1	X
ejpam-6590	136	55	+	+	CCONJ
ejpam-6590	136	56	ϕ1∥	ϕ1∥	VERB
ejpam-6590	136	57	,	,	PUNCT
ejpam-6590	136	58	∥ψ1	∥ψ1	VERB
ejpam-6590	136	59	−	−	PROPN
ejpam-6590	136	60	ϕ1∥	ϕ1∥	PROPN
ejpam-6590	136	61	)	)	PUNCT
ejpam-6590	137	1	+	+	CCONJ
ejpam-6590	137	2	max	max	PROPN
ejpam-6590	137	3	(	(	PUNCT
ejpam-6590	137	4	∥ψ2	∥ψ2	NOUN
ejpam-6590	137	5	+	+	CCONJ
ejpam-6590	137	6	ϕ2∥	ϕ2∥	ADJ
ejpam-6590	137	7	,	,	PUNCT
ejpam-6590	137	8	∥ψ2	∥ψ2	NOUN
ejpam-6590	138	1	−	−	PROPN
ejpam-6590	138	2	ϕ2∥	ϕ2∥	PROPN
ejpam-6590	138	3	)	)	PUNCT
ejpam-6590	138	4	(	(	PUNCT
ejpam-6590	138	5	by	by	ADP
ejpam-6590	138	6	lemma	lemma	PROPN
ejpam-6590	138	7	5	5	NUM
ejpam-6590	138	8	)	)	PUNCT
ejpam-6590	138	9	=	=	NOUN
ejpam-6590	138	10	∥ψ1	∥ψ1	NOUN
ejpam-6590	138	11	+	+	CCONJ
ejpam-6590	138	12	ϕ1∥+	ϕ1∥+	ADJ
ejpam-6590	138	13	∥ψ2	∥ψ2	NOUN
ejpam-6590	139	1	+	+	CCONJ
ejpam-6590	139	2	ϕ2∥	ϕ2∥	ADJ
ejpam-6590	139	3	,	,	PUNCT
ejpam-6590	139	4	(	(	PUNCT
ejpam-6590	139	5	since	since	SCONJ
ejpam-6590	139	6	ψ1	ψ1	NOUN
ejpam-6590	139	7	,	,	PUNCT
ejpam-6590	139	8	ψ2	ψ2	NOUN
ejpam-6590	139	9	,	,	PUNCT
ejpam-6590	139	10	ϕ1	ϕ1	NOUN
ejpam-6590	139	11	,	,	PUNCT
ejpam-6590	139	12	ϕ2	ϕ2	ADV
ejpam-6590	139	13	are	be	AUX
ejpam-6590	139	14	p.s.d	p.s.d	ADJ
ejpam-6590	139	15	)	)	PUNCT
ejpam-6590	140	1	=	=	NOUN
ejpam-6590	140	2	r(ψ1	r(ψ1	NOUN
ejpam-6590	140	3	+	+	CCONJ
ejpam-6590	140	4	ϕ1	ϕ1	NOUN
ejpam-6590	140	5	)	)	PUNCT
ejpam-6590	141	1	+	+	CCONJ
ejpam-6590	141	2	r(ψ2	r(ψ2	NOUN
ejpam-6590	141	3	+	+	CCONJ
ejpam-6590	141	4	ϕ2	ϕ2	ADV
ejpam-6590	141	5	)	)	PUNCT
ejpam-6590	141	6	(	(	PUNCT
ejpam-6590	141	7	by(3	by(3	NOUN
ejpam-6590	141	8	)	)	PUNCT
ejpam-6590	141	9	)	)	PUNCT
ejpam-6590	141	10	.	.	PUNCT
ejpam-6590	142	1	theorem	theorem	ADJ
ejpam-6590	142	2	4	4	NUM
ejpam-6590	142	3	.	.	PUNCT
ejpam-6590	143	1	let	let	AUX
ejpam-6590	143	2	ψ	ψ	PRON
ejpam-6590	143	3	∈mn(c	∈mn(c	NOUN
ejpam-6590	143	4	)	)	PUNCT
ejpam-6590	143	5	be	be	VERB
ejpam-6590	143	6	acc	acc	PROPN
ejpam-6590	143	7	-	-	PUNCT
ejpam-6590	143	8	dis	dis	PROPN
ejpam-6590	143	9	matrix	matrix	NOUN
ejpam-6590	143	10	with	with	ADP
ejpam-6590	143	11	cd	cd	PROPN
ejpam-6590	143	12	ψ	ψ	NOUN
ejpam-6590	143	13	=	=	SYM
ejpam-6590	143	14	ψ1	ψ1	NOUN
ejpam-6590	144	1	+	+	CCONJ
ejpam-6590	144	2	iψ2.then	iψ2.then	PROPN
ejpam-6590	144	3	r	r	NOUN
ejpam-6590	144	4	(	(	PUNCT
ejpam-6590	144	5	[	[	PUNCT
ejpam-6590	144	6	ψ	ψ	X
ejpam-6590	144	7	ψ	ψ	X
ejpam-6590	144	8	−ψ	−ψ	NOUN
ejpam-6590	144	9	−ψ	−ψ	NOUN
ejpam-6590	144	10	]	]	PUNCT
ejpam-6590	144	11	)	)	PUNCT
ejpam-6590	144	12	≤	≤	NUM
ejpam-6590	144	13	2r(ψ2	2r(ψ2	NUM
ejpam-6590	145	1	+	+	NUM
ejpam-6590	145	2	ψ2	ψ2	NOUN
ejpam-6590	145	3	)	)	PUNCT
ejpam-6590	145	4	.	.	PUNCT
ejpam-6590	146	1	proof	proof	NOUN
ejpam-6590	146	2	.	.	PUNCT
ejpam-6590	147	1	consider	consider	VERB
ejpam-6590	147	2	r	r	NOUN
ejpam-6590	147	3	(	(	PUNCT
ejpam-6590	147	4	[	[	PUNCT
ejpam-6590	147	5	ψ	ψ	X
ejpam-6590	147	6	ψ	ψ	X
ejpam-6590	147	7	−ψ	−ψ	NOUN
ejpam-6590	147	8	−ψ	−ψ	NOUN
ejpam-6590	147	9	]	]	PUNCT
ejpam-6590	147	10	)	)	PUNCT
ejpam-6590	148	1	=	=	SYM
ejpam-6590	148	2	r	r	NOUN
ejpam-6590	148	3	(	(	PUNCT
ejpam-6590	148	4	u	u	X
ejpam-6590	148	5	[	[	PUNCT
ejpam-6590	148	6	ψ	ψ	X
ejpam-6590	148	7	ψ	ψ	X
ejpam-6590	148	8	−ψ	−ψ	NOUN
ejpam-6590	148	9	−ψ	−ψ	NOUN
ejpam-6590	148	10	]	]	PUNCT
ejpam-6590	148	11	u∗	u∗	INTJ
ejpam-6590	148	12	)	)	PUNCT
ejpam-6590	148	13	,	,	PUNCT
ejpam-6590	148	14	(	(	PUNCT
ejpam-6590	148	15	by	by	ADP
ejpam-6590	148	16	(	(	PUNCT
ejpam-6590	148	17	8)	8)	NUM
ejpam-6590	148	18	)	)	PUNCT
ejpam-6590	148	19	,	,	PUNCT
ejpam-6590	148	20	where	where	SCONJ
ejpam-6590	148	21	u	u	PROPN
ejpam-6590	148	22	=	=	PROPN
ejpam-6590	148	23	1√	1√	PROPN
ejpam-6590	148	24	2	2	NUM
ejpam-6590	148	25	[	[	PUNCT
ejpam-6590	148	26	i	i	PRON
ejpam-6590	148	27	i	i	PRON
ejpam-6590	148	28	−i	−i	VERB
ejpam-6590	149	1	i	i	PRON
ejpam-6590	149	2	]	]	PUNCT
ejpam-6590	149	3	m.	m.	NOUN
ejpam-6590	149	4	sakkijha	sakkijha	PROPN
ejpam-6590	149	5	,	,	PUNCT
ejpam-6590	149	6	s.	s.	PROPN
ejpam-6590	149	7	hasan	hasan	PROPN
ejpam-6590	149	8	,	,	PUNCT
ejpam-6590	149	9	m.	m.	NOUN
ejpam-6590	149	10	alholi	alholi	PROPN
ejpam-6590	149	11	/	/	SYM
ejpam-6590	149	12	eur	eur	PROPN
ejpam-6590	149	13	.	.	PUNCT
ejpam-6590	150	1	j.	j.	PROPN
ejpam-6590	150	2	pure	pure	PROPN
ejpam-6590	150	3	appl	appl	PROPN
ejpam-6590	150	4	.	.	PROPN
ejpam-6590	150	5	math	math	PROPN
ejpam-6590	150	6	,	,	PUNCT
ejpam-6590	150	7	18	18	NUM
ejpam-6590	150	8	(	(	PUNCT
ejpam-6590	150	9	3	3	NUM
ejpam-6590	150	10	)	)	PUNCT
ejpam-6590	150	11	(	(	PUNCT
ejpam-6590	150	12	2025	2025	NUM
ejpam-6590	150	13	)	)	PUNCT
ejpam-6590	150	14	,	,	PUNCT
ejpam-6590	150	15	6590	6590	NUM
ejpam-6590	150	16	8	8	NUM
ejpam-6590	150	17	of	of	ADP
ejpam-6590	150	18	9	9	NUM
ejpam-6590	150	19	r	r	NOUN
ejpam-6590	150	20	(	(	PUNCT
ejpam-6590	150	21	[	[	PUNCT
ejpam-6590	150	22	ψ	ψ	X
ejpam-6590	150	23	ψ	ψ	X
ejpam-6590	150	24	−ψ	−ψ	NOUN
ejpam-6590	150	25	−ψ	−ψ	NOUN
ejpam-6590	150	26	]	]	PUNCT
ejpam-6590	150	27	)	)	PUNCT
ejpam-6590	150	28	=	=	SYM
ejpam-6590	150	29	1	1	NUM
ejpam-6590	150	30	2	2	NUM
ejpam-6590	150	31	r	r	NOUN
ejpam-6590	150	32	(	(	PUNCT
ejpam-6590	150	33	[	[	PUNCT
ejpam-6590	150	34	i	i	PRON
ejpam-6590	150	35	i	i	PRON
ejpam-6590	150	36	−i	−i	VERB
ejpam-6590	151	1	i	i	PRON
ejpam-6590	151	2	]	]	PUNCT
ejpam-6590	151	3	[	[	PUNCT
ejpam-6590	151	4	ψ	ψ	X
ejpam-6590	151	5	ψ	ψ	X
ejpam-6590	151	6	−ψ	−ψ	NOUN
ejpam-6590	151	7	−ψ	−ψ	NOUN
ejpam-6590	151	8	]	]	PUNCT
ejpam-6590	152	1	[	[	PUNCT
ejpam-6590	152	2	i	i	PRON
ejpam-6590	152	3	−i	−i	PROPN
ejpam-6590	152	4	i	i	PRON
ejpam-6590	152	5	i	i	PRON
ejpam-6590	152	6	]	]	X
ejpam-6590	152	7	)	)	PUNCT
ejpam-6590	152	8	=	=	SYM
ejpam-6590	152	9	1	1	NUM
ejpam-6590	152	10	2	2	NUM
ejpam-6590	152	11	r	r	NOUN
ejpam-6590	152	12	(	(	PUNCT
ejpam-6590	152	13	[	[	PUNCT
ejpam-6590	152	14	0	0	NUM
ejpam-6590	152	15	0	0	NUM
ejpam-6590	152	16	−4ψ	−4ψ	NOUN
ejpam-6590	152	17	0	0	NUM
ejpam-6590	152	18	]	]	PUNCT
ejpam-6590	152	19	)	)	PUNCT
ejpam-6590	153	1	=	=	SYM
ejpam-6590	153	2	2r	2r	NUM
ejpam-6590	153	3	(	(	PUNCT
ejpam-6590	153	4	[	[	PUNCT
ejpam-6590	153	5	0	0	NUM
ejpam-6590	153	6	0	0	NUM
ejpam-6590	153	7	ψ	ψ	NOUN
ejpam-6590	153	8	0	0	NUM
ejpam-6590	153	9	]	]	SYM
ejpam-6590	153	10	)	)	PUNCT
ejpam-6590	153	11	⩽	⩽	ADJ
ejpam-6590	153	12	2	2	NUM
ejpam-6590	153	13	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6590	153	14	[	[	PUNCT
ejpam-6590	153	15	0	0	NUM
ejpam-6590	153	16	0	0	NUM
ejpam-6590	153	17	ψ	ψ	NOUN
ejpam-6590	153	18	0	0	NUM
ejpam-6590	153	19	]	]	SYM
ejpam-6590	153	20	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6590	153	21	=	=	SYM
ejpam-6590	154	1	2∥ψ∥	2∥ψ∥	NUM
ejpam-6590	154	2	=	=	SYM
ejpam-6590	155	1	2∥ψ1	2∥ψ1	NUM
ejpam-6590	155	2	+	+	CCONJ
ejpam-6590	155	3	iψ2∥	iψ2∥	PROPN
ejpam-6590	155	4	⩽	⩽	NOUN
ejpam-6590	155	5	2∥ψ1	2∥ψ1	NUM
ejpam-6590	155	6	+	+	CCONJ
ejpam-6590	155	7	ψ2∥	ψ2∥	PROPN
ejpam-6590	155	8	(	(	PUNCT
ejpam-6590	155	9	by	by	ADP
ejpam-6590	155	10	lemma	lemma	PROPN
ejpam-6590	155	11	1	1	NUM
ejpam-6590	155	12	)	)	PUNCT
ejpam-6590	155	13	=	=	PUNCT
ejpam-6590	156	1	2r(ψ1	2r(ψ1	NOUN
ejpam-6590	156	2	+	+	NUM
ejpam-6590	156	3	ψ2	ψ2	NOUN
ejpam-6590	156	4	)	)	PUNCT
ejpam-6590	156	5	(	(	PUNCT
ejpam-6590	156	6	by	by	ADP
ejpam-6590	156	7	(	(	PUNCT
ejpam-6590	156	8	3	3	NUM
ejpam-6590	156	9	)	)	PUNCT
ejpam-6590	156	10	)	)	PUNCT
ejpam-6590	157	1	the	the	DET
ejpam-6590	157	2	following	follow	VERB
ejpam-6590	157	3	is	be	AUX
ejpam-6590	157	4	an	an	DET
ejpam-6590	157	5	example	example	NOUN
ejpam-6590	157	6	of	of	ADP
ejpam-6590	157	7	theorem	theorem	ADJ
ejpam-6590	157	8	4	4	NUM
ejpam-6590	157	9	.	.	NOUN
ejpam-6590	157	10	example	example	NOUN
ejpam-6590	158	1	1	1	NUM
ejpam-6590	158	2	.	.	PUNCT
ejpam-6590	159	1	let	let	VERB
ejpam-6590	159	2	ψ	ψ	VERB
ejpam-6590	160	1	=	=	X
ejpam-6590	161	1	[	[	PUNCT
ejpam-6590	161	2	1	1	NUM
ejpam-6590	161	3	1	1	NUM
ejpam-6590	161	4	1	1	NUM
ejpam-6590	161	5	1	1	NUM
ejpam-6590	161	6	]	]	PUNCT
ejpam-6590	162	1	+	+	CCONJ
ejpam-6590	162	2	i	i	PRON
ejpam-6590	162	3	[	[	PUNCT
ejpam-6590	162	4	1	1	NUM
ejpam-6590	162	5	0	0	NUM
ejpam-6590	162	6	0	0	NUM
ejpam-6590	162	7	1	1	NUM
ejpam-6590	162	8	]	]	PUNCT
ejpam-6590	162	9	=	=	PUNCT
ejpam-6590	162	10	[	[	PUNCT
ejpam-6590	162	11	1	1	NUM
ejpam-6590	162	12	+	+	CCONJ
ejpam-6590	162	13	i	i	NOUN
ejpam-6590	162	14	1	1	NUM
ejpam-6590	162	15	1	1	NUM
ejpam-6590	162	16	1	1	NUM
ejpam-6590	162	17	+	+	CCONJ
ejpam-6590	162	18	i	i	PRON
ejpam-6590	162	19	]	]	PUNCT
ejpam-6590	162	20	.	.	PUNCT
ejpam-6590	163	1	note	note	VERB
ejpam-6590	163	2	that	that	SCONJ
ejpam-6590	164	1	r	r	NOUN
ejpam-6590	164	2	(	(	PUNCT
ejpam-6590	164	3	[	[	PUNCT
ejpam-6590	164	4	ψ	ψ	X
ejpam-6590	164	5	ψ	ψ	X
ejpam-6590	164	6	−ψ	−ψ	NOUN
ejpam-6590	164	7	−ψ	−ψ	NOUN
ejpam-6590	164	8	]	]	PUNCT
ejpam-6590	164	9	)	)	PUNCT
ejpam-6590	165	1	=	=	SYM
ejpam-6590	165	2	r	r	NOUN
ejpam-6590	165	3	(	(	PUNCT
ejpam-6590	165	4	u	u	X
ejpam-6590	165	5	[	[	PUNCT
ejpam-6590	165	6	ψ	ψ	X
ejpam-6590	165	7	ψ	ψ	X
ejpam-6590	165	8	−ψ	−ψ	NOUN
ejpam-6590	165	9	−ψ	−ψ	NOUN
ejpam-6590	165	10	]	]	PUNCT
ejpam-6590	165	11	u∗	u∗	ADV
ejpam-6590	165	12	)	)	PUNCT
ejpam-6590	165	13	=	=	SYM
ejpam-6590	165	14	1	1	NUM
ejpam-6590	165	15	2	2	NUM
ejpam-6590	165	16	r	r	NOUN
ejpam-6590	165	17	(	(	PUNCT
ejpam-6590	165	18	[	[	PUNCT
ejpam-6590	165	19	0	0	NUM
ejpam-6590	165	20	0	0	NUM
ejpam-6590	165	21	−4ψ	−4ψ	NOUN
ejpam-6590	165	22	0	0	NUM
ejpam-6590	165	23	]	]	PUNCT
ejpam-6590	165	24	)	)	PUNCT
ejpam-6590	166	1	=	=	SYM
ejpam-6590	167	1	2∥ψ∥	2∥ψ∥	NUM
ejpam-6590	167	2	=	=	SYM
ejpam-6590	167	3	2r(ψ	2r(ψ	NUM
ejpam-6590	167	4	)	)	PUNCT
ejpam-6590	167	5	,	,	PUNCT
ejpam-6590	167	6	where	where	SCONJ
ejpam-6590	167	7	u	u	PROPN
ejpam-6590	167	8	=	=	PROPN
ejpam-6590	167	9	1√	1√	PROPN
ejpam-6590	167	10	2	2	NUM
ejpam-6590	167	11	[	[	PUNCT
ejpam-6590	167	12	i	i	PRON
ejpam-6590	167	13	i	i	PRON
ejpam-6590	167	14	−i	−i	VERB
ejpam-6590	167	15	i	i	PRON
ejpam-6590	167	16	]	]	PUNCT
ejpam-6590	167	17	.	.	PUNCT
ejpam-6590	168	1	to	to	PART
ejpam-6590	168	2	find	find	VERB
ejpam-6590	168	3	r(ψ	r(ψ	NOUN
ejpam-6590	168	4	)	)	PUNCT
ejpam-6590	168	5	,	,	PUNCT
ejpam-6590	168	6	we	we	PRON
ejpam-6590	168	7	compute	compute	VERB
ejpam-6590	168	8	the	the	DET
ejpam-6590	168	9	eigenvalues	eigenvalue	NOUN
ejpam-6590	168	10	of	of	ADP
ejpam-6590	168	11	ψ	ψ	NOUN
ejpam-6590	168	12	as	as	SCONJ
ejpam-6590	168	13	follows	follow	VERB
ejpam-6590	168	14	:	:	PUNCT
ejpam-6590	168	15	det(λi	det(λi	NUM
ejpam-6590	168	16	−ψ	−ψ	NOUN
ejpam-6590	168	17	)	)	PUNCT
ejpam-6590	169	1	=	=	SYM
ejpam-6590	169	2	det	det	PROPN
ejpam-6590	169	3	[	[	PUNCT
ejpam-6590	169	4	λ−	λ−	PROPN
ejpam-6590	169	5	1−	1−	NUM
ejpam-6590	169	6	i	i	PRON
ejpam-6590	169	7	−1	−1	VERB
ejpam-6590	169	8	−1	−1	ADV
ejpam-6590	169	9	λ−	λ−	PROPN
ejpam-6590	169	10	1−	1−	NUM
ejpam-6590	170	1	i	i	PRON
ejpam-6590	170	2	]	]	PUNCT
ejpam-6590	170	3	=	=	PUNCT
ejpam-6590	170	4	det	det	PROPN
ejpam-6590	170	5	[	[	PUNCT
ejpam-6590	170	6	λ−	λ−	PROPN
ejpam-6590	170	7	(	(	PUNCT
ejpam-6590	170	8	1	1	NUM
ejpam-6590	170	9	+	+	NUM
ejpam-6590	170	10	i	i	NOUN
ejpam-6590	170	11	)	)	PUNCT
ejpam-6590	170	12	−1	−1	VERB
ejpam-6590	170	13	−1	−1	NOUN
ejpam-6590	171	1	λ−	λ−	PROPN
ejpam-6590	171	2	(	(	PUNCT
ejpam-6590	171	3	1	1	X
ejpam-6590	171	4	+	+	CCONJ
ejpam-6590	171	5	i	i	NOUN
ejpam-6590	171	6	)	)	PUNCT
ejpam-6590	171	7	]	]	PUNCT
ejpam-6590	172	1	=	=	SYM
ejpam-6590	172	2	(	(	PUNCT
ejpam-6590	172	3	λ−	λ−	PROPN
ejpam-6590	172	4	(	(	PUNCT
ejpam-6590	172	5	1	1	NUM
ejpam-6590	172	6	+	+	NUM
ejpam-6590	172	7	i))2	i))2	NOUN
ejpam-6590	172	8	−	−	NOUN
ejpam-6590	172	9	1	1	NUM
ejpam-6590	172	10	=	=	SYM
ejpam-6590	172	11	0	0	NUM
ejpam-6590	172	12	.	.	PUNCT
ejpam-6590	173	1	⇒	⇒	NOUN
ejpam-6590	173	2	(	(	PUNCT
ejpam-6590	173	3	λ−	λ−	PROPN
ejpam-6590	173	4	(	(	PUNCT
ejpam-6590	173	5	1	1	NUM
ejpam-6590	173	6	+	+	NUM
ejpam-6590	173	7	i))2	i))2	NOUN
ejpam-6590	173	8	=	=	SYM
ejpam-6590	173	9	1	1	NUM
ejpam-6590	173	10	⇒	⇒	NOUN
ejpam-6590	173	11	λ	λ	X
ejpam-6590	173	12	∈	∈	PROPN
ejpam-6590	173	13	{	{	PUNCT
ejpam-6590	173	14	2	2	NUM
ejpam-6590	173	15	+	+	NUM
ejpam-6590	173	16	i	i	PROPN
ejpam-6590	173	17	,	,	PUNCT
ejpam-6590	173	18	i	i	PRON
ejpam-6590	173	19	}	}	PUNCT
ejpam-6590	173	20	.	.	PUNCT
ejpam-6590	174	1	so	so	ADV
ejpam-6590	174	2	,	,	PUNCT
ejpam-6590	174	3	r(ψ	r(ψ	PROPN
ejpam-6590	174	4	)	)	PUNCT
ejpam-6590	175	1	=	=	SYM
ejpam-6590	175	2	max	max	PROPN
ejpam-6590	175	3	|λ|	|λ|	PROPN
ejpam-6590	175	4	=	=	PUNCT
ejpam-6590	176	1	√	√	ADP
ejpam-6590	176	2	4	4	NUM
ejpam-6590	177	1	+	+	SYM
ejpam-6590	177	2	1	1	NUM
ejpam-6590	177	3	=	=	SYM
ejpam-6590	177	4	√	√	NUM
ejpam-6590	177	5	5	5	NUM
ejpam-6590	177	6	.	.	PUNCT
ejpam-6590	178	1	now	now	ADV
ejpam-6590	178	2	it	it	PRON
ejpam-6590	178	3	is	be	AUX
ejpam-6590	178	4	very	very	ADV
ejpam-6590	178	5	easy	easy	ADJ
ejpam-6590	178	6	to	to	PART
ejpam-6590	178	7	find	find	VERB
ejpam-6590	178	8	r(ψ1	r(ψ1	NOUN
ejpam-6590	178	9	+	+	CCONJ
ejpam-6590	178	10	ψ2	ψ2	NOUN
ejpam-6590	178	11	)	)	PUNCT
ejpam-6590	178	12	=	=	SYM
ejpam-6590	178	13	r	r	NOUN
ejpam-6590	178	14	(	(	PUNCT
ejpam-6590	178	15	[	[	PUNCT
ejpam-6590	178	16	2	2	NUM
ejpam-6590	178	17	1	1	NUM
ejpam-6590	178	18	1	1	NUM
ejpam-6590	178	19	2	2	NUM
ejpam-6590	178	20	]	]	PUNCT
ejpam-6590	178	21	)	)	PUNCT
ejpam-6590	178	22	by	by	ADP
ejpam-6590	178	23	calculating	calculate	VERB
ejpam-6590	178	24	their	their	PRON
ejpam-6590	178	25	eigenvalues	eigenvalue	NOUN
ejpam-6590	178	26	which	which	PRON
ejpam-6590	178	27	are	be	AUX
ejpam-6590	178	28	1	1	NUM
ejpam-6590	178	29	,	,	PUNCT
ejpam-6590	178	30	3	3	NUM
ejpam-6590	178	31	.	.	PUNCT
ejpam-6590	178	32	consequently	consequently	ADV
ejpam-6590	178	33	,	,	PUNCT
ejpam-6590	178	34	r(ψ1	r(ψ1	NOUN
ejpam-6590	178	35	+	+	CCONJ
ejpam-6590	178	36	ψ2	ψ2	NOUN
ejpam-6590	178	37	)	)	PUNCT
ejpam-6590	178	38	=	=	SYM
ejpam-6590	178	39	3	3	X
ejpam-6590	178	40	.	.	X
ejpam-6590	178	41	hence	hence	ADV
ejpam-6590	178	42	,	,	PUNCT
ejpam-6590	178	43	2	2	NUM
ejpam-6590	178	44	√	√	NUM
ejpam-6590	178	45	5	5	NUM
ejpam-6590	178	46	=	=	SYM
ejpam-6590	178	47	2r(ψ	2r(ψ	NUM
ejpam-6590	178	48	)	)	PUNCT
ejpam-6590	178	49	≤	≤	NUM
ejpam-6590	179	1	2r(ψ1	2r(ψ1	NUM
ejpam-6590	179	2	+	+	NUM
ejpam-6590	179	3	ψ2	ψ2	NOUN
ejpam-6590	179	4	)	)	PUNCT
ejpam-6590	179	5	=	=	SYM
ejpam-6590	179	6	6	6	NUM
ejpam-6590	179	7	as	as	SCONJ
ejpam-6590	179	8	it	it	PRON
ejpam-6590	179	9	was	be	AUX
ejpam-6590	179	10	concluded	conclude	VERB
ejpam-6590	179	11	by	by	ADP
ejpam-6590	179	12	theorem	theorem	NOUN
ejpam-6590	179	13	4	4	NUM
ejpam-6590	179	14	.	.	NOUN
ejpam-6590	179	15	4	4	NUM
ejpam-6590	179	16	.	.	X
ejpam-6590	179	17	conclusion	conclusion	VERB
ejpam-6590	179	18	new	new	ADJ
ejpam-6590	179	19	results	result	NOUN
ejpam-6590	179	20	for	for	ADP
ejpam-6590	179	21	spectral	spectral	ADJ
ejpam-6590	179	22	radius	radius	NOUN
ejpam-6590	179	23	of	of	ADP
ejpam-6590	179	24	2	2	NUM
ejpam-6590	179	25	×	×	NOUN
ejpam-6590	179	26	2	2	NUM
ejpam-6590	179	27	block	block	NOUN
ejpam-6590	179	28	matrices	matrix	NOUN
ejpam-6590	179	29	involving	involve	VERB
ejpam-6590	179	30	accretive	accretive	ADJ
ejpam-6590	179	31	-	-	PUNCT
ejpam-6590	179	32	dissipative	dissipative	ADJ
ejpam-6590	179	33	matrices	matrix	NOUN
ejpam-6590	179	34	were	be	AUX
ejpam-6590	179	35	discussed	discuss	VERB
ejpam-6590	179	36	and	and	CCONJ
ejpam-6590	179	37	proved	prove	VERB
ejpam-6590	179	38	,	,	PUNCT
ejpam-6590	179	39	also	also	ADV
ejpam-6590	179	40	an	an	DET
ejpam-6590	179	41	example	example	NOUN
ejpam-6590	179	42	is	be	AUX
ejpam-6590	179	43	given	give	VERB
ejpam-6590	179	44	.	.	PUNCT
ejpam-6590	180	1	m.	m.	NOUN
ejpam-6590	180	2	sakkijha	sakkijha	PROPN
ejpam-6590	180	3	,	,	PUNCT
ejpam-6590	180	4	s.	s.	PROPN
ejpam-6590	180	5	hasan	hasan	PROPN
ejpam-6590	180	6	,	,	PUNCT
ejpam-6590	180	7	m.	m.	NOUN
ejpam-6590	180	8	alholi	alholi	PROPN
ejpam-6590	180	9	/	/	SYM
ejpam-6590	180	10	eur	eur	PROPN
ejpam-6590	180	11	.	.	PUNCT
ejpam-6590	181	1	j.	j.	PROPN
ejpam-6590	181	2	pure	pure	PROPN
ejpam-6590	181	3	appl	appl	PROPN
ejpam-6590	181	4	.	.	PROPN
ejpam-6590	181	5	math	math	PROPN
ejpam-6590	181	6	,	,	PUNCT
ejpam-6590	181	7	18	18	NUM
ejpam-6590	181	8	(	(	PUNCT
ejpam-6590	181	9	3	3	NUM
ejpam-6590	181	10	)	)	PUNCT
ejpam-6590	181	11	(	(	PUNCT
ejpam-6590	181	12	2025	2025	NUM
ejpam-6590	181	13	)	)	PUNCT
ejpam-6590	181	14	,	,	PUNCT
ejpam-6590	181	15	6590	6590	NUM
ejpam-6590	181	16	9	9	NUM
ejpam-6590	181	17	of	of	ADP
ejpam-6590	181	18	9	9	NUM
ejpam-6590	181	19	in	in	ADP
ejpam-6590	181	20	future	future	NOUN
ejpam-6590	181	21	,	,	PUNCT
ejpam-6590	181	22	our	our	PRON
ejpam-6590	181	23	plan	plan	NOUN
ejpam-6590	181	24	is	be	AUX
ejpam-6590	181	25	going	go	VERB
ejpam-6590	181	26	to	to	PART
ejpam-6590	181	27	make	make	VERB
ejpam-6590	181	28	extension	extension	NOUN
ejpam-6590	181	29	of	of	ADP
ejpam-6590	181	30	our	our	PRON
ejpam-6590	181	31	inequalities	inequality	NOUN
ejpam-6590	181	32	for	for	ADP
ejpam-6590	181	33	accretive	accretive	ADJ
ejpam-6590	181	34	-	-	PUNCT
ejpam-6590	181	35	dissipative	dissipative	ADJ
ejpam-6590	181	36	matrices	matrix	NOUN
ejpam-6590	181	37	,	,	PUNCT
ejpam-6590	181	38	which	which	PRON
ejpam-6590	181	39	are	be	AUX
ejpam-6590	181	40	matrices	matrix	NOUN
ejpam-6590	181	41	whose	whose	DET
ejpam-6590	181	42	only	only	ADJ
ejpam-6590	181	43	real	real	ADJ
ejpam-6590	181	44	part	part	NOUN
ejpam-6590	181	45	is	be	AUX
ejpam-6590	181	46	p.s.d	p.s.d	NOUN
ejpam-6590	181	47	.	.	PUNCT
ejpam-6590	182	1	references	reference	NOUN
ejpam-6590	182	2	[	[	X
ejpam-6590	182	3	1	1	NUM
ejpam-6590	182	4	]	]	PUNCT
ejpam-6590	182	5	r.	r.	PROPN
ejpam-6590	182	6	bhatia	bhatia	PROPN
ejpam-6590	182	7	.	.	PUNCT
ejpam-6590	183	1	positive	positive	ADJ
ejpam-6590	183	2	definite	definite	ADJ
ejpam-6590	183	3	matrices	matrix	NOUN
ejpam-6590	183	4	.	.	PUNCT
ejpam-6590	184	1	princeton	princeton	PROPN
ejpam-6590	184	2	university	university	PROPN
ejpam-6590	184	3	press	press	NOUN
ejpam-6590	184	4	,	,	PUNCT
ejpam-6590	184	5	princeton	princeton	PROPN
ejpam-6590	184	6	and	and	CCONJ
ejpam-6590	184	7	oxford	oxford	PROPN
ejpam-6590	184	8	,	,	PUNCT
ejpam-6590	184	9	2007	2007	NUM
ejpam-6590	184	10	.	.	PUNCT
ejpam-6590	185	1	[	[	X
ejpam-6590	185	2	2	2	NUM
ejpam-6590	185	3	]	]	PUNCT
ejpam-6590	185	4	f.	f.	PROPN
ejpam-6590	185	5	kittaneh	kittaneh	PROPN
ejpam-6590	185	6	.	.	PUNCT
ejpam-6590	186	1	spectral	spectral	ADJ
ejpam-6590	186	2	radius	radius	NOUN
ejpam-6590	186	3	inequalities	inequality	NOUN
ejpam-6590	186	4	for	for	ADP
ejpam-6590	186	5	hilbert	hilbert	NOUN
ejpam-6590	186	6	space	space	NOUN
ejpam-6590	186	7	operators	operator	NOUN
ejpam-6590	186	8	.	.	PUNCT
ejpam-6590	187	1	proceedings	proceeding	NOUN
ejpam-6590	187	2	of	of	ADP
ejpam-6590	187	3	the	the	DET
ejpam-6590	187	4	american	american	PROPN
ejpam-6590	187	5	mathematical	mathematical	PROPN
ejpam-6590	187	6	society	society	NOUN
ejpam-6590	187	7	,	,	PUNCT
ejpam-6590	187	8	pages	page	NOUN
ejpam-6590	187	9	385–390	385–390	NUM
ejpam-6590	187	10	,	,	PUNCT
ejpam-6590	187	11	2006	2006	NUM
ejpam-6590	187	12	.	.	PUNCT
ejpam-6590	188	1	[	[	X
ejpam-6590	188	2	3	3	X
ejpam-6590	188	3	]	]	X
ejpam-6590	188	4	m.	m.	NOUN
ejpam-6590	188	5	el	el	PROPN
ejpam-6590	188	6	-	-	PROPN
ejpam-6590	188	7	haddad	haddad	PROPN
ejpam-6590	188	8	and	and	CCONJ
ejpam-6590	188	9	f.	f.	PROPN
ejpam-6590	188	10	kittaneh	kittaneh	PROPN
ejpam-6590	188	11	.	.	PUNCT
ejpam-6590	189	1	numerical	numerical	PROPN
ejpam-6590	189	2	radius	radius	PROPN
ejpam-6590	189	3	inequalities	inequality	NOUN
ejpam-6590	189	4	for	for	ADP
ejpam-6590	189	5	hilbert	hilbert	NOUN
ejpam-6590	189	6	space	space	NOUN
ejpam-6590	189	7	operators	operator	NOUN
ejpam-6590	189	8	.	.	PUNCT
ejpam-6590	190	1	ii	ii	PROPN
ejpam-6590	190	2	.	.	PUNCT
ejpam-6590	191	1	studia	studia	PROPN
ejpam-6590	191	2	mathematica	mathematica	PROPN
ejpam-6590	191	3	,	,	PUNCT
ejpam-6590	191	4	182:133–140	182:133–140	NUM
ejpam-6590	191	5	,	,	PUNCT
ejpam-6590	191	6	2007	2007	NUM
ejpam-6590	191	7	.	.	PUNCT
ejpam-6590	192	1	[	[	X
ejpam-6590	192	2	4	4	NUM
ejpam-6590	192	3	]	]	PUNCT
ejpam-6590	192	4	a.	a.	NOUN
ejpam-6590	192	5	abu	abu	PROPN
ejpam-6590	192	6	-	-	PUNCT
ejpam-6590	192	7	omar	omar	PROPN
ejpam-6590	192	8	and	and	CCONJ
ejpam-6590	192	9	f.	f.	PROPN
ejpam-6590	192	10	kittaneh	kittaneh	PROPN
ejpam-6590	192	11	.	.	PUNCT
ejpam-6590	193	1	notes	note	NOUN
ejpam-6590	193	2	on	on	ADP
ejpam-6590	193	3	some	some	DET
ejpam-6590	193	4	spectral	spectral	ADJ
ejpam-6590	193	5	radius	radius	NOUN
ejpam-6590	193	6	and	and	CCONJ
ejpam-6590	193	7	numerical	numerical	PROPN
ejpam-6590	193	8	radius	radius	PROPN
ejpam-6590	193	9	inequalities	inequality	NOUN
ejpam-6590	193	10	.	.	PUNCT
ejpam-6590	194	1	studia	studia	PROPN
ejpam-6590	194	2	mathematica	mathematica	PROPN
ejpam-6590	194	3	,	,	PUNCT
ejpam-6590	194	4	227:97–109	227:97–109	NUM
ejpam-6590	194	5	,	,	PUNCT
ejpam-6590	194	6	2015	2015	NUM
ejpam-6590	194	7	.	.	PUNCT
ejpam-6590	195	1	[	[	X
ejpam-6590	195	2	5	5	NUM
ejpam-6590	195	3	]	]	PUNCT
ejpam-6590	195	4	m.	m.	NOUN
ejpam-6590	195	5	sakkijha	sakkijha	PROPN
ejpam-6590	195	6	and	and	CCONJ
ejpam-6590	195	7	s.	s.	PROPN
ejpam-6590	195	8	hasan	hasan	PROPN
ejpam-6590	195	9	.	.	PUNCT
ejpam-6590	196	1	spectral	spectral	ADJ
ejpam-6590	196	2	radius	radius	NOUN
ejpam-6590	196	3	inequalities	inequality	NOUN
ejpam-6590	196	4	for	for	ADP
ejpam-6590	196	5	accretive	accretive	ADJ
ejpam-6590	196	6	-	-	PUNCT
ejpam-6590	196	7	dissipative	dissipative	ADJ
ejpam-6590	196	8	matrices	matrix	NOUN
ejpam-6590	196	9	.	.	PUNCT
ejpam-6590	197	1	international	international	ADJ
ejpam-6590	197	2	journal	journal	PROPN
ejpam-6590	197	3	of	of	ADP
ejpam-6590	197	4	neutrosophic	neutrosophic	ADJ
ejpam-6590	197	5	science	science	NOUN
ejpam-6590	197	6	(	(	PUNCT
ejpam-6590	197	7	ijns	ijns	PROPN
ejpam-6590	197	8	)	)	PUNCT
ejpam-6590	197	9	,	,	PUNCT
ejpam-6590	197	10	25(3	25(3	NUM
ejpam-6590	197	11	)	)	PUNCT
ejpam-6590	197	12	,	,	PUNCT
ejpam-6590	197	13	2025	2025	NUM
ejpam-6590	197	14	.	.	PUNCT
ejpam-6590	198	1	[	[	X
ejpam-6590	198	2	6	6	NUM
ejpam-6590	198	3	]	]	PUNCT
ejpam-6590	198	4	m.	m.	NOUN
ejpam-6590	198	5	d.	d.	PROPN
ejpam-6590	198	6	gunzburger	gunzburger	PROPN
ejpam-6590	198	7	and	and	CCONJ
ejpam-6590	198	8	r.	r.	PROPN
ejpam-6590	198	9	j.	j.	PROPN
ejpam-6590	198	10	plemmons	plemmons	PROPN
ejpam-6590	198	11	.	.	PUNCT
ejpam-6590	199	1	energy	energy	NOUN
ejpam-6590	199	2	-	-	PUNCT
ejpam-6590	199	3	conserving	conserve	VERB
ejpam-6590	199	4	norms	norm	NOUN
ejpam-6590	199	5	for	for	ADP
ejpam-6590	199	6	the	the	DET
ejpam-6590	199	7	solution	solution	NOUN
ejpam-6590	199	8	of	of	ADP
ejpam-6590	199	9	hyperbolic	hyperbolic	ADJ
ejpam-6590	199	10	systems	system	NOUN
ejpam-6590	199	11	of	of	ADP
ejpam-6590	199	12	partial	partial	ADJ
ejpam-6590	199	13	differential	differential	ADJ
ejpam-6590	199	14	equations	equation	NOUN
ejpam-6590	199	15	.	.	PUNCT
ejpam-6590	200	1	mathematics	mathematic	NOUN
ejpam-6590	200	2	of	of	ADP
ejpam-6590	200	3	computation	computation	NOUN
ejpam-6590	200	4	,	,	PUNCT
ejpam-6590	200	5	33(145):1–10	33(145):1–10	PROPN
ejpam-6590	200	6	,	,	PUNCT
ejpam-6590	200	7	1979	1979	NUM
ejpam-6590	200	8	.	.	PUNCT
ejpam-6590	201	1	[	[	X
ejpam-6590	201	2	7	7	X
ejpam-6590	201	3	]	]	PUNCT
ejpam-6590	201	4	a.	a.	NOUN
ejpam-6590	201	5	george	george	PROPN
ejpam-6590	201	6	and	and	CCONJ
ejpam-6590	201	7	k.	k.	PROPN
ejpam-6590	201	8	d.	d.	PROPN
ejpam-6590	201	9	ikramov	ikramov	PROPN
ejpam-6590	201	10	.	.	PUNCT
ejpam-6590	202	1	on	on	ADP
ejpam-6590	202	2	the	the	DET
ejpam-6590	202	3	properties	property	NOUN
ejpam-6590	202	4	of	of	ADP
ejpam-6590	202	5	accretive	accretive	ADJ
ejpam-6590	202	6	-	-	PUNCT
ejpam-6590	202	7	dissipative	dissipative	ADJ
ejpam-6590	202	8	matrices	matrix	NOUN
ejpam-6590	202	9	.	.	PUNCT
ejpam-6590	203	1	mathematical	mathematical	ADJ
ejpam-6590	203	2	notes	note	NOUN
ejpam-6590	203	3	,	,	PUNCT
ejpam-6590	203	4	77:767–776	77:767–776	PROPN
ejpam-6590	203	5	,	,	PUNCT
ejpam-6590	203	6	2005	2005	NUM
ejpam-6590	203	7	.	.	PUNCT
ejpam-6590	204	1	[	[	X
ejpam-6590	204	2	8	8	NUM
ejpam-6590	204	3	]	]	PUNCT
ejpam-6590	204	4	m.	m.	NOUN
ejpam-6590	204	5	sakkijha	sakkijha	PROPN
ejpam-6590	204	6	and	and	CCONJ
ejpam-6590	204	7	s.	s.	PROPN
ejpam-6590	204	8	hasan	hasan	PROPN
ejpam-6590	204	9	.	.	PUNCT
ejpam-6590	205	1	hadamard	hadamard	ADJ
ejpam-6590	205	2	determinant	determinant	ADJ
ejpam-6590	205	3	inequalities	inequality	NOUN
ejpam-6590	205	4	for	for	ADP
ejpam-6590	205	5	accretivedissipative	accretivedissipative	ADJ
ejpam-6590	205	6	matrices	matrix	NOUN
ejpam-6590	205	7	.	.	PUNCT
ejpam-6590	206	1	computer	computer	NOUN
ejpam-6590	206	2	science	science	NOUN
ejpam-6590	206	3	,	,	PUNCT
ejpam-6590	206	4	19(1):111–116	19(1):111–116	PROPN
ejpam-6590	206	5	,	,	PUNCT
ejpam-6590	206	6	2024	2024	NUM
ejpam-6590	206	7	.	.	PUNCT
ejpam-6590	207	1	[	[	X
ejpam-6590	207	2	9	9	NUM
ejpam-6590	207	3	]	]	PUNCT
ejpam-6590	207	4	r.	r.	PROPN
ejpam-6590	207	5	bhatia	bhatia	PROPN
ejpam-6590	207	6	and	and	CCONJ
ejpam-6590	207	7	f.	f.	PROPN
ejpam-6590	207	8	kittaneh	kittaneh	PROPN
ejpam-6590	207	9	.	.	PUNCT
ejpam-6590	208	1	the	the	DET
ejpam-6590	208	2	singular	singular	ADJ
ejpam-6590	208	3	values	value	NOUN
ejpam-6590	208	4	of	of	ADP
ejpam-6590	208	5	a	a	DET
ejpam-6590	208	6	+	+	NOUN
ejpam-6590	208	7	b	b	NOUN
ejpam-6590	208	8	and	and	CCONJ
ejpam-6590	208	9	a	a	DET
ejpam-6590	208	10	+	+	NOUN
ejpam-6590	208	11	ib	ib	NOUN
ejpam-6590	208	12	.	.	PUNCT
ejpam-6590	208	13	linear	linear	PROPN
ejpam-6590	208	14	algebra	algebra	PROPN
ejpam-6590	208	15	and	and	CCONJ
ejpam-6590	208	16	its	its	PRON
ejpam-6590	208	17	applications	application	NOUN
ejpam-6590	208	18	,	,	PUNCT
ejpam-6590	208	19	431(9):1502–1508	431(9):1502–1508	NOUN
ejpam-6590	208	20	,	,	PUNCT
ejpam-6590	208	21	2009	2009	NUM
ejpam-6590	208	22	.	.	PUNCT
ejpam-6590	209	1	[	[	X
ejpam-6590	209	2	10	10	NUM
ejpam-6590	209	3	]	]	X
ejpam-6590	209	4	f.	f.	PROPN
ejpam-6590	209	5	kittaneh	kittaneh	PROPN
ejpam-6590	209	6	.	.	PUNCT
ejpam-6590	210	1	norm	norm	NOUN
ejpam-6590	210	2	inequalities	inequality	NOUN
ejpam-6590	210	3	for	for	ADP
ejpam-6590	210	4	sums	sum	NOUN
ejpam-6590	210	5	and	and	CCONJ
ejpam-6590	210	6	differences	difference	NOUN
ejpam-6590	210	7	of	of	ADP
ejpam-6590	210	8	positive	positive	ADJ
ejpam-6590	210	9	operators	operator	NOUN
ejpam-6590	210	10	.	.	PUNCT
ejpam-6590	211	1	linear	linear	ADJ
ejpam-6590	211	2	algebra	algebra	NOUN
ejpam-6590	211	3	and	and	CCONJ
ejpam-6590	211	4	its	its	PRON
ejpam-6590	211	5	applications	application	NOUN
ejpam-6590	211	6	,	,	PUNCT
ejpam-6590	211	7	383:85–91	383:85–91	NUM
ejpam-6590	211	8	,	,	PUNCT
ejpam-6590	211	9	2004	2004	NUM
ejpam-6590	211	10	.	.	PUNCT
ejpam-6590	212	1	[	[	X
ejpam-6590	212	2	11	11	NUM
ejpam-6590	212	3	]	]	X
ejpam-6590	212	4	f.	f.	PROPN
ejpam-6590	212	5	kittaneh	kittaneh	PROPN
ejpam-6590	212	6	.	.	PUNCT
ejpam-6590	213	1	inequalities	inequality	NOUN
ejpam-6590	213	2	for	for	ADP
ejpam-6590	213	3	commutators	commutator	NOUN
ejpam-6590	213	4	of	of	ADP
ejpam-6590	213	5	positive	positive	ADJ
ejpam-6590	213	6	operators	operator	NOUN
ejpam-6590	213	7	.	.	PUNCT
ejpam-6590	214	1	journal	journal	NOUN
ejpam-6590	214	2	of	of	ADP
ejpam-6590	214	3	functional	functional	ADJ
ejpam-6590	214	4	analysis	analysis	NOUN
ejpam-6590	214	5	,	,	PUNCT
ejpam-6590	214	6	250(1):132–143	250(1):132–143	NUM
ejpam-6590	214	7	,	,	PUNCT
ejpam-6590	214	8	2007	2007	NUM
ejpam-6590	214	9	.	.	PUNCT
ejpam-6590	215	1	[	[	X
ejpam-6590	215	2	12	12	NUM
ejpam-6590	215	3	]	]	PUNCT
ejpam-6590	215	4	j.	j.	PROPN
ejpam-6590	215	5	c.	c.	PROPN
ejpam-6590	215	6	hou	hou	PROPN
ejpam-6590	215	7	and	and	CCONJ
ejpam-6590	215	8	h.	h.	PROPN
ejpam-6590	215	9	k.	k.	PROPN
ejpam-6590	215	10	du	du	PROPN
ejpam-6590	215	11	.	.	PROPN
ejpam-6590	216	1	norm	norm	PROPN
ejpam-6590	216	2	inequalities	inequality	NOUN
ejpam-6590	216	3	of	of	ADP
ejpam-6590	216	4	positive	positive	ADJ
ejpam-6590	216	5	operator	operator	NOUN
ejpam-6590	216	6	matrices	matrix	NOUN
ejpam-6590	216	7	.	.	PUNCT
ejpam-6590	217	1	integral	integral	ADJ
ejpam-6590	217	2	equations	equation	NOUN
ejpam-6590	217	3	and	and	CCONJ
ejpam-6590	217	4	operator	operator	NOUN
ejpam-6590	217	5	theory	theory	NOUN
ejpam-6590	217	6	,	,	PUNCT
ejpam-6590	217	7	22:281–294	22:281–294	NUM
ejpam-6590	217	8	,	,	PUNCT
ejpam-6590	217	9	1995	1995	NUM
ejpam-6590	217	10	.	.	PUNCT
ejpam-6590	218	1	[	[	X
ejpam-6590	218	2	13	13	NUM
ejpam-6590	218	3	]	]	PUNCT
ejpam-6590	218	4	r.	r.	PROPN
ejpam-6590	218	5	a.	a.	PROPN
ejpam-6590	218	6	horn	horn	PROPN
ejpam-6590	218	7	and	and	CCONJ
ejpam-6590	218	8	c.	c.	PROPN
ejpam-6590	218	9	r.	r.	PROPN
ejpam-6590	218	10	johnson	johnson	PROPN
ejpam-6590	218	11	.	.	PUNCT
ejpam-6590	219	1	topics	topic	NOUN
ejpam-6590	219	2	in	in	ADP
ejpam-6590	219	3	matrix	matrix	NOUN
ejpam-6590	219	4	analysis	analysis	NOUN
ejpam-6590	219	5	.	.	PUNCT
ejpam-6590	220	1	cambridge	cambridge	PROPN
ejpam-6590	220	2	university	university	PROPN
ejpam-6590	220	3	press	press	NOUN
ejpam-6590	220	4	,	,	PUNCT
ejpam-6590	220	5	1994	1994	NUM
ejpam-6590	220	6	.	.	PUNCT
ejpam-6590	221	1	[	[	X
ejpam-6590	221	2	14	14	NUM
ejpam-6590	221	3	]	]	PUNCT
ejpam-6590	221	4	t.	t.	PROPN
ejpam-6590	221	5	furuta	furuta	PROPN
ejpam-6590	221	6	.	.	PUNCT
ejpam-6590	222	1	norm	norm	NOUN
ejpam-6590	222	2	inequalities	inequality	NOUN
ejpam-6590	222	3	equivalent	equivalent	ADJ
ejpam-6590	222	4	to	to	ADP
ejpam-6590	222	5	loewner	loewner	NOUN
ejpam-6590	222	6	-	-	PUNCT
ejpam-6590	222	7	heinz	heinz	NOUN
ejpam-6590	222	8	theorem	theorem	NOUN
ejpam-6590	222	9	.	.	PUNCT
ejpam-6590	223	1	reviews	review	NOUN
ejpam-6590	223	2	in	in	ADP
ejpam-6590	223	3	mathematical	mathematical	ADJ
ejpam-6590	223	4	physics	physics	NOUN
ejpam-6590	223	5	,	,	PUNCT
ejpam-6590	223	6	1(1	1(1	NUM
ejpam-6590	223	7	)	)	PUNCT
ejpam-6590	223	8	,	,	PUNCT
ejpam-6590	223	9	1989	1989	NUM
ejpam-6590	223	10	.	.	PUNCT