id	sid	tid	token	lemma	pos
ejpam-6417	1	1	european	european	PROPN
ejpam-6417	1	2	journal	journal	PROPN
ejpam-6417	1	3	of	of	ADP
ejpam-6417	1	4	pure	pure	ADJ
ejpam-6417	1	5	and	and	CCONJ
ejpam-6417	1	6	applied	applied	ADJ
ejpam-6417	1	7	mathematics	mathematic	NOUN
ejpam-6417	1	8	2025	2025	NUM
ejpam-6417	1	9	,	,	PUNCT
ejpam-6417	1	10	vol	vol	NOUN
ejpam-6417	1	11	.	.	PROPN
ejpam-6417	1	12	18	18	NUM
ejpam-6417	1	13	,	,	PUNCT
ejpam-6417	1	14	issue	issue	NOUN
ejpam-6417	1	15	3	3	NUM
ejpam-6417	1	16	,	,	PUNCT
ejpam-6417	1	17	article	article	NOUN
ejpam-6417	1	18	number	number	NOUN
ejpam-6417	1	19	6417	6417	NUM
ejpam-6417	1	20	issn	issn	VERB
ejpam-6417	1	21	1307	1307	NUM
ejpam-6417	1	22	-	-	SYM
ejpam-6417	1	23	5543	5543	NUM
ejpam-6417	1	24	–	–	PUNCT
ejpam-6417	1	25	ejpam.com	ejpam.com	X
ejpam-6417	1	26	published	publish	VERB
ejpam-6417	1	27	by	by	ADP
ejpam-6417	1	28	new	new	PROPN
ejpam-6417	1	29	york	york	PROPN
ejpam-6417	1	30	business	business	PROPN
ejpam-6417	1	31	global	global	PROPN
ejpam-6417	1	32	a	a	DET
ejpam-6417	1	33	characterization	characterization	NOUN
ejpam-6417	1	34	of	of	ADP
ejpam-6417	1	35	diagonal	diagonal	ADJ
ejpam-6417	1	36	solutions	solution	NOUN
ejpam-6417	1	37	for	for	ADP
ejpam-6417	1	38	a	a	DET
ejpam-6417	1	39	class	class	NOUN
ejpam-6417	1	40	of	of	ADP
ejpam-6417	1	41	linear	linear	ADJ
ejpam-6417	1	42	matrix	matrix	NOUN
ejpam-6417	1	43	inequality	inequality	PROPN
ejpam-6417	1	44	ali	ali	PROPN
ejpam-6417	1	45	algefary1,∗	algefary1,∗	PROPN
ejpam-6417	1	46	,	,	PUNCT
ejpam-6417	1	47	tulin	tulin	PROPN
ejpam-6417	1	48	alhumaidan2	alhumaidan2	NOUN
ejpam-6417	1	49	1	1	NUM
ejpam-6417	1	50	department	department	NOUN
ejpam-6417	1	51	of	of	ADP
ejpam-6417	1	52	mathematics	mathematic	NOUN
ejpam-6417	1	53	,	,	PUNCT
ejpam-6417	1	54	college	college	NOUN
ejpam-6417	1	55	of	of	ADP
ejpam-6417	1	56	science	science	NOUN
ejpam-6417	1	57	,	,	PUNCT
ejpam-6417	1	58	qassim	qassim	PROPN
ejpam-6417	1	59	university	university	PROPN
ejpam-6417	1	60	,	,	PUNCT
ejpam-6417	1	61	p.o	p.o	PROPN
ejpam-6417	1	62	.	.	PROPN
ejpam-6417	1	63	box	box	PROPN
ejpam-6417	1	64	6644	6644	NUM
ejpam-6417	1	65	,	,	PUNCT
ejpam-6417	1	66	buraydah	buraydah	NOUN
ejpam-6417	1	67	51452	51452	NUM
ejpam-6417	1	68	,	,	PUNCT
ejpam-6417	1	69	saudi	saudi	PROPN
ejpam-6417	1	70	arabia	arabia	PROPN
ejpam-6417	1	71	2	2	NUM
ejpam-6417	1	72	department	department	NOUN
ejpam-6417	1	73	of	of	ADP
ejpam-6417	1	74	statistics	statistic	NOUN
ejpam-6417	1	75	and	and	CCONJ
ejpam-6417	1	76	operation	operation	NOUN
ejpam-6417	1	77	research	research	NOUN
ejpam-6417	1	78	,	,	PUNCT
ejpam-6417	1	79	college	college	NOUN
ejpam-6417	1	80	of	of	ADP
ejpam-6417	1	81	science	science	NOUN
ejpam-6417	1	82	,	,	PUNCT
ejpam-6417	1	83	qassim	qassim	PROPN
ejpam-6417	1	84	university	university	PROPN
ejpam-6417	1	85	,	,	PUNCT
ejpam-6417	1	86	p.o	p.o	PROPN
ejpam-6417	1	87	.	.	PROPN
ejpam-6417	1	88	box	box	PROPN
ejpam-6417	1	89	6644	6644	NUM
ejpam-6417	1	90	,	,	PUNCT
ejpam-6417	1	91	buraydah	buraydah	NOUN
ejpam-6417	1	92	51452	51452	NUM
ejpam-6417	1	93	,	,	PUNCT
ejpam-6417	1	94	saudi	saudi	PROPN
ejpam-6417	1	95	arabia	arabia	PROPN
ejpam-6417	1	96	abstract	abstract	NOUN
ejpam-6417	1	97	.	.	PUNCT
ejpam-6417	2	1	this	this	DET
ejpam-6417	2	2	paper	paper	NOUN
ejpam-6417	2	3	investigates	investigate	VERB
ejpam-6417	2	4	the	the	DET
ejpam-6417	2	5	existence	existence	NOUN
ejpam-6417	2	6	of	of	ADP
ejpam-6417	2	7	positive	positive	ADJ
ejpam-6417	2	8	diagonal	diagonal	ADJ
ejpam-6417	2	9	solutions	solution	NOUN
ejpam-6417	2	10	for	for	ADP
ejpam-6417	2	11	a	a	DET
ejpam-6417	2	12	class	class	NOUN
ejpam-6417	2	13	of	of	ADP
ejpam-6417	2	14	linear	linear	ADJ
ejpam-6417	2	15	matrix	matrix	NOUN
ejpam-6417	2	16	inequalities	inequality	NOUN
ejpam-6417	2	17	(	(	PUNCT
ejpam-6417	2	18	lmis	lmis	ADJ
ejpam-6417	2	19	)	)	PUNCT
ejpam-6417	2	20	involving	involve	VERB
ejpam-6417	2	21	a	a	DET
ejpam-6417	2	22	triple	triple	NOUN
ejpam-6417	2	23	of	of	ADP
ejpam-6417	2	24	real	real	ADJ
ejpam-6417	2	25	n	n	NUM
ejpam-6417	2	26	×	×	NOUN
ejpam-6417	2	27	n	n	PRON
ejpam-6417	2	28	matrices	matrix	NOUN
ejpam-6417	2	29	(	(	PUNCT
ejpam-6417	2	30	a1	a1	NOUN
ejpam-6417	2	31	,	,	PUNCT
ejpam-6417	2	32	a2	a2	PROPN
ejpam-6417	2	33	,	,	PUNCT
ejpam-6417	2	34	a3	a3	NOUN
ejpam-6417	2	35	)	)	PUNCT
ejpam-6417	2	36	.	.	PUNCT
ejpam-6417	3	1	we	we	PRON
ejpam-6417	3	2	provide	provide	VERB
ejpam-6417	3	3	equivalent	equivalent	ADJ
ejpam-6417	3	4	conditions	condition	NOUN
ejpam-6417	3	5	linking	link	VERB
ejpam-6417	3	6	the	the	DET
ejpam-6417	3	7	negative	negative	ADJ
ejpam-6417	3	8	definiteness	definiteness	NOUN
ejpam-6417	3	9	of	of	ADP
ejpam-6417	3	10	a	a	DET
ejpam-6417	3	11	structured	structured	ADJ
ejpam-6417	3	12	block	block	NOUN
ejpam-6417	3	13	matrix	matrix	NOUN
ejpam-6417	3	14	to	to	ADP
ejpam-6417	3	15	properties	property	NOUN
ejpam-6417	3	16	of	of	ADP
ejpam-6417	3	17	positive	positive	ADJ
ejpam-6417	3	18	semidefinite	semidefinite	NOUN
ejpam-6417	3	19	test	test	NOUN
ejpam-6417	3	20	matrices	matrix	NOUN
ejpam-6417	3	21	and	and	CCONJ
ejpam-6417	3	22	p	p	NOUN
ejpam-6417	3	23	-matrices	-matrice	NOUN
ejpam-6417	3	24	under	under	ADP
ejpam-6417	3	25	hadamard	hadamard	ADJ
ejpam-6417	3	26	transformations	transformation	NOUN
ejpam-6417	3	27	.	.	PUNCT
ejpam-6417	4	1	our	our	PRON
ejpam-6417	4	2	results	result	NOUN
ejpam-6417	4	3	extend	extend	VERB
ejpam-6417	4	4	classical	classical	ADJ
ejpam-6417	4	5	stability	stability	NOUN
ejpam-6417	4	6	results	result	NOUN
ejpam-6417	4	7	to	to	ADP
ejpam-6417	4	8	multi	multi	ADJ
ejpam-6417	4	9	-	-	ADJ
ejpam-6417	4	10	matrix	matrix	ADJ
ejpam-6417	4	11	settings	setting	NOUN
ejpam-6417	4	12	with	with	ADP
ejpam-6417	4	13	applications	application	NOUN
ejpam-6417	4	14	to	to	PART
ejpam-6417	4	15	control	control	VERB
ejpam-6417	4	16	theory	theory	NOUN
ejpam-6417	4	17	and	and	CCONJ
ejpam-6417	4	18	network	network	NOUN
ejpam-6417	4	19	dynamics	dynamic	NOUN
ejpam-6417	4	20	.	.	PUNCT
ejpam-6417	5	1	2020	2020	NUM
ejpam-6417	5	2	mathematics	mathematic	NOUN
ejpam-6417	5	3	subject	subject	NOUN
ejpam-6417	5	4	classifications	classification	NOUN
ejpam-6417	5	5	:	:	PUNCT
ejpam-6417	5	6	15a45	15a45	NUM
ejpam-6417	5	7	,	,	PUNCT
ejpam-6417	5	8	15b48	15b48	NUM
ejpam-6417	5	9	,	,	PUNCT
ejpam-6417	5	10	93d05	93d05	NUM
ejpam-6417	5	11	,	,	PUNCT
ejpam-6417	5	12	34k25	34k25	NUM
ejpam-6417	5	13	,	,	PUNCT
ejpam-6417	5	14	34k05	34k05	PRON
ejpam-6417	5	15	key	key	ADJ
ejpam-6417	5	16	words	word	NOUN
ejpam-6417	5	17	and	and	CCONJ
ejpam-6417	5	18	phrases	phrase	NOUN
ejpam-6417	5	19	:	:	PUNCT
ejpam-6417	5	20	diagonal	diagonal	ADJ
ejpam-6417	5	21	matrices	matrix	NOUN
ejpam-6417	5	22	,	,	PUNCT
ejpam-6417	5	23	p	p	PROPN
ejpam-6417	5	24	-matrix	-matrix	NOUN
ejpam-6417	5	25	,	,	PUNCT
ejpam-6417	5	26	positive	positive	ADJ
ejpam-6417	5	27	definite	definite	ADJ
ejpam-6417	5	28	matrix	matrix	NOUN
ejpam-6417	5	29	,	,	PUNCT
ejpam-6417	5	30	matrix	matrix	NOUN
ejpam-6417	5	31	inequality	inequality	NOUN
ejpam-6417	5	32	,	,	PUNCT
ejpam-6417	5	33	matrix	matrix	NOUN
ejpam-6417	5	34	stability	stability	NOUN
ejpam-6417	5	35	1	1	NUM
ejpam-6417	5	36	.	.	PUNCT
ejpam-6417	5	37	introduction	introduction	NOUN
ejpam-6417	5	38	linear	linear	PROPN
ejpam-6417	5	39	matrix	matrix	NOUN
ejpam-6417	5	40	inequalities	inequality	NOUN
ejpam-6417	5	41	(	(	PUNCT
ejpam-6417	5	42	lmis	lmis	ADJ
ejpam-6417	5	43	)	)	PUNCT
ejpam-6417	5	44	play	play	VERB
ejpam-6417	5	45	a	a	DET
ejpam-6417	5	46	fundamental	fundamental	ADJ
ejpam-6417	5	47	role	role	NOUN
ejpam-6417	5	48	in	in	ADP
ejpam-6417	5	49	various	various	ADJ
ejpam-6417	5	50	fields	field	NOUN
ejpam-6417	5	51	of	of	ADP
ejpam-6417	5	52	applied	applied	ADJ
ejpam-6417	5	53	mathematics	mathematic	NOUN
ejpam-6417	5	54	,	,	PUNCT
ejpam-6417	5	55	including	include	VERB
ejpam-6417	5	56	control	control	NOUN
ejpam-6417	5	57	theory	theory	NOUN
ejpam-6417	5	58	[	[	X
ejpam-6417	5	59	1–3	1–3	NOUN
ejpam-6417	5	60	]	]	X
ejpam-6417	5	61	,	,	PUNCT
ejpam-6417	5	62	optimization	optimization	NOUN
ejpam-6417	5	63	[	[	X
ejpam-6417	5	64	4	4	NUM
ejpam-6417	5	65	]	]	PUNCT
ejpam-6417	5	66	,	,	PUNCT
ejpam-6417	5	67	and	and	CCONJ
ejpam-6417	5	68	stability	stability	NOUN
ejpam-6417	5	69	analysis	analysis	NOUN
ejpam-6417	5	70	of	of	ADP
ejpam-6417	5	71	dynamical	dynamical	ADJ
ejpam-6417	5	72	systems	system	NOUN
ejpam-6417	5	73	[	[	X
ejpam-6417	5	74	5	5	NUM
ejpam-6417	5	75	]	]	PUNCT
ejpam-6417	5	76	.	.	PUNCT
ejpam-6417	6	1	these	these	DET
ejpam-6417	6	2	inequalities	inequality	NOUN
ejpam-6417	6	3	often	often	ADV
ejpam-6417	6	4	arise	arise	VERB
ejpam-6417	6	5	in	in	ADP
ejpam-6417	6	6	the	the	DET
ejpam-6417	6	7	study	study	NOUN
ejpam-6417	6	8	of	of	ADP
ejpam-6417	6	9	matrix	matrix	NOUN
ejpam-6417	6	10	stability	stability	NOUN
ejpam-6417	6	11	properties	property	NOUN
ejpam-6417	6	12	,	,	PUNCT
ejpam-6417	6	13	such	such	ADJ
ejpam-6417	6	14	as	as	ADP
ejpam-6417	6	15	lyapunov	lyapunov	ADJ
ejpam-6417	6	16	stability	stability	NOUN
ejpam-6417	6	17	,	,	PUNCT
ejpam-6417	6	18	and	and	CCONJ
ejpam-6417	6	19	are	be	AUX
ejpam-6417	6	20	instrumental	instrumental	ADJ
ejpam-6417	6	21	in	in	ADP
ejpam-6417	6	22	characterizing	characterize	VERB
ejpam-6417	6	23	the	the	DET
ejpam-6417	6	24	behavior	behavior	NOUN
ejpam-6417	6	25	of	of	ADP
ejpam-6417	6	26	complex	complex	ADJ
ejpam-6417	6	27	systems	system	NOUN
ejpam-6417	6	28	.	.	PUNCT
ejpam-6417	7	1	a	a	DET
ejpam-6417	7	2	particularly	particularly	ADV
ejpam-6417	7	3	interesting	interesting	ADJ
ejpam-6417	7	4	and	and	CCONJ
ejpam-6417	7	5	challenging	challenging	ADJ
ejpam-6417	7	6	problem	problem	NOUN
ejpam-6417	7	7	within	within	ADP
ejpam-6417	7	8	this	this	DET
ejpam-6417	7	9	domain	domain	NOUN
ejpam-6417	7	10	is	be	AUX
ejpam-6417	7	11	the	the	DET
ejpam-6417	7	12	identification	identification	NOUN
ejpam-6417	7	13	of	of	ADP
ejpam-6417	7	14	diagonal	diagonal	ADJ
ejpam-6417	7	15	solutions	solution	NOUN
ejpam-6417	7	16	—	—	PUNCT
ejpam-6417	7	17	specifically	specifically	ADV
ejpam-6417	7	18	,	,	PUNCT
ejpam-6417	7	19	positive	positive	ADJ
ejpam-6417	7	20	diagonal	diagonal	ADJ
ejpam-6417	7	21	matrices	matrix	NOUN
ejpam-6417	7	22	—	—	PUNCT
ejpam-6417	7	23	that	that	PRON
ejpam-6417	7	24	satisfy	satisfy	VERB
ejpam-6417	7	25	certain	certain	ADJ
ejpam-6417	7	26	lmis	lmis	ADJ
ejpam-6417	7	27	.	.	PUNCT
ejpam-6417	8	1	such	such	ADJ
ejpam-6417	8	2	solutions	solution	NOUN
ejpam-6417	8	3	are	be	AUX
ejpam-6417	8	4	not	not	PART
ejpam-6417	8	5	only	only	ADV
ejpam-6417	8	6	mathematically	mathematically	ADV
ejpam-6417	8	7	intriguing	intriguing	ADJ
ejpam-6417	8	8	but	but	CCONJ
ejpam-6417	8	9	also	also	ADV
ejpam-6417	8	10	have	have	VERB
ejpam-6417	8	11	practical	practical	ADJ
ejpam-6417	8	12	implications	implication	NOUN
ejpam-6417	8	13	in	in	ADP
ejpam-6417	8	14	areas	area	NOUN
ejpam-6417	8	15	such	such	ADJ
ejpam-6417	8	16	as	as	ADP
ejpam-6417	8	17	network	network	NOUN
ejpam-6417	8	18	control	control	NOUN
ejpam-6417	8	19	[	[	X
ejpam-6417	8	20	6	6	NUM
ejpam-6417	8	21	,	,	PUNCT
ejpam-6417	8	22	7	7	NUM
ejpam-6417	8	23	]	]	PUNCT
ejpam-6417	8	24	and	and	CCONJ
ejpam-6417	8	25	evolutionary	evolutionary	ADJ
ejpam-6417	8	26	dynamics	dynamic	NOUN
ejpam-6417	8	27	[	[	X
ejpam-6417	8	28	8	8	NUM
ejpam-6417	8	29	]	]	PUNCT
ejpam-6417	8	30	.	.	PUNCT
ejpam-6417	9	1	lyapunov	lyapunov	ADJ
ejpam-6417	9	2	stability	stability	NOUN
ejpam-6417	9	3	is	be	AUX
ejpam-6417	9	4	a	a	DET
ejpam-6417	9	5	cornerstone	cornerstone	NOUN
ejpam-6417	9	6	of	of	ADP
ejpam-6417	9	7	dynamical	dynamical	ADJ
ejpam-6417	9	8	systems	system	NOUN
ejpam-6417	9	9	theory	theory	NOUN
ejpam-6417	9	10	,	,	PUNCT
ejpam-6417	9	11	providing	provide	VERB
ejpam-6417	9	12	a	a	DET
ejpam-6417	9	13	framework	framework	NOUN
ejpam-6417	9	14	to	to	PART
ejpam-6417	9	15	assess	assess	VERB
ejpam-6417	9	16	the	the	DET
ejpam-6417	9	17	stability	stability	NOUN
ejpam-6417	9	18	of	of	ADP
ejpam-6417	9	19	equilibrium	equilibrium	NOUN
ejpam-6417	9	20	points	point	NOUN
ejpam-6417	9	21	without	without	ADP
ejpam-6417	9	22	explicitly	explicitly	ADV
ejpam-6417	9	23	solving	solve	VERB
ejpam-6417	9	24	differential	differential	ADJ
ejpam-6417	9	25	equations	equation	NOUN
ejpam-6417	9	26	[	[	X
ejpam-6417	9	27	5	5	NUM
ejpam-6417	9	28	,	,	PUNCT
ejpam-6417	9	29	9	9	NUM
ejpam-6417	9	30	]	]	PUNCT
ejpam-6417	9	31	.	.	PUNCT
ejpam-6417	10	1	for	for	ADP
ejpam-6417	10	2	a	a	DET
ejpam-6417	10	3	linear	linear	ADJ
ejpam-6417	10	4	system	system	NOUN
ejpam-6417	10	5	ẋ	ẋ	PUNCT
ejpam-6417	10	6	=	=	PUNCT
ejpam-6417	10	7	ax	ax	NOUN
ejpam-6417	10	8	,	,	PUNCT
ejpam-6417	10	9	where	where	SCONJ
ejpam-6417	10	10	a	a	DET
ejpam-6417	10	11	∈	∈	ADJ
ejpam-6417	10	12	rn×n	rn×n	NOUN
ejpam-6417	10	13	,	,	PUNCT
ejpam-6417	10	14	the	the	DET
ejpam-6417	10	15	system	system	NOUN
ejpam-6417	10	16	is	be	AUX
ejpam-6417	10	17	said	say	VERB
ejpam-6417	10	18	to	to	PART
ejpam-6417	10	19	be	be	AUX
ejpam-6417	10	20	lyapunov	lyapunov	ADJ
ejpam-6417	10	21	stable	stable	ADJ
ejpam-6417	10	22	if	if	SCONJ
ejpam-6417	10	23	there	there	PRON
ejpam-6417	10	24	exists	exist	VERB
ejpam-6417	10	25	a	a	DET
ejpam-6417	10	26	symmetric	symmetric	ADJ
ejpam-6417	10	27	positive	positive	ADJ
ejpam-6417	10	28	definite	definite	ADJ
ejpam-6417	10	29	matrix	matrix	NOUN
ejpam-6417	10	30	p	p	X
ejpam-6417	10	31	≻	≻	PROPN
ejpam-6417	10	32	0	0	NUM
ejpam-6417	10	33	such	such	ADJ
ejpam-6417	10	34	that	that	SCONJ
ejpam-6417	10	35	the	the	DET
ejpam-6417	10	36	∗corresponding	∗corresponde	VERB
ejpam-6417	10	37	author	author	NOUN
ejpam-6417	10	38	.	.	PUNCT
ejpam-6417	11	1	doi	doi	NOUN
ejpam-6417	11	2	:	:	PUNCT
ejpam-6417	11	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6417	https://doi.org/10.29020/nybg.ejpam.v18i3.6417	DET
ejpam-6417	11	4	email	email	NOUN
ejpam-6417	11	5	addresses	address	VERB
ejpam-6417	11	6	:	:	PUNCT
ejpam-6417	11	7	a.algefary@qu.edu.sa	a.algefary@qu.edu.sa	PROPN
ejpam-6417	11	8	(	(	PUNCT
ejpam-6417	11	9	a.	a.	NOUN
ejpam-6417	11	10	algefary	algefary	ADJ
ejpam-6417	11	11	)	)	PUNCT
ejpam-6417	11	12	,	,	PUNCT
ejpam-6417	11	13	432206678@qu.edu.sa	432206678@qu.edu.sa	NOUN
ejpam-6417	11	14	(	(	PUNCT
ejpam-6417	11	15	t.	t.	PROPN
ejpam-6417	11	16	alhumaidan	alhumaidan	PROPN
ejpam-6417	11	17	)	)	PUNCT
ejpam-6417	11	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6417	11	19	1	1	NUM
ejpam-6417	11	20	copyright	copyright	NOUN
ejpam-6417	11	21	:	:	PUNCT
ejpam-6417	12	1	©	©	PROPN
ejpam-6417	12	2	2025	2025	NUM
ejpam-6417	12	3	the	the	DET
ejpam-6417	12	4	author(s	author(s	NOUN
ejpam-6417	12	5	)	)	PUNCT
ejpam-6417	12	6	.	.	PUNCT
ejpam-6417	13	1	(	(	PUNCT
ejpam-6417	13	2	cc	cc	NOUN
ejpam-6417	13	3	by	by	ADP
ejpam-6417	13	4	-	-	PUNCT
ejpam-6417	13	5	nc	nc	PROPN
ejpam-6417	13	6	4.0	4.0	NUM
ejpam-6417	13	7	)	)	PUNCT
ejpam-6417	13	8	a.	a.	NOUN
ejpam-6417	13	9	algefary	algefary	ADJ
ejpam-6417	13	10	,	,	PUNCT
ejpam-6417	13	11	t.	t.	PROPN
ejpam-6417	13	12	alhumaidan	alhumaidan	PROPN
ejpam-6417	13	13	/	/	SYM
ejpam-6417	13	14	eur	eur	PROPN
ejpam-6417	13	15	.	.	PUNCT
ejpam-6417	14	1	j.	j.	PROPN
ejpam-6417	14	2	pure	pure	PROPN
ejpam-6417	14	3	appl	appl	PROPN
ejpam-6417	14	4	.	.	PROPN
ejpam-6417	14	5	math	math	PROPN
ejpam-6417	14	6	,	,	PUNCT
ejpam-6417	14	7	18	18	NUM
ejpam-6417	14	8	(	(	PUNCT
ejpam-6417	14	9	3	3	NUM
ejpam-6417	14	10	)	)	PUNCT
ejpam-6417	14	11	(	(	PUNCT
ejpam-6417	14	12	2025	2025	NUM
ejpam-6417	14	13	)	)	PUNCT
ejpam-6417	14	14	,	,	PUNCT
ejpam-6417	14	15	6417	6417	NUM
ejpam-6417	14	16	2	2	NUM
ejpam-6417	14	17	of	of	ADP
ejpam-6417	14	18	10	10	NUM
ejpam-6417	14	19	lyapunov	lyapunov	ADJ
ejpam-6417	14	20	inequality	inequality	NOUN
ejpam-6417	14	21	atp+pa	atp+pa	NOUN
ejpam-6417	14	22	≺	≺	NOUN
ejpam-6417	14	23	0	0	NUM
ejpam-6417	14	24	holds	hold	NOUN
ejpam-6417	14	25	,	,	PUNCT
ejpam-6417	14	26	ensuring	ensure	VERB
ejpam-6417	14	27	that	that	SCONJ
ejpam-6417	14	28	the	the	DET
ejpam-6417	14	29	quadratic	quadratic	ADJ
ejpam-6417	14	30	form	form	NOUN
ejpam-6417	14	31	v	v	NOUN
ejpam-6417	14	32	(	(	PUNCT
ejpam-6417	14	33	x	x	NOUN
ejpam-6417	14	34	)	)	PUNCT
ejpam-6417	14	35	=	=	PUNCT
ejpam-6417	14	36	xtpx	xtpx	PROPN
ejpam-6417	14	37	serves	serve	VERB
ejpam-6417	14	38	as	as	ADP
ejpam-6417	14	39	a	a	DET
ejpam-6417	14	40	lyapunov	lyapunov	NOUN
ejpam-6417	14	41	function	function	NOUN
ejpam-6417	14	42	whose	whose	DET
ejpam-6417	14	43	time	time	NOUN
ejpam-6417	14	44	derivative	derivative	ADJ
ejpam-6417	14	45	is	be	AUX
ejpam-6417	14	46	negative	negative	ADJ
ejpam-6417	14	47	definite	definite	ADJ
ejpam-6417	14	48	along	along	ADP
ejpam-6417	14	49	system	system	NOUN
ejpam-6417	14	50	trajectories	trajectory	NOUN
ejpam-6417	14	51	[	[	X
ejpam-6417	14	52	1	1	NUM
ejpam-6417	14	53	]	]	PUNCT
ejpam-6417	14	54	.	.	PUNCT
ejpam-6417	15	1	this	this	DET
ejpam-6417	15	2	condition	condition	NOUN
ejpam-6417	15	3	guarantees	guarantee	VERB
ejpam-6417	15	4	asymptotic	asymptotic	ADJ
ejpam-6417	15	5	stability	stability	NOUN
ejpam-6417	15	6	,	,	PUNCT
ejpam-6417	15	7	meaning	mean	VERB
ejpam-6417	15	8	solutions	solution	NOUN
ejpam-6417	15	9	converge	converge	VERB
ejpam-6417	15	10	to	to	ADP
ejpam-6417	15	11	the	the	DET
ejpam-6417	15	12	origin	origin	NOUN
ejpam-6417	15	13	as	as	SCONJ
ejpam-6417	15	14	time	time	NOUN
ejpam-6417	15	15	progresses	progress	VERB
ejpam-6417	15	16	.	.	PUNCT
ejpam-6417	16	1	a	a	DET
ejpam-6417	16	2	related	related	ADJ
ejpam-6417	16	3	and	and	CCONJ
ejpam-6417	16	4	more	more	ADV
ejpam-6417	16	5	specific	specific	ADJ
ejpam-6417	16	6	concept	concept	NOUN
ejpam-6417	16	7	,	,	PUNCT
ejpam-6417	16	8	lyapunov	lyapunov	PROPN
ejpam-6417	16	9	diagonal	diagonal	ADJ
ejpam-6417	16	10	stability	stability	NOUN
ejpam-6417	16	11	,	,	PUNCT
ejpam-6417	16	12	applies	apply	VERB
ejpam-6417	16	13	when	when	SCONJ
ejpam-6417	16	14	such	such	DET
ejpam-6417	16	15	a	a	DET
ejpam-6417	16	16	p	p	NOUN
ejpam-6417	16	17	can	can	AUX
ejpam-6417	16	18	be	be	AUX
ejpam-6417	16	19	chosen	choose	VERB
ejpam-6417	16	20	as	as	ADP
ejpam-6417	16	21	a	a	DET
ejpam-6417	16	22	positive	positive	ADJ
ejpam-6417	16	23	diagonal	diagonal	ADJ
ejpam-6417	16	24	matrix	matrix	NOUN
ejpam-6417	16	25	[	[	X
ejpam-6417	16	26	10	10	NUM
ejpam-6417	16	27	]	]	PUNCT
ejpam-6417	16	28	.	.	PUNCT
ejpam-6417	17	1	this	this	DET
ejpam-6417	17	2	property	property	NOUN
ejpam-6417	17	3	is	be	AUX
ejpam-6417	17	4	particularly	particularly	ADV
ejpam-6417	17	5	significant	significant	ADJ
ejpam-6417	17	6	in	in	ADP
ejpam-6417	17	7	the	the	DET
ejpam-6417	17	8	context	context	NOUN
ejpam-6417	17	9	of	of	ADP
ejpam-6417	17	10	linear	linear	ADJ
ejpam-6417	17	11	matrix	matrix	NOUN
ejpam-6417	17	12	inequalities	inequality	NOUN
ejpam-6417	17	13	(	(	PUNCT
ejpam-6417	17	14	lmis	lmis	ADJ
ejpam-6417	17	15	)	)	PUNCT
ejpam-6417	17	16	,	,	PUNCT
ejpam-6417	17	17	as	as	SCONJ
ejpam-6417	17	18	it	it	PRON
ejpam-6417	17	19	imposes	impose	VERB
ejpam-6417	17	20	a	a	DET
ejpam-6417	17	21	structured	structured	ADJ
ejpam-6417	17	22	constraint	constraint	NOUN
ejpam-6417	17	23	on	on	ADP
ejpam-6417	17	24	the	the	DET
ejpam-6417	17	25	solution	solution	NOUN
ejpam-6417	17	26	space	space	NOUN
ejpam-6417	17	27	,	,	PUNCT
ejpam-6417	17	28	linking	link	VERB
ejpam-6417	17	29	stability	stability	NOUN
ejpam-6417	17	30	to	to	ADP
ejpam-6417	17	31	the	the	DET
ejpam-6417	17	32	existence	existence	NOUN
ejpam-6417	17	33	of	of	ADP
ejpam-6417	17	34	diagonal	diagonal	ADJ
ejpam-6417	17	35	matrices	matrix	NOUN
ejpam-6417	17	36	that	that	PRON
ejpam-6417	17	37	satisfy	satisfy	VERB
ejpam-6417	17	38	inequalities	inequality	NOUN
ejpam-6417	17	39	like	like	ADP
ejpam-6417	17	40	those	those	PRON
ejpam-6417	17	41	studied	study	VERB
ejpam-6417	17	42	in	in	ADP
ejpam-6417	17	43	this	this	DET
ejpam-6417	17	44	work	work	NOUN
ejpam-6417	17	45	.	.	PUNCT
ejpam-6417	18	1	for	for	ADP
ejpam-6417	18	2	a	a	DET
ejpam-6417	18	3	matrix	matrix	NOUN
ejpam-6417	18	4	a	a	PRON
ejpam-6417	18	5	to	to	PART
ejpam-6417	18	6	be	be	AUX
ejpam-6417	18	7	lyapunov	lyapunov	NOUN
ejpam-6417	18	8	diagonally	diagonally	ADV
ejpam-6417	18	9	stable	stable	ADJ
ejpam-6417	18	10	,	,	PUNCT
ejpam-6417	18	11	−a	−a	NOUN
ejpam-6417	18	12	must	must	AUX
ejpam-6417	18	13	often	often	ADV
ejpam-6417	18	14	exhibit	exhibit	VERB
ejpam-6417	18	15	properties	property	NOUN
ejpam-6417	18	16	such	such	ADJ
ejpam-6417	18	17	as	as	ADP
ejpam-6417	18	18	being	be	AUX
ejpam-6417	18	19	a	a	DET
ejpam-6417	18	20	p	p	NOUN
ejpam-6417	18	21	-matrix	-matrix	NOUN
ejpam-6417	19	1	[	[	X
ejpam-6417	19	2	11	11	NUM
ejpam-6417	19	3	,	,	PUNCT
ejpam-6417	19	4	12	12	NUM
ejpam-6417	19	5	]	]	PUNCT
ejpam-6417	19	6	,	,	PUNCT
ejpam-6417	19	7	a	a	DET
ejpam-6417	19	8	connection	connection	NOUN
ejpam-6417	19	9	that	that	PRON
ejpam-6417	19	10	underpins	underpin	VERB
ejpam-6417	19	11	our	our	PRON
ejpam-6417	19	12	analysis	analysis	NOUN
ejpam-6417	19	13	of	of	ADP
ejpam-6417	19	14	diagonal	diagonal	ADJ
ejpam-6417	19	15	solutions	solution	NOUN
ejpam-6417	19	16	for	for	ADP
ejpam-6417	19	17	the	the	DET
ejpam-6417	19	18	triple	triple	ADJ
ejpam-6417	19	19	(	(	PUNCT
ejpam-6417	19	20	a1	a1	NOUN
ejpam-6417	19	21	,	,	PUNCT
ejpam-6417	19	22	a2	a2	PROPN
ejpam-6417	19	23	,	,	PUNCT
ejpam-6417	19	24	a3	a3	NOUN
ejpam-6417	19	25	)	)	PUNCT
ejpam-6417	19	26	.	.	PUNCT
ejpam-6417	20	1	the	the	DET
ejpam-6417	20	2	importance	importance	NOUN
ejpam-6417	20	3	of	of	ADP
ejpam-6417	20	4	lyapunov	lyapunov	ADJ
ejpam-6417	20	5	diagonal	diagonal	ADJ
ejpam-6417	20	6	stability	stability	NOUN
ejpam-6417	20	7	extends	extend	VERB
ejpam-6417	20	8	beyond	beyond	ADP
ejpam-6417	20	9	theoretical	theoretical	ADJ
ejpam-6417	20	10	elegance	elegance	NOUN
ejpam-6417	20	11	;	;	PUNCT
ejpam-6417	20	12	it	it	PRON
ejpam-6417	20	13	arises	arise	VERB
ejpam-6417	20	14	naturally	naturally	ADV
ejpam-6417	20	15	in	in	ADP
ejpam-6417	20	16	applications	application	NOUN
ejpam-6417	20	17	where	where	SCONJ
ejpam-6417	20	18	system	system	NOUN
ejpam-6417	20	19	matrices	matrix	NOUN
ejpam-6417	20	20	possess	possess	VERB
ejpam-6417	20	21	inherent	inherent	ADJ
ejpam-6417	20	22	structural	structural	ADJ
ejpam-6417	20	23	properties	property	NOUN
ejpam-6417	20	24	,	,	PUNCT
ejpam-6417	20	25	such	such	ADJ
ejpam-6417	20	26	as	as	ADP
ejpam-6417	20	27	in	in	ADP
ejpam-6417	20	28	networked	networked	ADJ
ejpam-6417	20	29	control	control	NOUN
ejpam-6417	20	30	systems	system	NOUN
ejpam-6417	20	31	[	[	X
ejpam-6417	20	32	6	6	NUM
ejpam-6417	20	33	,	,	PUNCT
ejpam-6417	20	34	13	13	NUM
ejpam-6417	20	35	]	]	PUNCT
ejpam-6417	20	36	or	or	CCONJ
ejpam-6417	20	37	compartmental	compartmental	ADJ
ejpam-6417	20	38	models	model	NOUN
ejpam-6417	20	39	in	in	ADP
ejpam-6417	20	40	biology	biology	NOUN
ejpam-6417	20	41	[	[	X
ejpam-6417	20	42	14	14	NUM
ejpam-6417	20	43	]	]	PUNCT
ejpam-6417	20	44	.	.	PUNCT
ejpam-6417	21	1	by	by	ADP
ejpam-6417	21	2	restricting	restrict	VERB
ejpam-6417	21	3	p	p	NOUN
ejpam-6417	21	4	to	to	PART
ejpam-6417	21	5	be	be	AUX
ejpam-6417	21	6	diagonal	diagonal	ADJ
ejpam-6417	21	7	,	,	PUNCT
ejpam-6417	21	8	we	we	PRON
ejpam-6417	21	9	enforce	enforce	VERB
ejpam-6417	21	10	a	a	DET
ejpam-6417	21	11	decoupling	decoupling	NOUN
ejpam-6417	21	12	of	of	ADP
ejpam-6417	21	13	variables	variable	NOUN
ejpam-6417	21	14	that	that	PRON
ejpam-6417	21	15	simplifies	simplify	VERB
ejpam-6417	21	16	stability	stability	NOUN
ejpam-6417	21	17	analysis	analysis	NOUN
ejpam-6417	21	18	and	and	CCONJ
ejpam-6417	21	19	computation	computation	NOUN
ejpam-6417	21	20	,	,	PUNCT
ejpam-6417	21	21	a	a	DET
ejpam-6417	21	22	feature	feature	NOUN
ejpam-6417	21	23	exploited	exploit	VERB
ejpam-6417	21	24	in	in	ADP
ejpam-6417	21	25	our	our	PRON
ejpam-6417	21	26	characterizations	characterization	NOUN
ejpam-6417	21	27	of	of	ADP
ejpam-6417	21	28	positive	positive	ADJ
ejpam-6417	21	29	diagonal	diagonal	ADJ
ejpam-6417	21	30	solutions	solution	NOUN
ejpam-6417	21	31	[	[	X
ejpam-6417	21	32	15	15	NUM
ejpam-6417	21	33	]	]	PUNCT
ejpam-6417	21	34	.	.	PUNCT
ejpam-6417	22	1	this	this	DET
ejpam-6417	22	2	paper	paper	NOUN
ejpam-6417	22	3	builds	build	VERB
ejpam-6417	22	4	on	on	ADP
ejpam-6417	22	5	these	these	DET
ejpam-6417	22	6	concepts	concept	NOUN
ejpam-6417	22	7	to	to	PART
ejpam-6417	22	8	explore	explore	VERB
ejpam-6417	22	9	conditions	condition	NOUN
ejpam-6417	22	10	under	under	ADP
ejpam-6417	22	11	which	which	PRON
ejpam-6417	22	12	a	a	DET
ejpam-6417	22	13	structured	structured	ADJ
ejpam-6417	22	14	block	block	NOUN
ejpam-6417	22	15	matrix	matrix	NOUN
ejpam-6417	22	16	,	,	PUNCT
ejpam-6417	22	17	involving	involve	VERB
ejpam-6417	22	18	multiple	multiple	ADJ
ejpam-6417	22	19	matrices	matrix	NOUN
ejpam-6417	22	20	a1	a1	NOUN
ejpam-6417	22	21	,	,	PUNCT
ejpam-6417	22	22	a2	a2	PROPN
ejpam-6417	22	23	,	,	PUNCT
ejpam-6417	22	24	a3	a3	NOUN
ejpam-6417	22	25	,	,	PUNCT
ejpam-6417	22	26	admits	admit	VERB
ejpam-6417	22	27	such	such	ADJ
ejpam-6417	22	28	diagonal	diagonal	ADJ
ejpam-6417	22	29	solutions	solution	NOUN
ejpam-6417	22	30	,	,	PUNCT
ejpam-6417	22	31	thereby	thereby	ADV
ejpam-6417	22	32	generalizing	generalize	VERB
ejpam-6417	22	33	classical	classical	ADJ
ejpam-6417	22	34	stability	stability	NOUN
ejpam-6417	22	35	results	result	NOUN
ejpam-6417	22	36	to	to	ADP
ejpam-6417	22	37	multi	multi	ADJ
ejpam-6417	22	38	-	-	ADJ
ejpam-6417	22	39	matrix	matrix	ADJ
ejpam-6417	22	40	settings	setting	NOUN
ejpam-6417	22	41	with	with	ADP
ejpam-6417	22	42	practical	practical	ADJ
ejpam-6417	22	43	implications	implication	NOUN
ejpam-6417	22	44	in	in	ADP
ejpam-6417	22	45	control	control	NOUN
ejpam-6417	22	46	and	and	CCONJ
ejpam-6417	22	47	dynamics	dynamic	NOUN
ejpam-6417	22	48	.	.	PUNCT
ejpam-6417	23	1	in	in	ADP
ejpam-6417	23	2	this	this	DET
ejpam-6417	23	3	paper	paper	NOUN
ejpam-6417	23	4	,	,	PUNCT
ejpam-6417	23	5	we	we	PRON
ejpam-6417	23	6	focus	focus	VERB
ejpam-6417	23	7	on	on	ADP
ejpam-6417	23	8	a	a	DET
ejpam-6417	23	9	specific	specific	ADJ
ejpam-6417	23	10	class	class	NOUN
ejpam-6417	23	11	of	of	ADP
ejpam-6417	23	12	lmis	lmis	ADJ
ejpam-6417	23	13	involving	involve	VERB
ejpam-6417	23	14	a	a	DET
ejpam-6417	23	15	triple	triple	NOUN
ejpam-6417	23	16	of	of	ADP
ejpam-6417	23	17	real	real	ADJ
ejpam-6417	23	18	n	n	NUM
ejpam-6417	23	19	×	×	NOUN
ejpam-6417	23	20	n	n	PRON
ejpam-6417	23	21	matrices	matrix	NOUN
ejpam-6417	23	22	(	(	PUNCT
ejpam-6417	23	23	a1	a1	NOUN
ejpam-6417	23	24	,	,	PUNCT
ejpam-6417	23	25	a2	a2	PROPN
ejpam-6417	23	26	,	,	PUNCT
ejpam-6417	23	27	a3	a3	NOUN
ejpam-6417	23	28	)	)	PUNCT
ejpam-6417	23	29	.	.	PUNCT
ejpam-6417	24	1	our	our	PRON
ejpam-6417	24	2	objective	objective	NOUN
ejpam-6417	24	3	is	be	AUX
ejpam-6417	24	4	to	to	PART
ejpam-6417	24	5	characterize	characterize	VERB
ejpam-6417	24	6	the	the	DET
ejpam-6417	24	7	conditions	condition	NOUN
ejpam-6417	24	8	under	under	ADP
ejpam-6417	24	9	which	which	PRON
ejpam-6417	24	10	this	this	DET
ejpam-6417	24	11	triple	triple	NOUN
ejpam-6417	24	12	admits	admit	VERB
ejpam-6417	24	13	a	a	DET
ejpam-6417	24	14	positive	positive	ADJ
ejpam-6417	24	15	diagonal	diagonal	ADJ
ejpam-6417	24	16	solution	solution	NOUN
ejpam-6417	24	17	,	,	PUNCT
ejpam-6417	24	18	defined	define	VERB
ejpam-6417	24	19	as	as	ADP
ejpam-6417	24	20	a	a	DET
ejpam-6417	24	21	set	set	NOUN
ejpam-6417	24	22	of	of	ADP
ejpam-6417	24	23	positive	positive	ADJ
ejpam-6417	24	24	diagonal	diagonal	ADJ
ejpam-6417	24	25	matrices	matrix	NOUN
ejpam-6417	24	26	p1	p1	NOUN
ejpam-6417	24	27	,	,	PUNCT
ejpam-6417	24	28	p2	p2	NOUN
ejpam-6417	24	29	,	,	PUNCT
ejpam-6417	24	30	p3	p3	PROPN
ejpam-6417	24	31	∈	∈	PROPN
ejpam-6417	24	32	rn×n	rn×n	PROPN
ejpam-6417	24	33	such	such	ADJ
ejpam-6417	24	34	that	that	SCONJ
ejpam-6417	24	35	the	the	DET
ejpam-6417	24	36	block	block	NOUN
ejpam-6417	24	37	matrix	matrix	NOUN
ejpam-6417	24	38	b	b	NOUN
ejpam-6417	25	1	=	=	SYM
ejpam-6417	25	2	at	at	PROPN
ejpam-6417	25	3	1	1	NUM
ejpam-6417	25	4	p1	p1	NOUN
ejpam-6417	25	5	+	+	CCONJ
ejpam-6417	25	6	p1a1	p1a1	NOUN
ejpam-6417	25	7	+	+	CCONJ
ejpam-6417	25	8	p2	p2	X
ejpam-6417	25	9	+	+	CCONJ
ejpam-6417	25	10	p3	p3	NOUN
ejpam-6417	25	11	p1a2	p1a2	X
ejpam-6417	25	12	p1a3	p1a3	NOUN
ejpam-6417	25	13	at	at	ADP
ejpam-6417	25	14	2	2	NUM
ejpam-6417	25	15	p1	p1	NOUN
ejpam-6417	25	16	−p2	−p2	PROPN
ejpam-6417	25	17	0	0	PUNCT
ejpam-6417	26	1	at	at	ADP
ejpam-6417	26	2	3	3	NUM
ejpam-6417	26	3	p1	p1	NOUN
ejpam-6417	26	4	0	0	PUNCT
ejpam-6417	27	1	−p3	−p3	ADJ
ejpam-6417	27	2			NOUN
ejpam-6417	27	3	is	be	AUX
ejpam-6417	27	4	negative	negative	ADJ
ejpam-6417	27	5	definite	definite	ADJ
ejpam-6417	27	6	.	.	PUNCT
ejpam-6417	28	1	this	this	DET
ejpam-6417	28	2	formulation	formulation	NOUN
ejpam-6417	28	3	generalizes	generalize	VERB
ejpam-6417	28	4	classical	classical	ADJ
ejpam-6417	28	5	stability	stability	NOUN
ejpam-6417	28	6	problems	problem	NOUN
ejpam-6417	28	7	and	and	CCONJ
ejpam-6417	28	8	introduces	introduce	VERB
ejpam-6417	28	9	additional	additional	ADJ
ejpam-6417	28	10	complexity	complexity	NOUN
ejpam-6417	28	11	due	due	ADP
ejpam-6417	28	12	to	to	ADP
ejpam-6417	28	13	the	the	DET
ejpam-6417	28	14	interplay	interplay	NOUN
ejpam-6417	28	15	between	between	ADP
ejpam-6417	28	16	the	the	DET
ejpam-6417	28	17	matrices	matrix	NOUN
ejpam-6417	28	18	a1	a1	NOUN
ejpam-6417	28	19	,	,	PUNCT
ejpam-6417	28	20	a2	a2	PROPN
ejpam-6417	28	21	,	,	PUNCT
ejpam-6417	28	22	a3	a3	NOUN
ejpam-6417	28	23	and	and	CCONJ
ejpam-6417	28	24	the	the	DET
ejpam-6417	28	25	diagonal	diagonal	ADJ
ejpam-6417	28	26	structure	structure	NOUN
ejpam-6417	28	27	of	of	ADP
ejpam-6417	28	28	p1	p1	NOUN
ejpam-6417	28	29	,	,	PUNCT
ejpam-6417	28	30	p2	p2	NOUN
ejpam-6417	28	31	,	,	PUNCT
ejpam-6417	28	32	p3	p3	NOUN
ejpam-6417	28	33	.	.	PUNCT
ejpam-6417	29	1	2	2	NUM
ejpam-6417	29	2	.	.	X
ejpam-6417	29	3	background	background	NOUN
ejpam-6417	29	4	to	to	PART
ejpam-6417	29	5	establish	establish	VERB
ejpam-6417	29	6	a	a	DET
ejpam-6417	29	7	foundation	foundation	NOUN
ejpam-6417	29	8	for	for	ADP
ejpam-6417	29	9	our	our	PRON
ejpam-6417	29	10	results	result	NOUN
ejpam-6417	29	11	,	,	PUNCT
ejpam-6417	29	12	we	we	PRON
ejpam-6417	29	13	introduce	introduce	VERB
ejpam-6417	29	14	several	several	ADJ
ejpam-6417	29	15	key	key	ADJ
ejpam-6417	29	16	concepts	concept	NOUN
ejpam-6417	29	17	.	.	PUNCT
ejpam-6417	30	1	all	all	DET
ejpam-6417	30	2	matrices	matrix	NOUN
ejpam-6417	30	3	considered	consider	VERB
ejpam-6417	30	4	in	in	ADP
ejpam-6417	30	5	this	this	DET
ejpam-6417	30	6	work	work	NOUN
ejpam-6417	30	7	are	be	AUX
ejpam-6417	30	8	real	real	ADJ
ejpam-6417	30	9	.	.	PUNCT
ejpam-6417	31	1	additionally	additionally	ADV
ejpam-6417	31	2	,	,	PUNCT
ejpam-6417	31	3	a	a	DET
ejpam-6417	31	4	matrix	matrix	NOUN
ejpam-6417	31	5	is	be	AUX
ejpam-6417	31	6	positive	positive	ADJ
ejpam-6417	31	7	(	(	PUNCT
ejpam-6417	31	8	negative	negative	ADJ
ejpam-6417	31	9	,	,	PUNCT
ejpam-6417	31	10	respectively	respectively	ADV
ejpam-6417	31	11	)	)	PUNCT
ejpam-6417	31	12	definite	definite	ADJ
ejpam-6417	31	13	if	if	SCONJ
ejpam-6417	31	14	all	all	DET
ejpam-6417	31	15	its	its	PRON
ejpam-6417	31	16	eigenvalues	eigenvalue	NOUN
ejpam-6417	31	17	are	be	AUX
ejpam-6417	31	18	positive	positive	ADJ
ejpam-6417	31	19	(	(	PUNCT
ejpam-6417	31	20	negative	negative	ADJ
ejpam-6417	31	21	,	,	PUNCT
ejpam-6417	31	22	respectively	respectively	ADV
ejpam-6417	31	23	)	)	PUNCT
ejpam-6417	31	24	;	;	PUNCT
ejpam-6417	31	25	meanwhile	meanwhile	ADV
ejpam-6417	31	26	,	,	PUNCT
ejpam-6417	31	27	we	we	PRON
ejpam-6417	31	28	say	say	VERB
ejpam-6417	31	29	it	it	PRON
ejpam-6417	31	30	is	be	AUX
ejpam-6417	31	31	positive	positive	ADJ
ejpam-6417	31	32	(	(	PUNCT
ejpam-6417	31	33	negative	negative	ADJ
ejpam-6417	31	34	,	,	PUNCT
ejpam-6417	31	35	respectively	respectively	ADV
ejpam-6417	31	36	)	)	PUNCT
ejpam-6417	31	37	semidefinite	semidefinite	NOUN
ejpam-6417	31	38	if	if	SCONJ
ejpam-6417	31	39	all	all	DET
ejpam-6417	31	40	its	its	PRON
ejpam-6417	31	41	eigenvalues	eigenvalue	NOUN
ejpam-6417	31	42	are	be	AUX
ejpam-6417	31	43	nonnegative	nonnegative	ADJ
ejpam-6417	31	44	(	(	PUNCT
ejpam-6417	31	45	nonpositive	nonpositive	ADJ
ejpam-6417	31	46	,	,	PUNCT
ejpam-6417	31	47	respectively	respectively	ADV
ejpam-6417	31	48	)	)	PUNCT
ejpam-6417	31	49	.	.	PUNCT
ejpam-6417	32	1	we	we	PRON
ejpam-6417	32	2	shall	shall	AUX
ejpam-6417	32	3	adopt	adopt	VERB
ejpam-6417	32	4	the	the	DET
ejpam-6417	32	5	notation	notation	NOUN
ejpam-6417	32	6	x	x	PUNCT
ejpam-6417	32	7	≻	≻	PROPN
ejpam-6417	32	8	0	0	NUM
ejpam-6417	32	9	(	(	PUNCT
ejpam-6417	32	10	x	x	NOUN
ejpam-6417	32	11	≺	≺	NOUN
ejpam-6417	32	12	0	0	NUM
ejpam-6417	32	13	,	,	PUNCT
ejpam-6417	32	14	respectively	respectively	ADV
ejpam-6417	32	15	)	)	PUNCT
ejpam-6417	32	16	to	to	PART
ejpam-6417	32	17	indicate	indicate	VERB
ejpam-6417	32	18	that	that	SCONJ
ejpam-6417	32	19	a	a	DET
ejpam-6417	32	20	matrix	matrix	NOUN
ejpam-6417	32	21	x	x	SYM
ejpam-6417	32	22	∈	∈	NOUN
ejpam-6417	32	23	rn×n	rn×n	NOUN
ejpam-6417	32	24	is	be	AUX
ejpam-6417	32	25	positive	positive	ADJ
ejpam-6417	32	26	definite	definite	ADJ
ejpam-6417	32	27	(	(	PUNCT
ejpam-6417	32	28	negative	negative	ADJ
ejpam-6417	32	29	definite	definite	ADJ
ejpam-6417	32	30	,	,	PUNCT
ejpam-6417	32	31	respectively	respectively	ADV
ejpam-6417	32	32	)	)	PUNCT
ejpam-6417	32	33	.	.	PUNCT
ejpam-6417	33	1	similarly	similarly	ADV
ejpam-6417	33	2	,	,	PUNCT
ejpam-6417	33	3	we	we	PRON
ejpam-6417	33	4	denote	denote	VERB
ejpam-6417	33	5	a	a	DET
ejpam-6417	33	6	positive	positive	ADJ
ejpam-6417	33	7	semidefinite	semidefinite	NOUN
ejpam-6417	33	8	(	(	PUNCT
ejpam-6417	33	9	negative	negative	ADJ
ejpam-6417	33	10	semidefinite	semidefinite	NOUN
ejpam-6417	33	11	,	,	PUNCT
ejpam-6417	33	12	respectively	respectively	ADV
ejpam-6417	33	13	)	)	PUNCT
ejpam-6417	33	14	matrix	matrix	NOUN
ejpam-6417	33	15	by	by	ADP
ejpam-6417	33	16	x	x	PUNCT
ejpam-6417	33	17	⪰	⪰	NOUN
ejpam-6417	33	18	0	0	PUNCT
ejpam-6417	33	19	(	(	PUNCT
ejpam-6417	33	20	x	x	X
ejpam-6417	33	21	⪯	⪯	NOUN
ejpam-6417	33	22	0	0	NUM
ejpam-6417	33	23	,	,	PUNCT
ejpam-6417	33	24	respectively	respectively	ADV
ejpam-6417	33	25	)	)	PUNCT
ejpam-6417	33	26	.	.	PUNCT
ejpam-6417	34	1	unless	unless	SCONJ
ejpam-6417	34	2	stated	state	VERB
ejpam-6417	34	3	otherwise	otherwise	ADV
ejpam-6417	34	4	,	,	PUNCT
ejpam-6417	34	5	a	a	DET
ejpam-6417	34	6	positive	positive	ADJ
ejpam-6417	34	7	or	or	CCONJ
ejpam-6417	34	8	negative	negative	ADJ
ejpam-6417	34	9	definite	definite	ADJ
ejpam-6417	34	10	or	or	CCONJ
ejpam-6417	34	11	semidefinite	semidefinite	NOUN
ejpam-6417	34	12	matrix	matrix	NOUN
ejpam-6417	34	13	is	be	AUX
ejpam-6417	34	14	assumed	assume	VERB
ejpam-6417	34	15	to	to	PART
ejpam-6417	34	16	be	be	AUX
ejpam-6417	34	17	symmetric	symmetric	ADJ
ejpam-6417	34	18	.	.	PUNCT
ejpam-6417	35	1	if	if	SCONJ
ejpam-6417	35	2	x	x	PRON
ejpam-6417	35	3	is	be	AUX
ejpam-6417	35	4	a	a	DET
ejpam-6417	35	5	diagonal	diagonal	ADJ
ejpam-6417	35	6	positive	positive	ADJ
ejpam-6417	35	7	definite	definite	ADJ
ejpam-6417	35	8	a.	a.	NOUN
ejpam-6417	35	9	algefary	algefary	ADJ
ejpam-6417	35	10	,	,	PUNCT
ejpam-6417	35	11	t.	t.	PROPN
ejpam-6417	35	12	alhumaidan	alhumaidan	PROPN
ejpam-6417	35	13	/	/	SYM
ejpam-6417	35	14	eur	eur	PROPN
ejpam-6417	35	15	.	.	PUNCT
ejpam-6417	36	1	j.	j.	PROPN
ejpam-6417	36	2	pure	pure	PROPN
ejpam-6417	36	3	appl	appl	PROPN
ejpam-6417	36	4	.	.	PROPN
ejpam-6417	36	5	math	math	PROPN
ejpam-6417	36	6	,	,	PUNCT
ejpam-6417	36	7	18	18	NUM
ejpam-6417	36	8	(	(	PUNCT
ejpam-6417	36	9	3	3	NUM
ejpam-6417	36	10	)	)	PUNCT
ejpam-6417	36	11	(	(	PUNCT
ejpam-6417	36	12	2025	2025	NUM
ejpam-6417	36	13	)	)	PUNCT
ejpam-6417	36	14	,	,	PUNCT
ejpam-6417	36	15	6417	6417	NUM
ejpam-6417	36	16	3	3	NUM
ejpam-6417	36	17	of	of	ADP
ejpam-6417	36	18	10	10	NUM
ejpam-6417	36	19	matrix	matrix	NOUN
ejpam-6417	37	1	,	,	PUNCT
ejpam-6417	37	2	we	we	PRON
ejpam-6417	37	3	write	write	VERB
ejpam-6417	37	4	positive	positive	ADJ
ejpam-6417	37	5	diagonal	diagonal	ADJ
ejpam-6417	37	6	matrix	matrix	NOUN
ejpam-6417	37	7	since	since	SCONJ
ejpam-6417	37	8	it	it	PRON
ejpam-6417	37	9	is	be	AUX
ejpam-6417	37	10	clear	clear	ADJ
ejpam-6417	37	11	that	that	SCONJ
ejpam-6417	37	12	a	a	DET
ejpam-6417	37	13	diagonal	diagonal	ADJ
ejpam-6417	37	14	positive	positive	ADJ
ejpam-6417	37	15	definite	definite	ADJ
ejpam-6417	37	16	matrix	matrix	NOUN
ejpam-6417	37	17	has	have	VERB
ejpam-6417	37	18	all	all	DET
ejpam-6417	37	19	its	its	PRON
ejpam-6417	37	20	diagonal	diagonal	ADJ
ejpam-6417	37	21	elements	element	NOUN
ejpam-6417	37	22	positive	positive	ADJ
ejpam-6417	37	23	.	.	PUNCT
ejpam-6417	38	1	let	let	VERB
ejpam-6417	38	2	x	x	PUNCT
ejpam-6417	38	3	∈	∈	PROPN
ejpam-6417	38	4	rn×n	rn×n	PROPN
ejpam-6417	38	5	and	and	CCONJ
ejpam-6417	38	6	u	u	NOUN
ejpam-6417	38	7	,	,	PUNCT
ejpam-6417	38	8	v	v	PROPN
ejpam-6417	38	9	∈	∈	PROPN
ejpam-6417	38	10	rn	rn	PROPN
ejpam-6417	38	11	.	.	PUNCT
ejpam-6417	39	1	the	the	DET
ejpam-6417	39	2	trace	trace	NOUN
ejpam-6417	39	3	of	of	ADP
ejpam-6417	39	4	x	x	PROPN
ejpam-6417	39	5	is	be	AUX
ejpam-6417	39	6	denoted	denote	VERB
ejpam-6417	39	7	by	by	ADP
ejpam-6417	39	8	tr(x	tr(x	NOUN
ejpam-6417	39	9	)	)	PUNCT
ejpam-6417	39	10	,	,	PUNCT
ejpam-6417	39	11	and	and	CCONJ
ejpam-6417	39	12	diag(x	diag(x	VERB
ejpam-6417	39	13	)	)	PUNCT
ejpam-6417	39	14	represents	represent	VERB
ejpam-6417	39	15	the	the	DET
ejpam-6417	39	16	vector	vector	NOUN
ejpam-6417	39	17	in	in	ADP
ejpam-6417	39	18	rn	rn	PROPN
ejpam-6417	39	19	whose	whose	DET
ejpam-6417	39	20	j	j	PROPN
ejpam-6417	39	21	-	-	PUNCT
ejpam-6417	39	22	th	th	VERB
ejpam-6417	39	23	component	component	NOUN
ejpam-6417	39	24	corresponds	correspond	VERB
ejpam-6417	39	25	to	to	ADP
ejpam-6417	39	26	the	the	DET
ejpam-6417	39	27	j	j	PROPN
ejpam-6417	39	28	-	-	PUNCT
ejpam-6417	39	29	th	th	X
ejpam-6417	39	30	diagonal	diagonal	ADJ
ejpam-6417	39	31	element	element	NOUN
ejpam-6417	39	32	of	of	ADP
ejpam-6417	39	33	x.	x.	NOUN
ejpam-6417	39	34	we	we	PRON
ejpam-6417	39	35	shall	shall	AUX
ejpam-6417	39	36	employ	employ	VERB
ejpam-6417	39	37	the	the	DET
ejpam-6417	39	38	notation	notation	NOUN
ejpam-6417	39	39	u	u	PROPN
ejpam-6417	39	40	≥	≥	NOUN
ejpam-6417	39	41	v	v	NOUN
ejpam-6417	39	42	to	to	PART
ejpam-6417	39	43	indicate	indicate	VERB
ejpam-6417	39	44	that	that	SCONJ
ejpam-6417	39	45	uj	uj	PROPN
ejpam-6417	39	46	≥	≥	PROPN
ejpam-6417	39	47	vj	vj	PROPN
ejpam-6417	39	48	for	for	ADP
ejpam-6417	39	49	all	all	PRON
ejpam-6417	39	50	j	j	NOUN
ejpam-6417	39	51	=	=	SYM
ejpam-6417	39	52	1	1	NUM
ejpam-6417	39	53	,	,	PUNCT
ejpam-6417	39	54	.	.	PUNCT
ejpam-6417	39	55	.	.	PUNCT
ejpam-6417	40	1	.	.	PUNCT
ejpam-6417	41	1	,	,	PUNCT
ejpam-6417	41	2	n	n	CCONJ
ejpam-6417	41	3	,	,	PUNCT
ejpam-6417	41	4	and	and	CCONJ
ejpam-6417	41	5	we	we	PRON
ejpam-6417	41	6	use	use	VERB
ejpam-6417	41	7	u	u	NOUN
ejpam-6417	41	8	⩾	⩾	NOUN
ejpam-6417	41	9	v	v	INTJ
ejpam-6417	41	10	if	if	SCONJ
ejpam-6417	41	11	uj	uj	PROPN
ejpam-6417	41	12	⩾	⩾	PROPN
ejpam-6417	41	13	vj	vj	PROPN
ejpam-6417	41	14	for	for	ADP
ejpam-6417	41	15	all	all	DET
ejpam-6417	41	16	j	j	NOUN
ejpam-6417	41	17	=	=	SYM
ejpam-6417	41	18	1	1	NUM
ejpam-6417	41	19	,	,	PUNCT
ejpam-6417	41	20	.	.	PUNCT
ejpam-6417	41	21	.	.	PUNCT
ejpam-6417	42	1	.	.	PUNCT
ejpam-6417	43	1	,	,	PUNCT
ejpam-6417	43	2	n.	n.	NOUN
ejpam-6417	43	3	we	we	PRON
ejpam-6417	43	4	denote	denote	VERB
ejpam-6417	43	5	the	the	DET
ejpam-6417	43	6	hadamard	hadamard	ADJ
ejpam-6417	43	7	product	product	NOUN
ejpam-6417	43	8	of	of	ADP
ejpam-6417	43	9	two	two	NUM
ejpam-6417	43	10	matrices	matrix	NOUN
ejpam-6417	43	11	x	x	PUNCT
ejpam-6417	43	12	and	and	CCONJ
ejpam-6417	43	13	y	y	PROPN
ejpam-6417	43	14	,	,	PUNCT
ejpam-6417	43	15	both	both	CCONJ
ejpam-6417	43	16	in	in	ADP
ejpam-6417	43	17	rn×n	rn×n	NOUN
ejpam-6417	43	18	,	,	PUNCT
ejpam-6417	43	19	as	as	ADP
ejpam-6417	43	20	x	x	X
ejpam-6417	43	21	◦	◦	NOUN
ejpam-6417	43	22	y	y	PROPN
ejpam-6417	43	23	,	,	PUNCT
ejpam-6417	43	24	where	where	SCONJ
ejpam-6417	43	25	(	(	PUNCT
ejpam-6417	43	26	x	x	SYM
ejpam-6417	43	27	◦	◦	NOUN
ejpam-6417	43	28	y	y	PROPN
ejpam-6417	43	29	)	)	PUNCT
ejpam-6417	43	30	ij	ij	NOUN
ejpam-6417	43	31	=	=	PUNCT
ejpam-6417	43	32	xijyij	xijyij	PROPN
ejpam-6417	43	33	.	.	PUNCT
ejpam-6417	44	1	a	a	DET
ejpam-6417	44	2	matrix	matrix	NOUN
ejpam-6417	44	3	x	x	SYM
ejpam-6417	44	4	∈	∈	PROPN
ejpam-6417	44	5	rn×n	rn×n	NOUN
ejpam-6417	44	6	is	be	AUX
ejpam-6417	44	7	a	a	DET
ejpam-6417	44	8	p	p	NOUN
ejpam-6417	44	9	-matrix	-matrix	NOUN
ejpam-6417	44	10	if	if	SCONJ
ejpam-6417	44	11	every	every	DET
ejpam-6417	44	12	principal	principal	ADJ
ejpam-6417	44	13	minor	minor	NOUN
ejpam-6417	44	14	of	of	ADP
ejpam-6417	44	15	x	x	SYM
ejpam-6417	44	16	is	be	AUX
ejpam-6417	44	17	positive	positive	ADJ
ejpam-6417	44	18	.	.	PUNCT
ejpam-6417	45	1	it	it	PRON
ejpam-6417	45	2	is	be	AUX
ejpam-6417	45	3	a	a	DET
ejpam-6417	45	4	well	well	ADV
ejpam-6417	45	5	-	-	PUNCT
ejpam-6417	45	6	established	establish	VERB
ejpam-6417	45	7	result	result	NOUN
ejpam-6417	45	8	(	(	PUNCT
ejpam-6417	45	9	see	see	VERB
ejpam-6417	45	10	theorem	theorem	VERB
ejpam-6417	45	11	6.2.3	6.2.3	NUM
ejpam-6417	45	12	of	of	ADP
ejpam-6417	45	13	[	[	X
ejpam-6417	45	14	11	11	NUM
ejpam-6417	45	15	]	]	PUNCT
ejpam-6417	45	16	)	)	PUNCT
ejpam-6417	45	17	that	that	SCONJ
ejpam-6417	45	18	this	this	DET
ejpam-6417	45	19	condition	condition	NOUN
ejpam-6417	45	20	is	be	AUX
ejpam-6417	45	21	equivalent	equivalent	ADJ
ejpam-6417	45	22	to	to	ADP
ejpam-6417	45	23	the	the	DET
ejpam-6417	45	24	requirement	requirement	NOUN
ejpam-6417	45	25	that	that	SCONJ
ejpam-6417	45	26	,	,	PUNCT
ejpam-6417	45	27	for	for	ADP
ejpam-6417	45	28	every	every	DET
ejpam-6417	45	29	non	non	ADJ
ejpam-6417	45	30	-	-	ADJ
ejpam-6417	45	31	zero	zero	NUM
ejpam-6417	45	32	u	u	NOUN
ejpam-6417	45	33	∈	∈	PROPN
ejpam-6417	45	34	rn	rn	PROPN
ejpam-6417	45	35	,	,	PUNCT
ejpam-6417	45	36	there	there	PRON
ejpam-6417	45	37	exists	exist	VERB
ejpam-6417	45	38	an	an	DET
ejpam-6417	45	39	index	index	NOUN
ejpam-6417	45	40	i	i	PRON
ejpam-6417	45	41	such	such	VERB
ejpam-6417	45	42	that	that	SCONJ
ejpam-6417	45	43	ui(xu)i	ui(xu)i	ADV
ejpam-6417	45	44	>	>	X
ejpam-6417	45	45	0	0	X
ejpam-6417	45	46	.	.	PUNCT
ejpam-6417	46	1	for	for	ADP
ejpam-6417	46	2	a	a	DET
ejpam-6417	46	3	block	block	NOUN
ejpam-6417	46	4	matrix	matrix	NOUN
ejpam-6417	46	5	h	h	NOUN
ejpam-6417	46	6	∈	∈	PROPN
ejpam-6417	46	7	r3n×3n	r3n×3n	PROPN
ejpam-6417	46	8	,	,	PUNCT
ejpam-6417	46	9	partitioned	partition	VERB
ejpam-6417	46	10	as	as	ADP
ejpam-6417	46	11	h	h	NOUN
ejpam-6417	46	12	=	=	SYM
ejpam-6417	46	13	h11	h11	PROPN
ejpam-6417	46	14	h12	h12	NOUN
ejpam-6417	46	15	h13	h13	NOUN
ejpam-6417	46	16	ht	ht	PROPN
ejpam-6417	46	17	12	12	NUM
ejpam-6417	46	18	h22	h22	PROPN
ejpam-6417	46	19	h23	h23	PROPN
ejpam-6417	46	20	ht	ht	PROPN
ejpam-6417	46	21	13	13	NUM
ejpam-6417	46	22	ht	ht	PROPN
ejpam-6417	46	23	23	23	NUM
ejpam-6417	46	24	h33	h33	NOUN
ejpam-6417	46	25			NOUN
ejpam-6417	46	26	,	,	PUNCT
ejpam-6417	46	27	we	we	PRON
ejpam-6417	46	28	assume	assume	VERB
ejpam-6417	46	29	each	each	DET
ejpam-6417	46	30	block	block	NOUN
ejpam-6417	46	31	hij	hij	PROPN
ejpam-6417	46	32	∈	∈	NOUN
ejpam-6417	46	33	rn×n	rn×n	NOUN
ejpam-6417	46	34	,	,	PUNCT
ejpam-6417	46	35	and	and	CCONJ
ejpam-6417	46	36	denote	denote	VERB
ejpam-6417	46	37	the	the	DET
ejpam-6417	46	38	(	(	PUNCT
ejpam-6417	46	39	i	i	PROPN
ejpam-6417	46	40	,	,	PUNCT
ejpam-6417	46	41	j)-th	j)-th	PROPN
ejpam-6417	46	42	entry	entry	NOUN
ejpam-6417	46	43	of	of	ADP
ejpam-6417	46	44	h11	h11	PROPN
ejpam-6417	46	45	as	as	ADP
ejpam-6417	46	46	h11ij	h11ij	NOUN
ejpam-6417	46	47	=	=	SYM
ejpam-6417	46	48	(	(	PUNCT
ejpam-6417	46	49	h11)ij	h11)ij	NOUN
ejpam-6417	46	50	.	.	PUNCT
ejpam-6417	47	1	our	our	PRON
ejpam-6417	47	2	analysis	analysis	NOUN
ejpam-6417	47	3	builds	build	VERB
ejpam-6417	47	4	on	on	ADP
ejpam-6417	47	5	several	several	ADJ
ejpam-6417	47	6	foundational	foundational	ADJ
ejpam-6417	47	7	results	result	NOUN
ejpam-6417	47	8	.	.	PUNCT
ejpam-6417	48	1	for	for	ADP
ejpam-6417	48	2	instance	instance	NOUN
ejpam-6417	48	3	,	,	PUNCT
ejpam-6417	48	4	it	it	PRON
ejpam-6417	48	5	is	be	AUX
ejpam-6417	48	6	well	well	ADV
ejpam-6417	48	7	-	-	PUNCT
ejpam-6417	48	8	known	know	VERB
ejpam-6417	48	9	that	that	SCONJ
ejpam-6417	48	10	the	the	DET
ejpam-6417	48	11	hadamard	hadamard	ADJ
ejpam-6417	48	12	product	product	NOUN
ejpam-6417	48	13	of	of	ADP
ejpam-6417	48	14	two	two	NUM
ejpam-6417	48	15	positive	positive	ADJ
ejpam-6417	48	16	semidefinite	semidefinite	NOUN
ejpam-6417	48	17	matrices	matrix	NOUN
ejpam-6417	48	18	is	be	AUX
ejpam-6417	48	19	positive	positive	ADJ
ejpam-6417	48	20	semidefinite	semidefinite	NOUN
ejpam-6417	48	21	,	,	PUNCT
ejpam-6417	48	22	and	and	CCONJ
ejpam-6417	48	23	if	if	SCONJ
ejpam-6417	48	24	both	both	PRON
ejpam-6417	48	25	are	be	AUX
ejpam-6417	48	26	positive	positive	ADJ
ejpam-6417	48	27	definite	definite	ADJ
ejpam-6417	48	28	,	,	PUNCT
ejpam-6417	48	29	their	their	PRON
ejpam-6417	48	30	product	product	NOUN
ejpam-6417	48	31	remains	remain	VERB
ejpam-6417	48	32	positive	positive	ADJ
ejpam-6417	48	33	definite	definite	ADJ
ejpam-6417	48	34	.	.	PUNCT
ejpam-6417	49	1	furthermore	furthermore	ADV
ejpam-6417	49	2	,	,	PUNCT
ejpam-6417	49	3	if	if	SCONJ
ejpam-6417	49	4	a	a	DET
ejpam-6417	49	5	matrix	matrix	NOUN
ejpam-6417	49	6	is	be	AUX
ejpam-6417	49	7	lyapunov	lyapunov	NOUN
ejpam-6417	49	8	diagonally	diagonally	ADV
ejpam-6417	49	9	stable	stable	ADJ
ejpam-6417	49	10	—	—	PUNCT
ejpam-6417	49	11	meaning	mean	VERB
ejpam-6417	49	12	there	there	PRON
ejpam-6417	49	13	exists	exist	VERB
ejpam-6417	49	14	a	a	DET
ejpam-6417	49	15	positive	positive	ADJ
ejpam-6417	49	16	diagonal	diagonal	ADJ
ejpam-6417	49	17	matrix	matrix	NOUN
ejpam-6417	49	18	p	p	NOUN
ejpam-6417	49	19	such	such	ADJ
ejpam-6417	49	20	that	that	DET
ejpam-6417	49	21	atp	atp	PROPN
ejpam-6417	49	22	+	+	CCONJ
ejpam-6417	49	23	pa	pa	PROPN
ejpam-6417	49	24	is	be	AUX
ejpam-6417	49	25	negative	negative	ADJ
ejpam-6417	49	26	definite	definite	ADJ
ejpam-6417	49	27	—	—	PUNCT
ejpam-6417	49	28	then	then	ADV
ejpam-6417	49	29	its	its	PRON
ejpam-6417	49	30	negative	negative	NOUN
ejpam-6417	49	31	is	be	AUX
ejpam-6417	49	32	a	a	DET
ejpam-6417	49	33	p	p	NOUN
ejpam-6417	49	34	-matrix	-matrix	NOUN
ejpam-6417	49	35	.	.	PUNCT
ejpam-6417	50	1	these	these	DET
ejpam-6417	50	2	properties	property	NOUN
ejpam-6417	50	3	underpin	underpin	VERB
ejpam-6417	50	4	our	our	PRON
ejpam-6417	50	5	exploration	exploration	NOUN
ejpam-6417	50	6	of	of	ADP
ejpam-6417	50	7	diagonal	diagonal	ADJ
ejpam-6417	50	8	solutions	solution	NOUN
ejpam-6417	50	9	and	and	CCONJ
ejpam-6417	50	10	their	their	PRON
ejpam-6417	50	11	stability	stability	NOUN
ejpam-6417	50	12	characteristics	characteristic	NOUN
ejpam-6417	50	13	.	.	PUNCT
ejpam-6417	51	1	lemma	lemma	PROPN
ejpam-6417	51	2	1	1	NUM
ejpam-6417	51	3	(	(	PUNCT
ejpam-6417	51	4	[	[	X
ejpam-6417	51	5	16	16	NUM
ejpam-6417	51	6	,	,	PUNCT
ejpam-6417	51	7	17	17	NUM
ejpam-6417	51	8	]	]	PUNCT
ejpam-6417	51	9	)	)	PUNCT
ejpam-6417	51	10	.	.	PUNCT
ejpam-6417	52	1	suppose	suppose	VERB
ejpam-6417	52	2	a	a	PRON
ejpam-6417	52	3	and	and	CCONJ
ejpam-6417	52	4	b	b	NOUN
ejpam-6417	52	5	are	be	AUX
ejpam-6417	52	6	n	n	PRON
ejpam-6417	52	7	×	×	ADJ
ejpam-6417	52	8	n	n	CCONJ
ejpam-6417	52	9	positive	positive	ADJ
ejpam-6417	52	10	semidefinite	semidefinite	NOUN
ejpam-6417	52	11	matrices	matrix	NOUN
ejpam-6417	52	12	.	.	PUNCT
ejpam-6417	53	1	then	then	ADV
ejpam-6417	53	2	the	the	DET
ejpam-6417	53	3	hadamard	hadamard	ADJ
ejpam-6417	53	4	product	product	NOUN
ejpam-6417	53	5	a	a	DET
ejpam-6417	53	6	◦	◦	NOUN
ejpam-6417	53	7	b	b	NOUN
ejpam-6417	53	8	is	be	AUX
ejpam-6417	53	9	also	also	ADV
ejpam-6417	53	10	positive	positive	ADJ
ejpam-6417	53	11	semidefinite	semidefinite	NOUN
ejpam-6417	53	12	.	.	PUNCT
ejpam-6417	54	1	moreover	moreover	ADV
ejpam-6417	54	2	,	,	PUNCT
ejpam-6417	54	3	if	if	SCONJ
ejpam-6417	54	4	a	a	PRON
ejpam-6417	54	5	and	and	CCONJ
ejpam-6417	54	6	b	b	NOUN
ejpam-6417	54	7	are	be	AUX
ejpam-6417	54	8	both	both	ADV
ejpam-6417	54	9	positive	positive	ADJ
ejpam-6417	54	10	definite	definite	ADJ
ejpam-6417	54	11	,	,	PUNCT
ejpam-6417	54	12	their	their	PRON
ejpam-6417	54	13	hadamard	hadamard	ADJ
ejpam-6417	54	14	product	product	NOUN
ejpam-6417	54	15	a	a	DET
ejpam-6417	54	16	◦	◦	NOUN
ejpam-6417	54	17	b	b	NOUN
ejpam-6417	54	18	will	will	AUX
ejpam-6417	54	19	be	be	AUX
ejpam-6417	54	20	positive	positive	ADJ
ejpam-6417	54	21	definite	definite	ADJ
ejpam-6417	54	22	.	.	PUNCT
ejpam-6417	55	1	lemma	lemma	PROPN
ejpam-6417	55	2	2	2	NUM
ejpam-6417	55	3	(	(	PUNCT
ejpam-6417	55	4	[	[	X
ejpam-6417	55	5	10	10	NUM
ejpam-6417	55	6	,	,	PUNCT
ejpam-6417	55	7	12	12	NUM
ejpam-6417	55	8	]	]	PUNCT
ejpam-6417	55	9	)	)	PUNCT
ejpam-6417	55	10	.	.	PUNCT
ejpam-6417	56	1	if	if	SCONJ
ejpam-6417	56	2	a	a	DET
ejpam-6417	56	3	matrix	matrix	NOUN
ejpam-6417	56	4	a	a	DET
ejpam-6417	56	5	∈	∈	ADJ
ejpam-6417	56	6	rn×n	rn×n	NOUN
ejpam-6417	56	7	is	be	AUX
ejpam-6417	56	8	lyapunov	lyapunov	NOUN
ejpam-6417	56	9	diagonally	diagonally	ADV
ejpam-6417	56	10	stable	stable	ADJ
ejpam-6417	56	11	,	,	PUNCT
ejpam-6417	56	12	then	then	ADV
ejpam-6417	56	13	−a	−a	VERB
ejpam-6417	56	14	is	be	AUX
ejpam-6417	56	15	a	a	DET
ejpam-6417	56	16	p	p	NOUN
ejpam-6417	56	17	-matrix	-matrix	NOUN
ejpam-6417	56	18	.	.	PUNCT
ejpam-6417	57	1	let	let	VERB
ejpam-6417	57	2	a1	a1	NOUN
ejpam-6417	57	3	,	,	PUNCT
ejpam-6417	57	4	a2	a2	PROPN
ejpam-6417	57	5	,	,	PUNCT
ejpam-6417	57	6	a3	a3	NOUN
ejpam-6417	57	7	∈	∈	PROPN
ejpam-6417	57	8	rn×n	rn×n	NOUN
ejpam-6417	57	9	.	.	PUNCT
ejpam-6417	58	1	we	we	PRON
ejpam-6417	58	2	say	say	VERB
ejpam-6417	58	3	that	that	SCONJ
ejpam-6417	58	4	the	the	DET
ejpam-6417	58	5	triple	triple	ADJ
ejpam-6417	58	6	(	(	PUNCT
ejpam-6417	58	7	a1	a1	NOUN
ejpam-6417	58	8	,	,	PUNCT
ejpam-6417	58	9	a2	a2	PROPN
ejpam-6417	58	10	,	,	PUNCT
ejpam-6417	58	11	a3	a3	NOUN
ejpam-6417	58	12	)	)	PUNCT
ejpam-6417	58	13	admits	admit	VERB
ejpam-6417	58	14	a	a	DET
ejpam-6417	58	15	positive	positive	ADJ
ejpam-6417	58	16	diagonal	diagonal	ADJ
ejpam-6417	58	17	solution	solution	NOUN
ejpam-6417	58	18	if	if	SCONJ
ejpam-6417	58	19	there	there	PRON
ejpam-6417	58	20	exist	exist	VERB
ejpam-6417	58	21	positive	positive	ADJ
ejpam-6417	58	22	diagonal	diagonal	ADJ
ejpam-6417	58	23	matrices	matrix	NOUN
ejpam-6417	58	24	p1	p1	NOUN
ejpam-6417	58	25	,	,	PUNCT
ejpam-6417	58	26	p2	p2	NOUN
ejpam-6417	58	27	,	,	PUNCT
ejpam-6417	58	28	p3	p3	PROPN
ejpam-6417	58	29	∈	∈	PROPN
ejpam-6417	58	30	rn×n	rn×n	PROPN
ejpam-6417	58	31	such	such	ADJ
ejpam-6417	58	32	that	that	SCONJ
ejpam-6417	58	33	the	the	DET
ejpam-6417	58	34	block	block	NOUN
ejpam-6417	58	35	matrix	matrix	NOUN
ejpam-6417	58	36	at	at	PROPN
ejpam-6417	58	37	1	1	NUM
ejpam-6417	58	38	p1	p1	NOUN
ejpam-6417	58	39	+	+	CCONJ
ejpam-6417	58	40	p1a1	p1a1	NOUN
ejpam-6417	58	41	+	+	CCONJ
ejpam-6417	58	42	p2	p2	X
ejpam-6417	58	43	+	+	CCONJ
ejpam-6417	58	44	p3	p3	NOUN
ejpam-6417	58	45	p1a2	p1a2	X
ejpam-6417	58	46	p1a3	p1a3	NOUN
ejpam-6417	58	47	at	at	ADP
ejpam-6417	58	48	2	2	NUM
ejpam-6417	58	49	p1	p1	NOUN
ejpam-6417	58	50	−p2	−p2	PROPN
ejpam-6417	58	51	0	0	PUNCT
ejpam-6417	58	52	at	at	ADP
ejpam-6417	58	53	3	3	NUM
ejpam-6417	58	54	p1	p1	NOUN
ejpam-6417	58	55	0	0	PUNCT
ejpam-6417	59	1	−p3	−p3	ADJ
ejpam-6417	59	2			NOUN
ejpam-6417	59	3	(	(	PUNCT
ejpam-6417	59	4	1	1	X
ejpam-6417	59	5	)	)	PUNCT
ejpam-6417	59	6	is	be	AUX
ejpam-6417	59	7	negative	negative	ADJ
ejpam-6417	59	8	definite	definite	ADJ
ejpam-6417	59	9	.	.	PUNCT
ejpam-6417	60	1	furthermore	furthermore	ADV
ejpam-6417	60	2	,	,	PUNCT
ejpam-6417	60	3	we	we	PRON
ejpam-6417	60	4	say	say	VERB
ejpam-6417	60	5	that	that	SCONJ
ejpam-6417	60	6	(	(	PUNCT
ejpam-6417	60	7	p1	p1	NOUN
ejpam-6417	60	8	,	,	PUNCT
ejpam-6417	60	9	p2	p2	NOUN
ejpam-6417	60	10	,	,	PUNCT
ejpam-6417	60	11	p3	p3	PROPN
ejpam-6417	60	12	)	)	PUNCT
ejpam-6417	60	13	is	be	AUX
ejpam-6417	60	14	a	a	DET
ejpam-6417	60	15	positive	positive	ADJ
ejpam-6417	60	16	diagonal	diagonal	ADJ
ejpam-6417	60	17	solution	solution	NOUN
ejpam-6417	60	18	for	for	ADP
ejpam-6417	60	19	the	the	DET
ejpam-6417	60	20	triple	triple	ADJ
ejpam-6417	60	21	(	(	PUNCT
ejpam-6417	60	22	a1	a1	NOUN
ejpam-6417	60	23	,	,	PUNCT
ejpam-6417	60	24	a2	a2	PROPN
ejpam-6417	60	25	,	,	PUNCT
ejpam-6417	60	26	a3	a3	NOUN
ejpam-6417	60	27	)	)	PUNCT
ejpam-6417	60	28	.	.	PUNCT
ejpam-6417	61	1	lemma	lemma	PROPN
ejpam-6417	61	2	3	3	NUM
ejpam-6417	61	3	(	(	PUNCT
ejpam-6417	61	4	[	[	X
ejpam-6417	61	5	18	18	NUM
ejpam-6417	61	6	]	]	NUM
ejpam-6417	61	7	)	)	PUNCT
ejpam-6417	61	8	.	.	PUNCT
ejpam-6417	62	1	let	let	VERB
ejpam-6417	62	2	a1	a1	NOUN
ejpam-6417	62	3	,	,	PUNCT
ejpam-6417	62	4	a2	a2	PROPN
ejpam-6417	62	5	,	,	PUNCT
ejpam-6417	62	6	and	and	CCONJ
ejpam-6417	62	7	a3	a3	NOUN
ejpam-6417	62	8	be	be	VERB
ejpam-6417	62	9	real	real	ADJ
ejpam-6417	62	10	n	n	NUM
ejpam-6417	62	11	×	×	NOUN
ejpam-6417	62	12	n	n	PRON
ejpam-6417	62	13	matrices	matrix	NOUN
ejpam-6417	62	14	.	.	PUNCT
ejpam-6417	63	1	if	if	SCONJ
ejpam-6417	63	2	the	the	DET
ejpam-6417	63	3	triple	triple	ADJ
ejpam-6417	63	4	(	(	PUNCT
ejpam-6417	63	5	a1	a1	NOUN
ejpam-6417	63	6	,	,	PUNCT
ejpam-6417	63	7	a2	a2	PROPN
ejpam-6417	63	8	,	,	PUNCT
ejpam-6417	63	9	a3	a3	NOUN
ejpam-6417	63	10	)	)	PUNCT
ejpam-6417	63	11	admits	admit	VERB
ejpam-6417	63	12	a	a	DET
ejpam-6417	63	13	positive	positive	ADJ
ejpam-6417	63	14	diagonal	diagonal	ADJ
ejpam-6417	63	15	solution	solution	NOUN
ejpam-6417	63	16	,	,	PUNCT
ejpam-6417	63	17	then	then	ADV
ejpam-6417	63	18	a1	a1	NOUN
ejpam-6417	63	19	+	+	CCONJ
ejpam-6417	63	20	a2	a2	PROPN
ejpam-6417	63	21	+	+	CCONJ
ejpam-6417	63	22	a3	a3	NOUN
ejpam-6417	63	23	is	be	AUX
ejpam-6417	63	24	a	a	DET
ejpam-6417	63	25	lyapunov	lyapunov	NOUN
ejpam-6417	63	26	diagonally	diagonally	ADV
ejpam-6417	63	27	stable	stable	ADJ
ejpam-6417	63	28	matrix	matrix	NOUN
ejpam-6417	63	29	.	.	PUNCT
ejpam-6417	64	1	a.	a.	PROPN
ejpam-6417	64	2	algefary	algefary	PROPN
ejpam-6417	64	3	,	,	PUNCT
ejpam-6417	64	4	t.	t.	PROPN
ejpam-6417	64	5	alhumaidan	alhumaidan	PROPN
ejpam-6417	64	6	/	/	SYM
ejpam-6417	64	7	eur	eur	PROPN
ejpam-6417	64	8	.	.	PUNCT
ejpam-6417	65	1	j.	j.	PROPN
ejpam-6417	65	2	pure	pure	PROPN
ejpam-6417	65	3	appl	appl	PROPN
ejpam-6417	65	4	.	.	PROPN
ejpam-6417	65	5	math	math	PROPN
ejpam-6417	65	6	,	,	PUNCT
ejpam-6417	65	7	18	18	NUM
ejpam-6417	65	8	(	(	PUNCT
ejpam-6417	65	9	3	3	NUM
ejpam-6417	65	10	)	)	PUNCT
ejpam-6417	65	11	(	(	PUNCT
ejpam-6417	65	12	2025	2025	NUM
ejpam-6417	65	13	)	)	PUNCT
ejpam-6417	65	14	,	,	PUNCT
ejpam-6417	65	15	6417	6417	NUM
ejpam-6417	65	16	4	4	NUM
ejpam-6417	65	17	of	of	ADP
ejpam-6417	65	18	10	10	NUM
ejpam-6417	65	19	3	3	NUM
ejpam-6417	65	20	.	.	PUNCT
ejpam-6417	65	21	main	main	ADJ
ejpam-6417	65	22	results	result	NOUN
ejpam-6417	65	23	this	this	DET
ejpam-6417	65	24	section	section	NOUN
ejpam-6417	65	25	presents	present	VERB
ejpam-6417	65	26	our	our	PRON
ejpam-6417	65	27	key	key	ADJ
ejpam-6417	65	28	findings	finding	NOUN
ejpam-6417	65	29	on	on	ADP
ejpam-6417	65	30	positive	positive	ADJ
ejpam-6417	65	31	diagonal	diagonal	ADJ
ejpam-6417	65	32	solutions	solution	NOUN
ejpam-6417	65	33	for	for	ADP
ejpam-6417	65	34	the	the	DET
ejpam-6417	65	35	lmi	lmi	PROPN
ejpam-6417	65	36	defined	define	VERB
ejpam-6417	65	37	by	by	ADP
ejpam-6417	65	38	the	the	DET
ejpam-6417	65	39	triple	triple	ADJ
ejpam-6417	65	40	(	(	PUNCT
ejpam-6417	65	41	a1	a1	NOUN
ejpam-6417	65	42	,	,	PUNCT
ejpam-6417	65	43	a2	a2	PROPN
ejpam-6417	65	44	,	,	PUNCT
ejpam-6417	65	45	a3	a3	NOUN
ejpam-6417	65	46	)	)	PUNCT
ejpam-6417	65	47	and	and	CCONJ
ejpam-6417	65	48	the	the	DET
ejpam-6417	65	49	block	block	NOUN
ejpam-6417	65	50	matrix	matrix	NOUN
ejpam-6417	65	51	b.	b.	NOUN
ejpam-6417	65	52	extending	extend	VERB
ejpam-6417	65	53	classical	classical	ADJ
ejpam-6417	65	54	stability	stability	NOUN
ejpam-6417	65	55	criteria	criterion	NOUN
ejpam-6417	65	56	,	,	PUNCT
ejpam-6417	65	57	we	we	PRON
ejpam-6417	65	58	establish	establish	VERB
ejpam-6417	65	59	equivalent	equivalent	ADJ
ejpam-6417	65	60	conditions	condition	NOUN
ejpam-6417	65	61	linking	link	VERB
ejpam-6417	65	62	b	b	DET
ejpam-6417	65	63	negative	negative	ADJ
ejpam-6417	65	64	definiteness	definiteness	NOUN
ejpam-6417	65	65	to	to	PART
ejpam-6417	65	66	test	test	VERB
ejpam-6417	65	67	matrices	matrix	NOUN
ejpam-6417	65	68	and	and	CCONJ
ejpam-6417	65	69	p	p	NOUN
ejpam-6417	65	70	-matrix	-matrix	NOUN
ejpam-6417	65	71	properties	property	NOUN
ejpam-6417	65	72	under	under	ADP
ejpam-6417	65	73	hadamard	hadamard	ADJ
ejpam-6417	65	74	transformations	transformation	NOUN
ejpam-6417	65	75	.	.	PUNCT
ejpam-6417	66	1	we	we	PRON
ejpam-6417	66	2	begin	begin	VERB
ejpam-6417	66	3	with	with	ADP
ejpam-6417	66	4	preliminary	preliminary	ADJ
ejpam-6417	66	5	equivalences	equivalence	NOUN
ejpam-6417	66	6	(	(	PUNCT
ejpam-6417	66	7	theorems	theorem	NOUN
ejpam-6417	66	8	2.1	2.1	NUM
ejpam-6417	66	9	and	and	CCONJ
ejpam-6417	66	10	2.2	2.2	NUM
ejpam-6417	66	11	)	)	PUNCT
ejpam-6417	66	12	,	,	PUNCT
ejpam-6417	66	13	followed	follow	VERB
ejpam-6417	66	14	by	by	ADP
ejpam-6417	66	15	new	new	ADJ
ejpam-6417	66	16	characterizations	characterization	NOUN
ejpam-6417	66	17	(	(	PUNCT
ejpam-6417	66	18	theorems	theorem	NOUN
ejpam-6417	66	19	2.3	2.3	NUM
ejpam-6417	66	20	and	and	CCONJ
ejpam-6417	66	21	2.4	2.4	NUM
ejpam-6417	66	22	)	)	PUNCT
ejpam-6417	66	23	,	,	PUNCT
ejpam-6417	66	24	offering	offer	VERB
ejpam-6417	66	25	tools	tool	NOUN
ejpam-6417	66	26	for	for	ADP
ejpam-6417	66	27	stability	stability	NOUN
ejpam-6417	66	28	analysis	analysis	NOUN
ejpam-6417	66	29	in	in	ADP
ejpam-6417	66	30	multi	multi	ADJ
ejpam-6417	66	31	-	-	ADJ
ejpam-6417	66	32	matrix	matrix	ADJ
ejpam-6417	66	33	systems	system	NOUN
ejpam-6417	66	34	.	.	PUNCT
ejpam-6417	67	1	3.1	3.1	NUM
ejpam-6417	67	2	.	.	PUNCT
ejpam-6417	67	3	preliminaries	preliminary	NOUN
ejpam-6417	67	4	theorem	theorem	VERB
ejpam-6417	67	5	1	1	NUM
ejpam-6417	67	6	(	(	PUNCT
ejpam-6417	67	7	[	[	X
ejpam-6417	67	8	18	18	NUM
ejpam-6417	67	9	]	]	NUM
ejpam-6417	67	10	)	)	PUNCT
ejpam-6417	67	11	.	.	PUNCT
ejpam-6417	68	1	let	let	VERB
ejpam-6417	68	2	a1	a1	NOUN
ejpam-6417	68	3	,	,	PUNCT
ejpam-6417	68	4	a2	a2	PROPN
ejpam-6417	68	5	,	,	PUNCT
ejpam-6417	68	6	a3	a3	NOUN
ejpam-6417	68	7	∈	∈	PROPN
ejpam-6417	68	8	rn×n	rn×n	NOUN
ejpam-6417	68	9	.	.	PUNCT
ejpam-6417	69	1	then	then	ADV
ejpam-6417	69	2	,	,	PUNCT
ejpam-6417	69	3	the	the	DET
ejpam-6417	69	4	following	follow	VERB
ejpam-6417	69	5	statements	statement	NOUN
ejpam-6417	69	6	are	be	AUX
ejpam-6417	69	7	equivalent	equivalent	ADJ
ejpam-6417	69	8	:	:	PUNCT
ejpam-6417	69	9	(	(	PUNCT
ejpam-6417	69	10	i	i	NOUN
ejpam-6417	69	11	)	)	PUNCT
ejpam-6417	69	12	there	there	PRON
ejpam-6417	69	13	are	be	VERB
ejpam-6417	69	14	positive	positive	ADJ
ejpam-6417	69	15	diagonal	diagonal	ADJ
ejpam-6417	69	16	matrices	matrix	NOUN
ejpam-6417	69	17	p1	p1	NOUN
ejpam-6417	69	18	,	,	PUNCT
ejpam-6417	69	19	p2	p2	NOUN
ejpam-6417	69	20	,	,	PUNCT
ejpam-6417	69	21	and	and	CCONJ
ejpam-6417	69	22	p3	p3	NOUN
ejpam-6417	69	23	such	such	ADJ
ejpam-6417	69	24	that	that	DET
ejpam-6417	69	25	b	b	NOUN
ejpam-6417	69	26	=	=	SYM
ejpam-6417	69	27	at	at	PROPN
ejpam-6417	69	28	1	1	NUM
ejpam-6417	69	29	p1	p1	NOUN
ejpam-6417	69	30	+	+	CCONJ
ejpam-6417	69	31	p1a1	p1a1	NOUN
ejpam-6417	69	32	+	+	CCONJ
ejpam-6417	69	33	p2	p2	X
ejpam-6417	69	34	+	+	CCONJ
ejpam-6417	69	35	p3	p3	NOUN
ejpam-6417	70	1	p1a2	p1a2	X
ejpam-6417	70	2	p1a3	p1a3	NOUN
ejpam-6417	70	3	at	at	ADP
ejpam-6417	70	4	2	2	NUM
ejpam-6417	70	5	p1	p1	NOUN
ejpam-6417	70	6	−p2	−p2	PROPN
ejpam-6417	70	7	0	0	PUNCT
ejpam-6417	70	8	at	at	ADP
ejpam-6417	70	9	3	3	NUM
ejpam-6417	70	10	p1	p1	NOUN
ejpam-6417	70	11	0	0	PUNCT
ejpam-6417	71	1	−p3	−p3	VERB
ejpam-6417	71	2			NOUN
ejpam-6417	71	3	≺	≺	NOUN
ejpam-6417	71	4	0	0	NUM
ejpam-6417	71	5	.	.	PUNCT
ejpam-6417	72	1	(	(	PUNCT
ejpam-6417	72	2	2	2	NUM
ejpam-6417	72	3	)	)	PUNCT
ejpam-6417	72	4	(	(	PUNCT
ejpam-6417	72	5	ii	ii	NOUN
ejpam-6417	72	6	)	)	PUNCT
ejpam-6417	72	7	for	for	ADP
ejpam-6417	72	8	any	any	DET
ejpam-6417	72	9	nonzero	nonzero	ADJ
ejpam-6417	72	10	positive	positive	ADJ
ejpam-6417	72	11	semidefinite	semidefinite	NOUN
ejpam-6417	72	12	matrix	matrix	NOUN
ejpam-6417	72	13	h	h	PROPN
ejpam-6417	72	14	∈	∈	PROPN
ejpam-6417	72	15	r3n×3n	r3n×3n	PROPN
ejpam-6417	72	16	,	,	PUNCT
ejpam-6417	72	17	partitioned	partition	VERB
ejpam-6417	72	18	into	into	ADP
ejpam-6417	72	19	3	3	NUM
ejpam-6417	72	20	×	×	NOUN
ejpam-6417	72	21	3	3	NUM
ejpam-6417	72	22	block	block	NOUN
ejpam-6417	72	23	matrices	matrix	NOUN
ejpam-6417	72	24	with	with	ADP
ejpam-6417	72	25	each	each	DET
ejpam-6417	72	26	block	block	NOUN
ejpam-6417	72	27	in	in	ADP
ejpam-6417	72	28	rn×n	rn×n	PROPN
ejpam-6417	72	29	as	as	ADP
ejpam-6417	72	30	h	h	NOUN
ejpam-6417	72	31	=	=	SYM
ejpam-6417	72	32	h11	h11	PROPN
ejpam-6417	72	33	h12	h12	NOUN
ejpam-6417	72	34	h13	h13	NOUN
ejpam-6417	72	35	ht	ht	PROPN
ejpam-6417	72	36	12	12	NUM
ejpam-6417	72	37	h22	h22	PROPN
ejpam-6417	72	38	h23	h23	PROPN
ejpam-6417	72	39	ht	ht	PROPN
ejpam-6417	72	40	13	13	NUM
ejpam-6417	72	41	ht	ht	PROPN
ejpam-6417	72	42	23	23	NUM
ejpam-6417	72	43	h33	h33	NOUN
ejpam-6417	72	44			NOUN
ejpam-6417	72	45	,	,	PUNCT
ejpam-6417	72	46	(	(	PUNCT
ejpam-6417	72	47	3	3	X
ejpam-6417	72	48	)	)	PUNCT
ejpam-6417	72	49	satisfying	satisfy	VERB
ejpam-6417	72	50	the	the	DET
ejpam-6417	72	51	conditions	condition	NOUN
ejpam-6417	72	52	diag(h11	diag(h11	PROPN
ejpam-6417	72	53	)	)	PUNCT
ejpam-6417	72	54	≥	≥	NOUN
ejpam-6417	72	55	diag(h22	diag(h22	NOUN
ejpam-6417	72	56	)	)	PUNCT
ejpam-6417	72	57	and	and	CCONJ
ejpam-6417	72	58	diag(h11	diag(h11	PROPN
ejpam-6417	72	59	)	)	PUNCT
ejpam-6417	72	60	≥	≥	NOUN
ejpam-6417	72	61	diag(h33	diag(h33	NOUN
ejpam-6417	72	62	)	)	PUNCT
ejpam-6417	72	63	,	,	PUNCT
ejpam-6417	72	64	at	at	ADP
ejpam-6417	72	65	least	least	ADV
ejpam-6417	72	66	one	one	NUM
ejpam-6417	72	67	diagonal	diagonal	ADJ
ejpam-6417	72	68	element	element	NOUN
ejpam-6417	72	69	of	of	ADP
ejpam-6417	72	70	the	the	DET
ejpam-6417	72	71	matrix	matrix	NOUN
ejpam-6417	72	72	a1h11	a1h11	X
ejpam-6417	73	1	+	+	ADP
ejpam-6417	73	2	a2h	a2h	PROPN
ejpam-6417	73	3	t	t	PROPN
ejpam-6417	73	4	12	12	NUM
ejpam-6417	73	5	+	+	NOUN
ejpam-6417	73	6	a3h	a3h	PROPN
ejpam-6417	73	7	t	t	PROPN
ejpam-6417	73	8	13	13	NUM
ejpam-6417	73	9	is	be	AUX
ejpam-6417	73	10	negative	negative	ADJ
ejpam-6417	73	11	.	.	PUNCT
ejpam-6417	74	1	theorem	theorem	ADJ
ejpam-6417	74	2	2	2	NUM
ejpam-6417	74	3	(	(	PUNCT
ejpam-6417	74	4	[	[	X
ejpam-6417	74	5	18	18	NUM
ejpam-6417	74	6	]	]	NUM
ejpam-6417	74	7	)	)	PUNCT
ejpam-6417	74	8	.	.	PUNCT
ejpam-6417	75	1	let	let	VERB
ejpam-6417	75	2	a1	a1	NOUN
ejpam-6417	75	3	,	,	PUNCT
ejpam-6417	75	4	a2	a2	PROPN
ejpam-6417	75	5	,	,	PUNCT
ejpam-6417	75	6	a3	a3	NOUN
ejpam-6417	75	7	∈	∈	PROPN
ejpam-6417	75	8	rn×n	rn×n	NOUN
ejpam-6417	75	9	.	.	PUNCT
ejpam-6417	76	1	then	then	ADV
ejpam-6417	76	2	,	,	PUNCT
ejpam-6417	76	3	the	the	DET
ejpam-6417	76	4	following	follow	VERB
ejpam-6417	76	5	statements	statement	NOUN
ejpam-6417	76	6	are	be	AUX
ejpam-6417	76	7	equivalent	equivalent	ADJ
ejpam-6417	76	8	:	:	PUNCT
ejpam-6417	76	9	(	(	PUNCT
ejpam-6417	76	10	i	i	NOUN
ejpam-6417	76	11	)	)	PUNCT
ejpam-6417	76	12	there	there	PRON
ejpam-6417	76	13	are	be	VERB
ejpam-6417	76	14	positive	positive	ADJ
ejpam-6417	76	15	diagonal	diagonal	ADJ
ejpam-6417	76	16	matrices	matrix	NOUN
ejpam-6417	76	17	p1	p1	NOUN
ejpam-6417	76	18	,	,	PUNCT
ejpam-6417	76	19	p2	p2	NOUN
ejpam-6417	76	20	,	,	PUNCT
ejpam-6417	76	21	and	and	CCONJ
ejpam-6417	76	22	p3	p3	NOUN
ejpam-6417	76	23	such	such	ADJ
ejpam-6417	76	24	that	that	DET
ejpam-6417	76	25	b	b	NOUN
ejpam-6417	76	26	=	=	SYM
ejpam-6417	76	27	at	at	PROPN
ejpam-6417	76	28	1	1	NUM
ejpam-6417	76	29	p1	p1	NOUN
ejpam-6417	76	30	+	+	CCONJ
ejpam-6417	76	31	p1a1	p1a1	NOUN
ejpam-6417	76	32	+	+	CCONJ
ejpam-6417	76	33	p2	p2	X
ejpam-6417	76	34	+	+	CCONJ
ejpam-6417	76	35	p3	p3	NOUN
ejpam-6417	77	1	p1a2	p1a2	X
ejpam-6417	77	2	p1a3	p1a3	NOUN
ejpam-6417	77	3	at	at	ADP
ejpam-6417	77	4	2	2	NUM
ejpam-6417	77	5	p1	p1	NOUN
ejpam-6417	77	6	−p2	−p2	PROPN
ejpam-6417	77	7	0	0	PUNCT
ejpam-6417	77	8	at	at	ADP
ejpam-6417	77	9	3	3	NUM
ejpam-6417	77	10	p1	p1	NOUN
ejpam-6417	77	11	0	0	PUNCT
ejpam-6417	78	1	−p3	−p3	VERB
ejpam-6417	78	2			NOUN
ejpam-6417	78	3	≺	≺	NOUN
ejpam-6417	78	4	0	0	NUM
ejpam-6417	78	5	.	.	PUNCT
ejpam-6417	78	6	(	(	PUNCT
ejpam-6417	78	7	ii	ii	NOUN
ejpam-6417	78	8	)	)	PUNCT
ejpam-6417	78	9	for	for	ADP
ejpam-6417	78	10	any	any	DET
ejpam-6417	78	11	nonzero	nonzero	ADJ
ejpam-6417	78	12	positive	positive	ADJ
ejpam-6417	78	13	semidefinite	semidefinite	NOUN
ejpam-6417	78	14	matrix	matrix	NOUN
ejpam-6417	78	15	h	h	PROPN
ejpam-6417	78	16	∈	∈	PROPN
ejpam-6417	78	17	r3n×3n	r3n×3n	PROPN
ejpam-6417	78	18	,	,	PUNCT
ejpam-6417	78	19	partitioned	partition	VERB
ejpam-6417	78	20	into	into	ADP
ejpam-6417	78	21	3	3	NUM
ejpam-6417	78	22	×	×	NOUN
ejpam-6417	78	23	3	3	NUM
ejpam-6417	78	24	block	block	NOUN
ejpam-6417	78	25	matrices	matrix	NOUN
ejpam-6417	78	26	with	with	ADP
ejpam-6417	78	27	each	each	DET
ejpam-6417	78	28	block	block	NOUN
ejpam-6417	78	29	in	in	ADP
ejpam-6417	78	30	rn×n	rn×n	PROPN
ejpam-6417	78	31	as	as	ADP
ejpam-6417	78	32	h	h	NOUN
ejpam-6417	78	33	=	=	SYM
ejpam-6417	78	34	h11	h11	PROPN
ejpam-6417	78	35	h12	h12	NOUN
ejpam-6417	78	36	h13	h13	NOUN
ejpam-6417	78	37	ht	ht	PROPN
ejpam-6417	78	38	12	12	NUM
ejpam-6417	78	39	h22	h22	PROPN
ejpam-6417	78	40	h23	h23	PROPN
ejpam-6417	78	41	ht	ht	PROPN
ejpam-6417	78	42	13	13	NUM
ejpam-6417	78	43	ht	ht	PROPN
ejpam-6417	78	44	23	23	NUM
ejpam-6417	78	45	h33	h33	NOUN
ejpam-6417	78	46			NOUN
ejpam-6417	78	47	,	,	PUNCT
ejpam-6417	78	48	a.	a.	NOUN
ejpam-6417	78	49	algefary	algefary	ADJ
ejpam-6417	78	50	,	,	PUNCT
ejpam-6417	78	51	t.	t.	PROPN
ejpam-6417	78	52	alhumaidan	alhumaidan	PROPN
ejpam-6417	78	53	/	/	SYM
ejpam-6417	78	54	eur	eur	PROPN
ejpam-6417	78	55	.	.	PUNCT
ejpam-6417	79	1	j.	j.	PROPN
ejpam-6417	79	2	pure	pure	PROPN
ejpam-6417	79	3	appl	appl	PROPN
ejpam-6417	79	4	.	.	PROPN
ejpam-6417	79	5	math	math	PROPN
ejpam-6417	79	6	,	,	PUNCT
ejpam-6417	79	7	18	18	NUM
ejpam-6417	79	8	(	(	PUNCT
ejpam-6417	79	9	3	3	NUM
ejpam-6417	79	10	)	)	PUNCT
ejpam-6417	79	11	(	(	PUNCT
ejpam-6417	79	12	2025	2025	NUM
ejpam-6417	79	13	)	)	PUNCT
ejpam-6417	79	14	,	,	PUNCT
ejpam-6417	79	15	6417	6417	NUM
ejpam-6417	79	16	5	5	NUM
ejpam-6417	79	17	of	of	ADP
ejpam-6417	79	18	10	10	NUM
ejpam-6417	79	19	satisfying	satisfy	VERB
ejpam-6417	79	20	the	the	DET
ejpam-6417	79	21	conditions	condition	NOUN
ejpam-6417	79	22	diag(h11	diag(h11	PROPN
ejpam-6417	79	23	)	)	PUNCT
ejpam-6417	79	24	=	=	SYM
ejpam-6417	80	1	diag(h22	diag(h22	PROPN
ejpam-6417	80	2	)	)	PUNCT
ejpam-6417	80	3	=	=	SYM
ejpam-6417	80	4	diag(h33	diag(h33	PROPN
ejpam-6417	80	5	)	)	PUNCT
ejpam-6417	80	6	,	,	PUNCT
ejpam-6417	80	7	at	at	ADP
ejpam-6417	80	8	least	least	ADV
ejpam-6417	80	9	one	one	NUM
ejpam-6417	80	10	diagonal	diagonal	ADJ
ejpam-6417	80	11	element	element	NOUN
ejpam-6417	80	12	of	of	ADP
ejpam-6417	80	13	the	the	DET
ejpam-6417	80	14	matrix	matrix	NOUN
ejpam-6417	80	15	a1h11	a1h11	X
ejpam-6417	81	1	+	+	ADP
ejpam-6417	81	2	a2h	a2h	PROPN
ejpam-6417	81	3	t	t	PROPN
ejpam-6417	81	4	12	12	NUM
ejpam-6417	81	5	+	+	NOUN
ejpam-6417	81	6	a3h	a3h	PROPN
ejpam-6417	81	7	t	t	PROPN
ejpam-6417	81	8	13	13	NUM
ejpam-6417	81	9	is	be	AUX
ejpam-6417	81	10	negative	negative	ADJ
ejpam-6417	81	11	.	.	PUNCT
ejpam-6417	82	1	3.2	3.2	NUM
ejpam-6417	82	2	.	.	PUNCT
ejpam-6417	83	1	new	new	ADJ
ejpam-6417	83	2	characterizations	characterization	NOUN
ejpam-6417	83	3	theorem	theorem	VERB
ejpam-6417	83	4	3	3	X
ejpam-6417	83	5	.	.	PUNCT
ejpam-6417	84	1	let	let	VERB
ejpam-6417	84	2	a1	a1	NOUN
ejpam-6417	84	3	,	,	PUNCT
ejpam-6417	84	4	a2	a2	PROPN
ejpam-6417	84	5	,	,	PUNCT
ejpam-6417	84	6	a3	a3	NOUN
ejpam-6417	84	7	∈	∈	PROPN
ejpam-6417	84	8	rn×n	rn×n	NOUN
ejpam-6417	84	9	.	.	PUNCT
ejpam-6417	85	1	the	the	DET
ejpam-6417	85	2	triple	triple	ADJ
ejpam-6417	85	3	(	(	PUNCT
ejpam-6417	85	4	a1	a1	NOUN
ejpam-6417	85	5	,	,	PUNCT
ejpam-6417	85	6	a2	a2	PROPN
ejpam-6417	85	7	,	,	PUNCT
ejpam-6417	85	8	a3	a3	NOUN
ejpam-6417	85	9	)	)	PUNCT
ejpam-6417	85	10	admits	admit	VERB
ejpam-6417	85	11	a	a	DET
ejpam-6417	85	12	positive	positive	ADJ
ejpam-6417	85	13	diagonal	diagonal	ADJ
ejpam-6417	85	14	solution	solution	NOUN
ejpam-6417	85	15	with	with	ADP
ejpam-6417	85	16	respect	respect	NOUN
ejpam-6417	85	17	to	to	ADP
ejpam-6417	85	18	(	(	PUNCT
ejpam-6417	85	19	1	1	X
ejpam-6417	85	20	)	)	PUNCT
ejpam-6417	85	21	if	if	SCONJ
ejpam-6417	85	22	and	and	CCONJ
ejpam-6417	85	23	only	only	ADV
ejpam-6417	85	24	if	if	SCONJ
ejpam-6417	85	25	the	the	DET
ejpam-6417	85	26	triple	triple	ADJ
ejpam-6417	85	27	(	(	PUNCT
ejpam-6417	85	28	a1	a1	NOUN
ejpam-6417	85	29	◦	◦	NOUN
ejpam-6417	85	30	s11	s11	NOUN
ejpam-6417	85	31	,	,	PUNCT
ejpam-6417	85	32	a2	a2	PROPN
ejpam-6417	85	33	◦	◦	PROPN
ejpam-6417	85	34	s12	s12	PROPN
ejpam-6417	85	35	,	,	PUNCT
ejpam-6417	85	36	a3	a3	NOUN
ejpam-6417	85	37	◦	◦	PROPN
ejpam-6417	85	38	s13	s13	PROPN
ejpam-6417	85	39	)	)	PUNCT
ejpam-6417	85	40	also	also	ADV
ejpam-6417	85	41	admits	admit	VERB
ejpam-6417	85	42	a	a	DET
ejpam-6417	85	43	positive	positive	ADJ
ejpam-6417	85	44	diagonal	diagonal	ADJ
ejpam-6417	85	45	solution	solution	NOUN
ejpam-6417	85	46	with	with	ADP
ejpam-6417	85	47	respect	respect	NOUN
ejpam-6417	85	48	to	to	ADP
ejpam-6417	85	49	(	(	PUNCT
ejpam-6417	85	50	1	1	NUM
ejpam-6417	85	51	)	)	PUNCT
ejpam-6417	85	52	for	for	ADP
ejpam-6417	85	53	any	any	DET
ejpam-6417	85	54	positive	positive	ADJ
ejpam-6417	85	55	semidefinite	semidefinite	NOUN
ejpam-6417	85	56	matrix	matrix	NOUN
ejpam-6417	85	57	s	s	PART
ejpam-6417	85	58	∈	∈	NOUN
ejpam-6417	85	59	r3n×3n	r3n×3n	NOUN
ejpam-6417	85	60	of	of	ADP
ejpam-6417	85	61	the	the	DET
ejpam-6417	85	62	form	form	NOUN
ejpam-6417	85	63	s	s	PART
ejpam-6417	85	64	=	=	SYM
ejpam-6417	85	65	s11	s11	PROPN
ejpam-6417	85	66	s12	s12	PROPN
ejpam-6417	85	67	s13	s13	PROPN
ejpam-6417	85	68	st	st	PROPN
ejpam-6417	85	69	12	12	NUM
ejpam-6417	85	70	s22	s22	PROPN
ejpam-6417	85	71	s23	s23	PROPN
ejpam-6417	85	72	st	st	PROPN
ejpam-6417	85	73	13	13	NUM
ejpam-6417	85	74	st	st	PROPN
ejpam-6417	85	75	23	23	NUM
ejpam-6417	85	76	s33	s33	NOUN
ejpam-6417	85	77			NOUN
ejpam-6417	85	78	,	,	PUNCT
ejpam-6417	85	79	where	where	SCONJ
ejpam-6417	85	80	s11	s11	PROPN
ejpam-6417	85	81	,	,	PUNCT
ejpam-6417	85	82	s22	s22	NOUN
ejpam-6417	85	83	,	,	PUNCT
ejpam-6417	85	84	s33	s33	PROPN
ejpam-6417	85	85	satisfy	satisfy	VERB
ejpam-6417	85	86	the	the	DET
ejpam-6417	85	87	condition	condition	NOUN
ejpam-6417	85	88	diag(s11	diag(s11	PROPN
ejpam-6417	85	89	)	)	PUNCT
ejpam-6417	85	90	=	=	SYM
ejpam-6417	85	91	diag(s22	diag(s22	PROPN
ejpam-6417	85	92	)	)	PUNCT
ejpam-6417	85	93	=	=	SYM
ejpam-6417	85	94	diag(s33	diag(s33	PROPN
ejpam-6417	85	95	)	)	PUNCT
ejpam-6417	86	1	≫	≫	NOUN
ejpam-6417	86	2	0	0	NUM
ejpam-6417	86	3	.	.	PUNCT
ejpam-6417	87	1	proof	proof	NOUN
ejpam-6417	87	2	.	.	PUNCT
ejpam-6417	88	1	necessity	necessity	NOUN
ejpam-6417	88	2	:	:	PUNCT
ejpam-6417	88	3	suppose	suppose	VERB
ejpam-6417	88	4	that	that	SCONJ
ejpam-6417	88	5	h	h	NOUN
ejpam-6417	88	6	is	be	AUX
ejpam-6417	88	7	a	a	DET
ejpam-6417	88	8	nonzero	nonzero	ADJ
ejpam-6417	88	9	positive	positive	ADJ
ejpam-6417	88	10	semidefinite	semidefinite	NOUN
ejpam-6417	88	11	matrix	matrix	NOUN
ejpam-6417	88	12	in	in	ADP
ejpam-6417	88	13	r3n×3n	r3n×3n	PROPN
ejpam-6417	88	14	in	in	ADP
ejpam-6417	88	15	the	the	DET
ejpam-6417	88	16	form	form	NOUN
ejpam-6417	88	17	h	h	NOUN
ejpam-6417	88	18	=	=	SYM
ejpam-6417	88	19	h11	h11	NUM
ejpam-6417	88	20	h12	h12	NOUN
ejpam-6417	88	21	h13	h13	NOUN
ejpam-6417	88	22	ht	ht	PROPN
ejpam-6417	88	23	12	12	NUM
ejpam-6417	88	24	h22	h22	PROPN
ejpam-6417	88	25	h23	h23	PROPN
ejpam-6417	88	26	ht	ht	PROPN
ejpam-6417	88	27	13	13	NUM
ejpam-6417	88	28	ht	ht	PROPN
ejpam-6417	88	29	23	23	NUM
ejpam-6417	88	30	h33	h33	NOUN
ejpam-6417	88	31			NOUN
ejpam-6417	88	32	,	,	PUNCT
ejpam-6417	88	33	with	with	ADP
ejpam-6417	88	34	diag(h11	diag(h11	PROPN
ejpam-6417	88	35	)	)	PUNCT
ejpam-6417	88	36	=	=	SYM
ejpam-6417	89	1	diag(h22	diag(h22	PROPN
ejpam-6417	89	2	)	)	PUNCT
ejpam-6417	89	3	=	=	SYM
ejpam-6417	89	4	diag(h33	diag(h33	PROPN
ejpam-6417	89	5	)	)	PUNCT
ejpam-6417	89	6	.	.	PUNCT
ejpam-6417	90	1	now	now	ADV
ejpam-6417	90	2	,	,	PUNCT
ejpam-6417	90	3	define	define	VERB
ejpam-6417	90	4	the	the	DET
ejpam-6417	90	5	matrix	matrix	NOUN
ejpam-6417	90	6	k	k	NOUN
ejpam-6417	90	7	=	=	PUNCT
ejpam-6417	90	8	s	s	PART
ejpam-6417	90	9	◦	◦	NOUN
ejpam-6417	90	10	h.	h.	NOUN
ejpam-6417	90	11	according	accord	VERB
ejpam-6417	90	12	to	to	ADP
ejpam-6417	90	13	lemma	lemma	PROPN
ejpam-6417	90	14	1	1	NUM
ejpam-6417	90	15	,	,	PUNCT
ejpam-6417	90	16	k	k	PROPN
ejpam-6417	90	17	is	be	AUX
ejpam-6417	90	18	a	a	DET
ejpam-6417	90	19	positive	positive	ADJ
ejpam-6417	90	20	semidefinite	semidefinite	NOUN
ejpam-6417	90	21	matrix	matrix	NOUN
ejpam-6417	90	22	.	.	PUNCT
ejpam-6417	91	1	furthermore	furthermore	ADV
ejpam-6417	91	2	,	,	PUNCT
ejpam-6417	91	3	as	as	SCONJ
ejpam-6417	91	4	the	the	DET
ejpam-6417	91	5	diagonal	diagonal	ADJ
ejpam-6417	91	6	entries	entry	NOUN
ejpam-6417	91	7	of	of	ADP
ejpam-6417	91	8	s	s	NOUN
ejpam-6417	91	9	are	be	AUX
ejpam-6417	91	10	strictly	strictly	ADV
ejpam-6417	91	11	positive	positive	ADJ
ejpam-6417	91	12	and	and	CCONJ
ejpam-6417	91	13	h	h	NOUN
ejpam-6417	91	14	is	be	AUX
ejpam-6417	91	15	a	a	DET
ejpam-6417	91	16	nonzero	nonzero	NOUN
ejpam-6417	91	17	matrix	matrix	NOUN
ejpam-6417	91	18	,	,	PUNCT
ejpam-6417	91	19	then	then	ADV
ejpam-6417	91	20	k	k	PROPN
ejpam-6417	91	21	must	must	AUX
ejpam-6417	91	22	be	be	AUX
ejpam-6417	91	23	a	a	DET
ejpam-6417	91	24	nonzero	nonzero	ADJ
ejpam-6417	91	25	matrix	matrix	NOUN
ejpam-6417	91	26	.	.	PUNCT
ejpam-6417	92	1	additionally	additionally	ADV
ejpam-6417	92	2	,	,	PUNCT
ejpam-6417	92	3	by	by	ADP
ejpam-6417	92	4	the	the	DET
ejpam-6417	92	5	conditions	condition	NOUN
ejpam-6417	92	6	diag(h11	diag(h11	PROPN
ejpam-6417	92	7	)	)	PUNCT
ejpam-6417	92	8	=	=	SYM
ejpam-6417	92	9	diag(h22	diag(h22	PROPN
ejpam-6417	92	10	)	)	PUNCT
ejpam-6417	92	11	=	=	SYM
ejpam-6417	92	12	diag(h33	diag(h33	PROPN
ejpam-6417	92	13	)	)	PUNCT
ejpam-6417	92	14	and	and	CCONJ
ejpam-6417	92	15	diag(s11	diag(s11	PROPN
ejpam-6417	92	16	)	)	PUNCT
ejpam-6417	92	17	=	=	SYM
ejpam-6417	92	18	diag(s22	diag(s22	PROPN
ejpam-6417	92	19	)	)	PUNCT
ejpam-6417	92	20	=	=	SYM
ejpam-6417	92	21	diag(s33	diag(s33	PROPN
ejpam-6417	92	22	)	)	PUNCT
ejpam-6417	92	23	,	,	PUNCT
ejpam-6417	92	24	it	it	PRON
ejpam-6417	92	25	is	be	AUX
ejpam-6417	92	26	clear	clear	ADJ
ejpam-6417	92	27	that	that	SCONJ
ejpam-6417	92	28	the	the	DET
ejpam-6417	92	29	same	same	ADJ
ejpam-6417	92	30	condition	condition	NOUN
ejpam-6417	92	31	holds	hold	VERB
ejpam-6417	92	32	for	for	ADP
ejpam-6417	92	33	k	k	PROPN
ejpam-6417	92	34	as	as	ADV
ejpam-6417	92	35	well	well	ADV
ejpam-6417	92	36	,	,	PUNCT
ejpam-6417	92	37	i.e.	i.e.	X
ejpam-6417	92	38	,	,	PUNCT
ejpam-6417	92	39	diag(k11	diag(k11	NOUN
ejpam-6417	92	40	)	)	PUNCT
ejpam-6417	92	41	=	=	SYM
ejpam-6417	92	42	diag(k22	diag(k22	PROPN
ejpam-6417	92	43	)	)	PUNCT
ejpam-6417	93	1	=	=	SYM
ejpam-6417	93	2	diag(k33	diag(k33	PROPN
ejpam-6417	93	3	)	)	PUNCT
ejpam-6417	93	4	.	.	PUNCT
ejpam-6417	94	1	since	since	SCONJ
ejpam-6417	94	2	,	,	PUNCT
ejpam-6417	94	3	by	by	ADP
ejpam-6417	94	4	assumption	assumption	NOUN
ejpam-6417	94	5	,	,	PUNCT
ejpam-6417	94	6	the	the	DET
ejpam-6417	94	7	triple	triple	ADJ
ejpam-6417	94	8	(	(	PUNCT
ejpam-6417	94	9	a1	a1	NOUN
ejpam-6417	94	10	,	,	PUNCT
ejpam-6417	94	11	a2	a2	PROPN
ejpam-6417	94	12	,	,	PUNCT
ejpam-6417	94	13	a3	a3	NOUN
ejpam-6417	94	14	)	)	PUNCT
ejpam-6417	94	15	admits	admit	VERB
ejpam-6417	94	16	a	a	DET
ejpam-6417	94	17	positive	positive	ADJ
ejpam-6417	94	18	diagonal	diagonal	ADJ
ejpam-6417	94	19	solution	solution	NOUN
ejpam-6417	94	20	with	with	ADP
ejpam-6417	94	21	respect	respect	NOUN
ejpam-6417	94	22	to	to	ADP
ejpam-6417	94	23	(	(	PUNCT
ejpam-6417	94	24	1	1	NUM
ejpam-6417	94	25	)	)	PUNCT
ejpam-6417	94	26	,	,	PUNCT
ejpam-6417	94	27	then	then	ADV
ejpam-6417	94	28	,	,	PUNCT
ejpam-6417	94	29	by	by	ADP
ejpam-6417	94	30	theorem	theorem	NOUN
ejpam-6417	94	31	1	1	NUM
ejpam-6417	94	32	,	,	PUNCT
ejpam-6417	94	33	the	the	DET
ejpam-6417	94	34	matrix	matrix	NOUN
ejpam-6417	94	35	a1k11	a1k11	VERB
ejpam-6417	94	36	+	+	ADJ
ejpam-6417	94	37	a2k	a2k	ADJ
ejpam-6417	94	38	t	t	X
ejpam-6417	94	39	12	12	NUM
ejpam-6417	95	1	+	+	NOUN
ejpam-6417	95	2	a3k	a3k	PROPN
ejpam-6417	95	3	t	t	NOUN
ejpam-6417	95	4	13	13	NUM
ejpam-6417	95	5	a.	a.	NOUN
ejpam-6417	95	6	algefary	algefary	ADJ
ejpam-6417	95	7	,	,	PUNCT
ejpam-6417	95	8	t.	t.	PROPN
ejpam-6417	95	9	alhumaidan	alhumaidan	PROPN
ejpam-6417	95	10	/	/	SYM
ejpam-6417	95	11	eur	eur	PROPN
ejpam-6417	95	12	.	.	PUNCT
ejpam-6417	96	1	j.	j.	PROPN
ejpam-6417	96	2	pure	pure	PROPN
ejpam-6417	96	3	appl	appl	PROPN
ejpam-6417	96	4	.	.	PROPN
ejpam-6417	96	5	math	math	PROPN
ejpam-6417	96	6	,	,	PUNCT
ejpam-6417	96	7	18	18	NUM
ejpam-6417	96	8	(	(	PUNCT
ejpam-6417	96	9	3	3	NUM
ejpam-6417	96	10	)	)	PUNCT
ejpam-6417	96	11	(	(	PUNCT
ejpam-6417	96	12	2025	2025	NUM
ejpam-6417	96	13	)	)	PUNCT
ejpam-6417	96	14	,	,	PUNCT
ejpam-6417	96	15	6417	6417	NUM
ejpam-6417	96	16	6	6	NUM
ejpam-6417	96	17	of	of	ADP
ejpam-6417	96	18	10	10	NUM
ejpam-6417	96	19	has	have	VERB
ejpam-6417	96	20	at	at	ADV
ejpam-6417	96	21	least	least	ADV
ejpam-6417	96	22	one	one	NUM
ejpam-6417	96	23	diagonal	diagonal	ADJ
ejpam-6417	96	24	element	element	NOUN
ejpam-6417	96	25	that	that	PRON
ejpam-6417	96	26	is	be	AUX
ejpam-6417	96	27	less	less	ADJ
ejpam-6417	96	28	than	than	ADP
ejpam-6417	96	29	zero	zero	NUM
ejpam-6417	96	30	.	.	PUNCT
ejpam-6417	97	1	next	next	ADV
ejpam-6417	97	2	,	,	PUNCT
ejpam-6417	97	3	observe	observe	VERB
ejpam-6417	97	4	thatk11	thatk11	NOUN
ejpam-6417	97	5	=	=	SYM
ejpam-6417	97	6	s11	s11	PROPN
ejpam-6417	97	7	◦	◦	PROPN
ejpam-6417	97	8	h11	h11	PROPN
ejpam-6417	97	9	,	,	PUNCT
ejpam-6417	97	10	k12	k12	PROPN
ejpam-6417	97	11	=	=	SYM
ejpam-6417	97	12	s12	s12	PROPN
ejpam-6417	97	13	◦	◦	NOUN
ejpam-6417	97	14	h12	h12	NOUN
ejpam-6417	97	15	,	,	PUNCT
ejpam-6417	97	16	and	and	CCONJ
ejpam-6417	97	17	k13	k13	NOUN
ejpam-6417	97	18	=	=	SYM
ejpam-6417	97	19	s13	s13	NOUN
ejpam-6417	97	20	◦	◦	NOUN
ejpam-6417	97	21	h13	h13	NOUN
ejpam-6417	97	22	.	.	PUNCT
ejpam-6417	98	1	moreover	moreover	ADV
ejpam-6417	98	2	,	,	PUNCT
ejpam-6417	98	3	for	for	ADP
ejpam-6417	98	4	every	every	DET
ejpam-6417	98	5	k	k	PROPN
ejpam-6417	98	6	∈	∈	PROPN
ejpam-6417	98	7	{	{	PUNCT
ejpam-6417	98	8	1	1	NUM
ejpam-6417	98	9	,	,	PUNCT
ejpam-6417	98	10	.	.	PUNCT
ejpam-6417	98	11	.	.	PUNCT
ejpam-6417	98	12	.	.	PUNCT
ejpam-6417	98	13	,	,	PUNCT
ejpam-6417	98	14	n	n	CCONJ
ejpam-6417	98	15	}	}	PUNCT
ejpam-6417	98	16	,	,	PUNCT
ejpam-6417	98	17	we	we	PRON
ejpam-6417	98	18	have	have	VERB
ejpam-6417	98	19	(	(	PUNCT
ejpam-6417	98	20	a1k11)kk	a1k11)kk	NOUN
ejpam-6417	98	21	=	=	SYM
ejpam-6417	98	22	(	(	PUNCT
ejpam-6417	98	23	a1(s11	a1(s11	NOUN
ejpam-6417	98	24	◦	◦	NOUN
ejpam-6417	98	25	h11))kk	h11))kk	NOUN
ejpam-6417	99	1	=	=	SYM
ejpam-6417	99	2	n∑	n∑	NOUN
ejpam-6417	99	3	i=1	i=1	PROPN
ejpam-6417	99	4	a1ki(s11	a1ki(s11	AUX
ejpam-6417	99	5	◦	◦	NOUN
ejpam-6417	99	6	h11)ik	h11)ik	NOUN
ejpam-6417	99	7	=	=	SYM
ejpam-6417	99	8	n∑	n∑	PROPN
ejpam-6417	99	9	i=1	i=1	PROPN
ejpam-6417	100	1	a1kis	a1kis	PROPN
ejpam-6417	100	2	11	11	NUM
ejpam-6417	101	1	ikh	ikh	PROPN
ejpam-6417	101	2	11	11	NUM
ejpam-6417	101	3	ik	ik	PROPN
ejpam-6417	101	4	=	=	PROPN
ejpam-6417	101	5	n∑	n∑	PROPN
ejpam-6417	101	6	i=1	i=1	PROPN
ejpam-6417	101	7	a1kis	a1kis	PROPN
ejpam-6417	101	8	11	11	NUM
ejpam-6417	101	9	kih	kih	PROPN
ejpam-6417	101	10	11	11	NUM
ejpam-6417	101	11	ik	ik	PROPN
ejpam-6417	101	12	=	=	PROPN
ejpam-6417	101	13	n∑	n∑	PROPN
ejpam-6417	101	14	i=1	i=1	PROPN
ejpam-6417	102	1	(	(	PUNCT
ejpam-6417	102	2	a1	a1	NOUN
ejpam-6417	102	3	◦	◦	NOUN
ejpam-6417	102	4	s11)kih	s11)kih	ADJ
ejpam-6417	102	5	11	11	NUM
ejpam-6417	102	6	ik	ik	X
ejpam-6417	102	7	=	=	SYM
ejpam-6417	102	8	(	(	PUNCT
ejpam-6417	102	9	(	(	PUNCT
ejpam-6417	102	10	a1	a1	NOUN
ejpam-6417	102	11	◦	◦	NOUN
ejpam-6417	102	12	s11)h11)kk	s11)h11)kk	AUX
ejpam-6417	102	13	.	.	PUNCT
ejpam-6417	103	1	similarly	similarly	ADV
ejpam-6417	103	2	,	,	PUNCT
ejpam-6417	103	3	we	we	PRON
ejpam-6417	103	4	have	have	VERB
ejpam-6417	103	5	(	(	PUNCT
ejpam-6417	103	6	a2k	a2k	X
ejpam-6417	103	7	t	t	NOUN
ejpam-6417	103	8	12)kk	12)kk	NUM
ejpam-6417	104	1	=	=	SYM
ejpam-6417	105	1	(	(	PUNCT
ejpam-6417	105	2	a2(s	a2(s	NOUN
ejpam-6417	105	3	t	t	PROPN
ejpam-6417	105	4	12	12	NUM
ejpam-6417	105	5	◦	◦	NOUN
ejpam-6417	105	6	ht	ht	PROPN
ejpam-6417	105	7	12))kk	12))kk	NUM
ejpam-6417	106	1	=	=	SYM
ejpam-6417	106	2	n∑	n∑	PROPN
ejpam-6417	106	3	i=1	i=1	PROPN
ejpam-6417	107	1	a2ki(s	a2ki(s	ADV
ejpam-6417	107	2	t	t	PROPN
ejpam-6417	107	3	12	12	NUM
ejpam-6417	107	4	◦	◦	NOUN
ejpam-6417	107	5	ht	ht	PROPN
ejpam-6417	107	6	12)ik	12)ik	NUM
ejpam-6417	108	1	=	=	SYM
ejpam-6417	108	2	n∑	n∑	PROPN
ejpam-6417	108	3	i=1	i=1	PROPN
ejpam-6417	109	1	a2kis	a2kis	PROPN
ejpam-6417	109	2	12	12	NUM
ejpam-6417	109	3	kih	kih	PROPN
ejpam-6417	109	4	12	12	NUM
ejpam-6417	110	1	ki	ki	PROPN
ejpam-6417	110	2	=	=	SYM
ejpam-6417	111	1	n∑	n∑	PROPN
ejpam-6417	111	2	i=1	i=1	PROPN
ejpam-6417	111	3	(	(	PUNCT
ejpam-6417	111	4	a2	a2	PROPN
ejpam-6417	111	5	◦	◦	PROPN
ejpam-6417	111	6	s12)kih	s12)kih	PROPN
ejpam-6417	112	1	12	12	NUM
ejpam-6417	112	2	ki	ki	PROPN
ejpam-6417	113	1	=	=	SYM
ejpam-6417	114	1	(	(	PUNCT
ejpam-6417	114	2	(	(	PUNCT
ejpam-6417	114	3	a2	a2	PROPN
ejpam-6417	114	4	◦	◦	PROPN
ejpam-6417	114	5	s12)h	s12)h	PROPN
ejpam-6417	114	6	t	t	PROPN
ejpam-6417	114	7	12)kk	12)kk	NUM
ejpam-6417	114	8	,	,	PUNCT
ejpam-6417	114	9	and	and	CCONJ
ejpam-6417	114	10	using	use	VERB
ejpam-6417	114	11	the	the	DET
ejpam-6417	114	12	same	same	ADJ
ejpam-6417	114	13	computations	computation	NOUN
ejpam-6417	114	14	,	,	PUNCT
ejpam-6417	114	15	we	we	PRON
ejpam-6417	114	16	obtain	obtain	VERB
ejpam-6417	114	17	that	that	SCONJ
ejpam-6417	114	18	(	(	PUNCT
ejpam-6417	114	19	a3k	a3k	ADJ
ejpam-6417	114	20	t	t	NOUN
ejpam-6417	114	21	13)kk	13)kk	NUM
ejpam-6417	115	1	=	=	SYM
ejpam-6417	115	2	(	(	PUNCT
ejpam-6417	115	3	(	(	PUNCT
ejpam-6417	115	4	a3	a3	NOUN
ejpam-6417	115	5	◦	◦	NOUN
ejpam-6417	115	6	s13)h	s13)h	PROPN
ejpam-6417	115	7	t	t	NOUN
ejpam-6417	115	8	13)kk	13)kk	NUM
ejpam-6417	115	9	.	.	PUNCT
ejpam-6417	116	1	since	since	SCONJ
ejpam-6417	116	2	a1k11	a1k11	PRON
ejpam-6417	116	3	+	+	ADJ
ejpam-6417	116	4	a2k	a2k	ADJ
ejpam-6417	116	5	t	t	X
ejpam-6417	116	6	12	12	NUM
ejpam-6417	117	1	+	+	NOUN
ejpam-6417	117	2	a3k	a3k	ADJ
ejpam-6417	117	3	t	t	NOUN
ejpam-6417	117	4	13	13	NUM
ejpam-6417	117	5	has	have	VERB
ejpam-6417	117	6	at	at	ADV
ejpam-6417	117	7	least	least	ADV
ejpam-6417	117	8	one	one	NUM
ejpam-6417	117	9	diagonal	diagonal	ADJ
ejpam-6417	117	10	element	element	NOUN
ejpam-6417	117	11	,	,	PUNCT
ejpam-6417	117	12	i.e.	i.e.	X
ejpam-6417	117	13	,	,	PUNCT
ejpam-6417	117	14	there	there	PRON
ejpam-6417	117	15	is	be	VERB
ejpam-6417	117	16	some	some	DET
ejpam-6417	117	17	k	k	PROPN
ejpam-6417	117	18	∈	∈	PROPN
ejpam-6417	117	19	{	{	PUNCT
ejpam-6417	117	20	1	1	NUM
ejpam-6417	117	21	,	,	PUNCT
ejpam-6417	117	22	.	.	PUNCT
ejpam-6417	117	23	.	.	PUNCT
ejpam-6417	118	1	.	.	PUNCT
ejpam-6417	119	1	,	,	PUNCT
ejpam-6417	120	1	n	n	CCONJ
ejpam-6417	120	2	}	}	PUNCT
ejpam-6417	120	3	such	such	ADJ
ejpam-6417	120	4	that	that	SCONJ
ejpam-6417	120	5	(	(	PUNCT
ejpam-6417	120	6	a1k11	a1k11	VERB
ejpam-6417	120	7	+	+	ADJ
ejpam-6417	120	8	a2k	a2k	ADJ
ejpam-6417	120	9	t	t	X
ejpam-6417	120	10	12	12	NUM
ejpam-6417	121	1	+	+	NOUN
ejpam-6417	121	2	a3k	a3k	ADJ
ejpam-6417	121	3	t	t	NOUN
ejpam-6417	121	4	13)kk	13)kk	NUM
ejpam-6417	121	5	<	<	X
ejpam-6417	121	6	0	0	NUM
ejpam-6417	121	7	,	,	PUNCT
ejpam-6417	121	8	hence	hence	ADV
ejpam-6417	121	9	,	,	PUNCT
ejpam-6417	121	10	it	it	PRON
ejpam-6417	121	11	follows	follow	VERB
ejpam-6417	121	12	that	that	SCONJ
ejpam-6417	121	13	(	(	PUNCT
ejpam-6417	121	14	(	(	PUNCT
ejpam-6417	121	15	a1	a1	NOUN
ejpam-6417	121	16	◦	◦	NOUN
ejpam-6417	121	17	s11)h11)kk	s11)h11)kk	X
ejpam-6417	121	18	+	+	CCONJ
ejpam-6417	121	19	(	(	PUNCT
ejpam-6417	121	20	(	(	PUNCT
ejpam-6417	121	21	a2	a2	PROPN
ejpam-6417	121	22	◦	◦	PROPN
ejpam-6417	121	23	s12)h	s12)h	PROPN
ejpam-6417	121	24	t	t	PROPN
ejpam-6417	121	25	12)kk	12)kk	NUM
ejpam-6417	122	1	+	+	CCONJ
ejpam-6417	122	2	(	(	PUNCT
ejpam-6417	122	3	(	(	PUNCT
ejpam-6417	122	4	a3	a3	NOUN
ejpam-6417	122	5	◦	◦	NOUN
ejpam-6417	122	6	s13)h	s13)h	PROPN
ejpam-6417	122	7	t	t	NOUN
ejpam-6417	122	8	13)kk	13)kk	NUM
ejpam-6417	122	9	<	<	X
ejpam-6417	122	10	0	0	X
ejpam-6417	122	11	.	.	PUNCT
ejpam-6417	123	1	finally	finally	ADV
ejpam-6417	123	2	,	,	PUNCT
ejpam-6417	123	3	using	use	VERB
ejpam-6417	123	4	theorem	theorem	NOUN
ejpam-6417	123	5	2	2	NUM
ejpam-6417	123	6	,	,	PUNCT
ejpam-6417	123	7	this	this	PRON
ejpam-6417	123	8	implies	imply	VERB
ejpam-6417	123	9	that	that	SCONJ
ejpam-6417	123	10	the	the	DET
ejpam-6417	123	11	triple	triple	ADJ
ejpam-6417	123	12	(	(	PUNCT
ejpam-6417	123	13	a1	a1	NOUN
ejpam-6417	123	14	◦	◦	NOUN
ejpam-6417	123	15	s11	s11	NOUN
ejpam-6417	123	16	,	,	PUNCT
ejpam-6417	123	17	a2	a2	PROPN
ejpam-6417	123	18	◦	◦	PROPN
ejpam-6417	123	19	s12	s12	PROPN
ejpam-6417	123	20	,	,	PUNCT
ejpam-6417	123	21	a3	a3	NOUN
ejpam-6417	123	22	◦	◦	PROPN
ejpam-6417	123	23	s13	s13	PROPN
ejpam-6417	123	24	)	)	PUNCT
ejpam-6417	123	25	admits	admit	VERB
ejpam-6417	123	26	a	a	DET
ejpam-6417	123	27	positive	positive	ADJ
ejpam-6417	123	28	diagonal	diagonal	ADJ
ejpam-6417	123	29	solution	solution	NOUN
ejpam-6417	123	30	with	with	ADP
ejpam-6417	123	31	respect	respect	NOUN
ejpam-6417	123	32	to	to	ADP
ejpam-6417	123	33	(	(	PUNCT
ejpam-6417	123	34	1	1	NUM
ejpam-6417	123	35	)	)	PUNCT
ejpam-6417	123	36	.	.	PUNCT
ejpam-6417	124	1	a.	a.	PROPN
ejpam-6417	124	2	algefary	algefary	PROPN
ejpam-6417	124	3	,	,	PUNCT
ejpam-6417	124	4	t.	t.	PROPN
ejpam-6417	124	5	alhumaidan	alhumaidan	PROPN
ejpam-6417	124	6	/	/	SYM
ejpam-6417	124	7	eur	eur	PROPN
ejpam-6417	124	8	.	.	PUNCT
ejpam-6417	125	1	j.	j.	PROPN
ejpam-6417	125	2	pure	pure	PROPN
ejpam-6417	125	3	appl	appl	PROPN
ejpam-6417	125	4	.	.	PROPN
ejpam-6417	125	5	math	math	PROPN
ejpam-6417	125	6	,	,	PUNCT
ejpam-6417	125	7	18	18	NUM
ejpam-6417	125	8	(	(	PUNCT
ejpam-6417	125	9	3	3	NUM
ejpam-6417	125	10	)	)	PUNCT
ejpam-6417	125	11	(	(	PUNCT
ejpam-6417	125	12	2025	2025	NUM
ejpam-6417	125	13	)	)	PUNCT
ejpam-6417	125	14	,	,	PUNCT
ejpam-6417	125	15	6417	6417	NUM
ejpam-6417	125	16	7	7	NUM
ejpam-6417	125	17	of	of	ADP
ejpam-6417	125	18	10	10	NUM
ejpam-6417	125	19	sufficiency	sufficiency	NOUN
ejpam-6417	125	20	:	:	PUNCT
ejpam-6417	125	21	let	let	VERB
ejpam-6417	125	22	s	s	PRON
ejpam-6417	125	23	be	be	AUX
ejpam-6417	125	24	the	the	DET
ejpam-6417	125	25	3n×3n	3n×3n	NUM
ejpam-6417	125	26	matrix	matrix	NOUN
ejpam-6417	125	27	of	of	ADP
ejpam-6417	125	28	all	all	DET
ejpam-6417	125	29	ones	one	NOUN
ejpam-6417	125	30	,	,	PUNCT
ejpam-6417	125	31	which	which	PRON
ejpam-6417	125	32	is	be	AUX
ejpam-6417	125	33	positive	positive	ADJ
ejpam-6417	125	34	semidefinite	semidefinite	NOUN
ejpam-6417	125	35	with	with	ADP
ejpam-6417	125	36	diag(s11	diag(s11	PROPN
ejpam-6417	125	37	)	)	PUNCT
ejpam-6417	125	38	=	=	SYM
ejpam-6417	125	39	diag(s22	diag(s22	PROPN
ejpam-6417	125	40	)	)	PUNCT
ejpam-6417	125	41	=	=	SYM
ejpam-6417	126	1	diag(s33	diag(s33	PROPN
ejpam-6417	126	2	)	)	PUNCT
ejpam-6417	126	3	=	=	SYM
ejpam-6417	127	1	1	1	NUM
ejpam-6417	127	2	≫	≫	PROPN
ejpam-6417	127	3	0	0	NUM
ejpam-6417	127	4	.	.	PUNCT
ejpam-6417	128	1	then	then	ADV
ejpam-6417	128	2	,	,	PUNCT
ejpam-6417	128	3	for	for	ADP
ejpam-6417	128	4	each	each	DET
ejpam-6417	128	5	i	i	PRON
ejpam-6417	128	6	,	,	PUNCT
ejpam-6417	128	7	ai	ai	VERB
ejpam-6417	128	8	◦	◦	NOUN
ejpam-6417	128	9	sii	sii	PROPN
ejpam-6417	128	10	=	=	PUNCT
ejpam-6417	128	11	ai	ai	NOUN
ejpam-6417	128	12	,	,	PUNCT
ejpam-6417	128	13	and	and	CCONJ
ejpam-6417	128	14	the	the	DET
ejpam-6417	128	15	condition	condition	NOUN
ejpam-6417	128	16	reduces	reduce	VERB
ejpam-6417	128	17	to	to	ADP
ejpam-6417	128	18	the	the	DET
ejpam-6417	128	19	original	original	ADJ
ejpam-6417	128	20	triple	triple	ADJ
ejpam-6417	128	21	(	(	PUNCT
ejpam-6417	128	22	a1	a1	NOUN
ejpam-6417	128	23	,	,	PUNCT
ejpam-6417	128	24	a2	a2	PROPN
ejpam-6417	128	25	,	,	PUNCT
ejpam-6417	128	26	a3	a3	NOUN
ejpam-6417	128	27	)	)	PUNCT
ejpam-6417	128	28	,	,	PUNCT
ejpam-6417	128	29	which	which	PRON
ejpam-6417	128	30	holds	hold	VERB
ejpam-6417	128	31	by	by	ADP
ejpam-6417	128	32	assumption	assumption	NOUN
ejpam-6417	128	33	.	.	PUNCT
ejpam-6417	129	1	now	now	ADV
ejpam-6417	129	2	,	,	PUNCT
ejpam-6417	129	3	the	the	DET
ejpam-6417	129	4	proof	proof	NOUN
ejpam-6417	129	5	is	be	AUX
ejpam-6417	129	6	complete	complete	ADJ
ejpam-6417	129	7	.	.	PUNCT
ejpam-6417	130	1	theorem	theorem	ADJ
ejpam-6417	130	2	4	4	NUM
ejpam-6417	130	3	.	.	PUNCT
ejpam-6417	131	1	let	let	VERB
ejpam-6417	131	2	a1	a1	NOUN
ejpam-6417	131	3	,	,	PUNCT
ejpam-6417	131	4	a2	a2	PROPN
ejpam-6417	131	5	,	,	PUNCT
ejpam-6417	131	6	a3	a3	NOUN
ejpam-6417	131	7	∈	∈	PROPN
ejpam-6417	131	8	rn×n	rn×n	NOUN
ejpam-6417	131	9	.	.	PUNCT
ejpam-6417	132	1	the	the	DET
ejpam-6417	132	2	triple	triple	ADJ
ejpam-6417	132	3	(	(	PUNCT
ejpam-6417	132	4	a1	a1	NOUN
ejpam-6417	132	5	,	,	PUNCT
ejpam-6417	132	6	a2	a2	PROPN
ejpam-6417	132	7	,	,	PUNCT
ejpam-6417	132	8	a3	a3	NOUN
ejpam-6417	132	9	)	)	PUNCT
ejpam-6417	132	10	admits	admit	VERB
ejpam-6417	132	11	a	a	DET
ejpam-6417	132	12	positive	positive	ADJ
ejpam-6417	132	13	diagonal	diagonal	ADJ
ejpam-6417	132	14	solution	solution	NOUN
ejpam-6417	132	15	with	with	ADP
ejpam-6417	132	16	respect	respect	NOUN
ejpam-6417	132	17	to	to	ADP
ejpam-6417	132	18	(	(	PUNCT
ejpam-6417	132	19	1	1	X
ejpam-6417	132	20	)	)	PUNCT
ejpam-6417	132	21	if	if	SCONJ
ejpam-6417	132	22	and	and	CCONJ
ejpam-6417	132	23	only	only	ADV
ejpam-6417	132	24	if	if	SCONJ
ejpam-6417	132	25	−(a1	−(a1	NUM
ejpam-6417	132	26	◦	◦	NOUN
ejpam-6417	132	27	s11	s11	X
ejpam-6417	132	28	+	+	PROPN
ejpam-6417	132	29	a2	a2	PROPN
ejpam-6417	132	30	◦	◦	PROPN
ejpam-6417	132	31	s12	s12	PROPN
ejpam-6417	132	32	+	+	NOUN
ejpam-6417	132	33	a3	a3	PROPN
ejpam-6417	132	34	◦	◦	NOUN
ejpam-6417	132	35	s13	s13	NOUN
ejpam-6417	132	36	)	)	PUNCT
ejpam-6417	132	37	is	be	AUX
ejpam-6417	132	38	a	a	DET
ejpam-6417	132	39	p	p	X
ejpam-6417	132	40	-matrix	-matrix	NOUN
ejpam-6417	132	41	for	for	ADP
ejpam-6417	132	42	any	any	DET
ejpam-6417	132	43	positive	positive	ADJ
ejpam-6417	132	44	semidefinite	semidefinite	NOUN
ejpam-6417	132	45	matrix	matrix	NOUN
ejpam-6417	132	46	s	s	PART
ejpam-6417	132	47	∈	∈	NOUN
ejpam-6417	132	48	r3n×3n	r3n×3n	NOUN
ejpam-6417	132	49	of	of	ADP
ejpam-6417	132	50	the	the	DET
ejpam-6417	132	51	form	form	NOUN
ejpam-6417	132	52	s	s	PART
ejpam-6417	132	53	=	=	SYM
ejpam-6417	132	54	s11	s11	PROPN
ejpam-6417	132	55	s12	s12	PROPN
ejpam-6417	132	56	s13	s13	PROPN
ejpam-6417	132	57	st	st	PROPN
ejpam-6417	132	58	12	12	NUM
ejpam-6417	132	59	s22	s22	PROPN
ejpam-6417	132	60	s23	s23	PROPN
ejpam-6417	132	61	st	st	PROPN
ejpam-6417	132	62	13	13	NUM
ejpam-6417	132	63	st	st	PROPN
ejpam-6417	132	64	23	23	NUM
ejpam-6417	132	65	s33	s33	NOUN
ejpam-6417	132	66			NOUN
ejpam-6417	132	67	,	,	PUNCT
ejpam-6417	132	68	where	where	SCONJ
ejpam-6417	132	69	s11	s11	PROPN
ejpam-6417	132	70	,	,	PUNCT
ejpam-6417	132	71	s22	s22	NOUN
ejpam-6417	132	72	,	,	PUNCT
ejpam-6417	132	73	s33	s33	PROPN
ejpam-6417	132	74	satisfy	satisfy	VERB
ejpam-6417	132	75	the	the	DET
ejpam-6417	132	76	condition	condition	NOUN
ejpam-6417	132	77	diag(s11	diag(s11	PROPN
ejpam-6417	132	78	)	)	PUNCT
ejpam-6417	132	79	=	=	SYM
ejpam-6417	132	80	diag(s22	diag(s22	PROPN
ejpam-6417	132	81	)	)	PUNCT
ejpam-6417	132	82	=	=	SYM
ejpam-6417	132	83	diag(s33	diag(s33	PROPN
ejpam-6417	132	84	)	)	PUNCT
ejpam-6417	133	1	≫	≫	NOUN
ejpam-6417	133	2	0	0	NUM
ejpam-6417	133	3	.	.	PUNCT
ejpam-6417	134	1	proof	proof	NOUN
ejpam-6417	134	2	.	.	PUNCT
ejpam-6417	135	1	necessity	necessity	NOUN
ejpam-6417	135	2	:	:	PUNCT
ejpam-6417	135	3	by	by	ADP
ejpam-6417	135	4	assuming	assume	VERB
ejpam-6417	135	5	that	that	SCONJ
ejpam-6417	135	6	a1	a1	NOUN
ejpam-6417	135	7	,	,	PUNCT
ejpam-6417	135	8	a2	a2	PROPN
ejpam-6417	135	9	,	,	PUNCT
ejpam-6417	135	10	a3	a3	NOUN
ejpam-6417	135	11	∈	∈	PROPN
ejpam-6417	135	12	rn×n	rn×n	PROPN
ejpam-6417	135	13	admits	admit	VERB
ejpam-6417	135	14	a	a	DET
ejpam-6417	135	15	positive	positive	ADJ
ejpam-6417	135	16	diagonal	diagonal	ADJ
ejpam-6417	135	17	solution	solution	NOUN
ejpam-6417	135	18	,	,	PUNCT
ejpam-6417	135	19	it	it	PRON
ejpam-6417	135	20	follows	follow	VERB
ejpam-6417	135	21	,	,	PUNCT
ejpam-6417	135	22	by	by	ADP
ejpam-6417	135	23	theorem	theorem	NOUN
ejpam-6417	135	24	3	3	NUM
ejpam-6417	135	25	,	,	PUNCT
ejpam-6417	135	26	that	that	SCONJ
ejpam-6417	135	27	the	the	DET
ejpam-6417	135	28	triple	triple	ADJ
ejpam-6417	135	29	(	(	PUNCT
ejpam-6417	135	30	a1	a1	NOUN
ejpam-6417	135	31	◦	◦	NOUN
ejpam-6417	135	32	s11	s11	NOUN
ejpam-6417	135	33	,	,	PUNCT
ejpam-6417	135	34	a2	a2	PROPN
ejpam-6417	135	35	◦	◦	PROPN
ejpam-6417	135	36	s12	s12	PROPN
ejpam-6417	135	37	,	,	PUNCT
ejpam-6417	135	38	a3	a3	NOUN
ejpam-6417	135	39	◦	◦	PROPN
ejpam-6417	135	40	s13	s13	NOUN
ejpam-6417	135	41	)	)	PUNCT
ejpam-6417	135	42	has	have	VERB
ejpam-6417	135	43	a	a	DET
ejpam-6417	135	44	positive	positive	ADJ
ejpam-6417	135	45	diagonal	diagonal	ADJ
ejpam-6417	135	46	solution	solution	NOUN
ejpam-6417	135	47	as	as	ADV
ejpam-6417	135	48	well	well	ADV
ejpam-6417	135	49	.	.	PUNCT
ejpam-6417	136	1	thus	thus	ADV
ejpam-6417	136	2	,	,	PUNCT
ejpam-6417	136	3	by	by	ADP
ejpam-6417	136	4	lemma	lemma	PROPN
ejpam-6417	136	5	3	3	NUM
ejpam-6417	136	6	,	,	PUNCT
ejpam-6417	136	7	the	the	DET
ejpam-6417	136	8	matrix	matrix	NOUN
ejpam-6417	136	9	a1	a1	NOUN
ejpam-6417	136	10	◦	◦	NOUN
ejpam-6417	136	11	s11	s11	PROPN
ejpam-6417	136	12	+	+	PROPN
ejpam-6417	136	13	a2	a2	PROPN
ejpam-6417	136	14	◦	◦	PROPN
ejpam-6417	136	15	s12	s12	PROPN
ejpam-6417	136	16	+	+	NOUN
ejpam-6417	136	17	a3	a3	PROPN
ejpam-6417	136	18	◦	◦	NOUN
ejpam-6417	136	19	s13	s13	NOUN
ejpam-6417	136	20	is	be	AUX
ejpam-6417	136	21	lyapunov	lyapunov	NOUN
ejpam-6417	136	22	diagonally	diagonally	ADV
ejpam-6417	136	23	stable	stable	ADJ
ejpam-6417	136	24	.	.	PUNCT
ejpam-6417	137	1	finally	finally	ADV
ejpam-6417	137	2	,	,	PUNCT
ejpam-6417	137	3	according	accord	VERB
ejpam-6417	137	4	to	to	ADP
ejpam-6417	137	5	lemma	lemma	PROPN
ejpam-6417	137	6	2	2	NUM
ejpam-6417	137	7	,	,	PUNCT
ejpam-6417	137	8	this	this	PRON
ejpam-6417	137	9	means	mean	VERB
ejpam-6417	137	10	that	that	SCONJ
ejpam-6417	137	11	−(a1	−(a1	NUM
ejpam-6417	137	12	◦	◦	NOUN
ejpam-6417	137	13	s11	s11	X
ejpam-6417	137	14	+	+	PROPN
ejpam-6417	137	15	a2	a2	PROPN
ejpam-6417	137	16	◦	◦	PROPN
ejpam-6417	137	17	s12	s12	PROPN
ejpam-6417	137	18	+	+	NOUN
ejpam-6417	137	19	a3	a3	PROPN
ejpam-6417	137	20	◦	◦	NOUN
ejpam-6417	137	21	s13	s13	NOUN
ejpam-6417	137	22	)	)	PUNCT
ejpam-6417	137	23	is	be	AUX
ejpam-6417	137	24	a	a	DET
ejpam-6417	137	25	p	p	ADJ
ejpam-6417	137	26	-matrix	-matrix	NOUN
ejpam-6417	137	27	.	.	PUNCT
ejpam-6417	138	1	sufficiency	sufficiency	NOUN
ejpam-6417	138	2	:	:	PUNCT
ejpam-6417	138	3	suppose	suppose	VERB
ejpam-6417	138	4	that	that	SCONJ
ejpam-6417	138	5	h	h	NOUN
ejpam-6417	138	6	is	be	AUX
ejpam-6417	138	7	a	a	DET
ejpam-6417	138	8	nonzero	nonzero	ADJ
ejpam-6417	138	9	positive	positive	ADJ
ejpam-6417	138	10	semidefinite	semidefinite	NOUN
ejpam-6417	138	11	matrix	matrix	NOUN
ejpam-6417	138	12	in	in	ADP
ejpam-6417	138	13	r3n×3n	r3n×3n	PROPN
ejpam-6417	138	14	partitioned	partition	VERB
ejpam-6417	138	15	as	as	ADP
ejpam-6417	138	16	the	the	DET
ejpam-6417	138	17	following	follow	VERB
ejpam-6417	138	18	h	h	NOUN
ejpam-6417	138	19	=	=	X
ejpam-6417	138	20	h11	h11	PROPN
ejpam-6417	138	21	h12	h12	NOUN
ejpam-6417	138	22	h13	h13	NOUN
ejpam-6417	138	23	ht	ht	PROPN
ejpam-6417	138	24	12	12	NUM
ejpam-6417	138	25	h22	h22	PROPN
ejpam-6417	138	26	h23	h23	PROPN
ejpam-6417	138	27	ht	ht	PROPN
ejpam-6417	138	28	13	13	NUM
ejpam-6417	138	29	ht	ht	PROPN
ejpam-6417	138	30	23	23	NUM
ejpam-6417	138	31	h33	h33	NOUN
ejpam-6417	138	32			NOUN
ejpam-6417	138	33	,	,	PUNCT
ejpam-6417	138	34	and	and	CCONJ
ejpam-6417	138	35	satisfying	satisfy	VERB
ejpam-6417	138	36	the	the	DET
ejpam-6417	138	37	condition	condition	NOUN
ejpam-6417	138	38	diag(h11	diag(h11	PROPN
ejpam-6417	138	39	)	)	PUNCT
ejpam-6417	138	40	=	=	SYM
ejpam-6417	138	41	diag(h22	diag(h22	PROPN
ejpam-6417	138	42	)	)	PUNCT
ejpam-6417	138	43	=	=	SYM
ejpam-6417	138	44	diag(h33	diag(h33	PROPN
ejpam-6417	138	45	)	)	PUNCT
ejpam-6417	138	46	.	.	PUNCT
ejpam-6417	139	1	next	next	ADV
ejpam-6417	139	2	,	,	PUNCT
ejpam-6417	139	3	construct	construct	VERB
ejpam-6417	139	4	a	a	DET
ejpam-6417	139	5	matrix	matrix	NOUN
ejpam-6417	139	6	s	s	PART
ejpam-6417	139	7	∈	∈	NOUN
ejpam-6417	139	8	r3n×3n	r3n×3n	NOUN
ejpam-6417	139	9	to	to	PART
ejpam-6417	139	10	be	be	AUX
ejpam-6417	139	11	such	such	ADJ
ejpam-6417	139	12	that	that	SCONJ
ejpam-6417	139	13	sij	sij	PROPN
ejpam-6417	139	14	=	=	PUNCT
ejpam-6417	140	1			PRON
ejpam-6417	140	2	hij	hij	NOUN
ejpam-6417	140	3	if	if	SCONJ
ejpam-6417	140	4	i	i	PRON
ejpam-6417	140	5	̸=	̸=	PROPN
ejpam-6417	140	6	j	j	PROPN
ejpam-6417	140	7	hii	hii	VERB
ejpam-6417	140	8	if	if	SCONJ
ejpam-6417	140	9	i	i	PRON
ejpam-6417	140	10	=	=	SYM
ejpam-6417	140	11	j	j	PROPN
ejpam-6417	140	12	and	and	CCONJ
ejpam-6417	140	13	hii	hii	VERB
ejpam-6417	140	14	>	>	X
ejpam-6417	140	15	0	0	NUM
ejpam-6417	140	16	1	1	NUM
ejpam-6417	140	17	if	if	SCONJ
ejpam-6417	140	18	i	i	PRON
ejpam-6417	140	19	=	=	SYM
ejpam-6417	140	20	j	j	PROPN
ejpam-6417	140	21	and	and	CCONJ
ejpam-6417	140	22	hii	hii	VERB
ejpam-6417	140	23	=	=	SYM
ejpam-6417	140	24	0	0	X
ejpam-6417	140	25	.	.	PUNCT
ejpam-6417	141	1	clearly	clearly	ADV
ejpam-6417	141	2	,	,	PUNCT
ejpam-6417	141	3	s	s	VERB
ejpam-6417	141	4	is	be	AUX
ejpam-6417	141	5	positive	positive	ADJ
ejpam-6417	141	6	semidefinite	semidefinite	NOUN
ejpam-6417	141	7	with	with	ADP
ejpam-6417	141	8	strictly	strictly	ADV
ejpam-6417	141	9	positive	positive	ADJ
ejpam-6417	141	10	diagonal	diagonal	ADJ
ejpam-6417	141	11	entries	entry	NOUN
ejpam-6417	141	12	.	.	PUNCT
ejpam-6417	142	1	furthermore	furthermore	ADV
ejpam-6417	142	2	,	,	PUNCT
ejpam-6417	142	3	it	it	PRON
ejpam-6417	142	4	satisfies	satisfy	VERB
ejpam-6417	142	5	the	the	DET
ejpam-6417	142	6	condition	condition	NOUN
ejpam-6417	142	7	diag(s11	diag(s11	PROPN
ejpam-6417	142	8	)	)	PUNCT
ejpam-6417	142	9	=	=	SYM
ejpam-6417	142	10	diag(s22	diag(s22	PROPN
ejpam-6417	142	11	)	)	PUNCT
ejpam-6417	142	12	=	=	SYM
ejpam-6417	142	13	diag(s33	diag(s33	PROPN
ejpam-6417	142	14	)	)	PUNCT
ejpam-6417	142	15	because	because	SCONJ
ejpam-6417	142	16	diag(h11	diag(h11	PROPN
ejpam-6417	142	17	)	)	PUNCT
ejpam-6417	142	18	=	=	SYM
ejpam-6417	143	1	diag(h22	diag(h22	PROPN
ejpam-6417	143	2	)	)	PUNCT
ejpam-6417	143	3	=	=	SYM
ejpam-6417	144	1	diag(h33	diag(h33	PROPN
ejpam-6417	144	2	)	)	PUNCT
ejpam-6417	144	3	.	.	PUNCT
ejpam-6417	145	1	therefore	therefore	ADV
ejpam-6417	145	2	,	,	PUNCT
ejpam-6417	145	3	we	we	PRON
ejpam-6417	145	4	have	have	VERB
ejpam-6417	145	5	−(a1	−(a1	X
ejpam-6417	145	6	◦	◦	VERB
ejpam-6417	145	7	s11	s11	X
ejpam-6417	146	1	+	+	PROPN
ejpam-6417	146	2	a2	a2	PROPN
ejpam-6417	146	3	◦	◦	PROPN
ejpam-6417	146	4	s12	s12	PROPN
ejpam-6417	146	5	+	+	NOUN
ejpam-6417	146	6	a3	a3	PROPN
ejpam-6417	146	7	◦	◦	NOUN
ejpam-6417	146	8	s13	s13	NOUN
ejpam-6417	146	9	)	)	PUNCT
ejpam-6417	146	10	a.	a.	NOUN
ejpam-6417	146	11	algefary	algefary	ADJ
ejpam-6417	146	12	,	,	PUNCT
ejpam-6417	146	13	t.	t.	PROPN
ejpam-6417	146	14	alhumaidan	alhumaidan	PROPN
ejpam-6417	146	15	/	/	SYM
ejpam-6417	146	16	eur	eur	PROPN
ejpam-6417	146	17	.	.	PUNCT
ejpam-6417	147	1	j.	j.	PROPN
ejpam-6417	147	2	pure	pure	PROPN
ejpam-6417	147	3	appl	appl	PROPN
ejpam-6417	147	4	.	.	PROPN
ejpam-6417	147	5	math	math	PROPN
ejpam-6417	147	6	,	,	PUNCT
ejpam-6417	147	7	18	18	NUM
ejpam-6417	147	8	(	(	PUNCT
ejpam-6417	147	9	3	3	NUM
ejpam-6417	147	10	)	)	PUNCT
ejpam-6417	147	11	(	(	PUNCT
ejpam-6417	147	12	2025	2025	NUM
ejpam-6417	147	13	)	)	PUNCT
ejpam-6417	147	14	,	,	PUNCT
ejpam-6417	147	15	6417	6417	NUM
ejpam-6417	147	16	8	8	NUM
ejpam-6417	147	17	of	of	ADP
ejpam-6417	147	18	10	10	NUM
ejpam-6417	147	19	is	be	AUX
ejpam-6417	147	20	a	a	DET
ejpam-6417	147	21	p	p	ADJ
ejpam-6417	147	22	-matrix	-matrix	NOUN
ejpam-6417	147	23	.	.	PUNCT
ejpam-6417	148	1	now	now	ADV
ejpam-6417	148	2	,	,	PUNCT
ejpam-6417	148	3	construct	construct	VERB
ejpam-6417	148	4	v	v	ADP
ejpam-6417	148	5	∈	∈	PROPN
ejpam-6417	148	6	rn	rn	NOUN
ejpam-6417	148	7	to	to	PART
ejpam-6417	148	8	be	be	AUX
ejpam-6417	148	9	such	such	ADJ
ejpam-6417	148	10	that	that	DET
ejpam-6417	148	11	vk	vk	NOUN
ejpam-6417	148	12	=	=	SYM
ejpam-6417	148	13	1	1	NUM
ejpam-6417	148	14	when	when	SCONJ
ejpam-6417	148	15	hkk	hkk	X
ejpam-6417	148	16	>	>	X
ejpam-6417	148	17	0	0	PUNCT
ejpam-6417	148	18	and	and	CCONJ
ejpam-6417	148	19	vk	vk	X
ejpam-6417	148	20	=	=	SYM
ejpam-6417	148	21	0	0	NUM
ejpam-6417	148	22	when	when	SCONJ
ejpam-6417	148	23	hkk	hkk	NOUN
ejpam-6417	148	24	=	=	SYM
ejpam-6417	148	25	0	0	NUM
ejpam-6417	148	26	for	for	ADP
ejpam-6417	148	27	k	k	PROPN
ejpam-6417	148	28	∈	∈	PROPN
ejpam-6417	148	29	{	{	PUNCT
ejpam-6417	148	30	1	1	NUM
ejpam-6417	148	31	,	,	PUNCT
ejpam-6417	148	32	.	.	PUNCT
ejpam-6417	148	33	.	.	PUNCT
ejpam-6417	149	1	.	.	PUNCT
ejpam-6417	149	2	,	,	PUNCT
ejpam-6417	149	3	n	n	CCONJ
ejpam-6417	149	4	}	}	PUNCT
ejpam-6417	149	5	.	.	PUNCT
ejpam-6417	150	1	hence	hence	ADV
ejpam-6417	150	2	,	,	PUNCT
ejpam-6417	150	3	using	use	VERB
ejpam-6417	150	4	the	the	DET
ejpam-6417	150	5	p	p	PROPN
ejpam-6417	150	6	-matrix	-matrix	NOUN
ejpam-6417	150	7	properties	property	NOUN
ejpam-6417	150	8	,	,	PUNCT
ejpam-6417	150	9	there	there	PRON
ejpam-6417	150	10	is	be	VERB
ejpam-6417	150	11	an	an	DET
ejpam-6417	150	12	index	index	NOUN
ejpam-6417	150	13	k	k	ADP
ejpam-6417	150	14	such	such	ADJ
ejpam-6417	150	15	that	that	SCONJ
ejpam-6417	150	16	vk[(a1	vk[(a1	PROPN
ejpam-6417	150	17	◦	◦	PROPN
ejpam-6417	150	18	s11	s11	PROPN
ejpam-6417	150	19	+	+	PROPN
ejpam-6417	150	20	a2	a2	PROPN
ejpam-6417	150	21	◦	◦	PROPN
ejpam-6417	150	22	s12	s12	PROPN
ejpam-6417	150	23	+	+	NOUN
ejpam-6417	150	24	a3	a3	NOUN
ejpam-6417	150	25	◦	◦	NOUN
ejpam-6417	150	26	s13)v]k	s13)v]k	X
ejpam-6417	150	27	<	<	X
ejpam-6417	150	28	0	0	X
ejpam-6417	150	29	.	.	PUNCT
ejpam-6417	151	1	this	this	DET
ejpam-6417	151	2	inequality	inequality	NOUN
ejpam-6417	151	3	means	mean	VERB
ejpam-6417	151	4	that	that	SCONJ
ejpam-6417	151	5	n∑	n∑	NOUN
ejpam-6417	151	6	i=1	i=1	X
ejpam-6417	152	1	a1kih	a1kih	PROPN
ejpam-6417	152	2	11	11	NUM
ejpam-6417	153	1	ki	ki	PROPN
ejpam-6417	154	1	+	+	CCONJ
ejpam-6417	154	2	n∑	n∑	ADJ
ejpam-6417	154	3	i=1	i=1	PROPN
ejpam-6417	155	1	a2kih	a2kih	PROPN
ejpam-6417	155	2	12	12	NUM
ejpam-6417	155	3	ki	ki	PROPN
ejpam-6417	156	1	+	+	CCONJ
ejpam-6417	156	2	n∑	n∑	NOUN
ejpam-6417	156	3	i=1	i=1	PROPN
ejpam-6417	157	1	a3kih	a3kih	PROPN
ejpam-6417	157	2	13	13	NUM
ejpam-6417	158	1	ki	ki	PROPN
ejpam-6417	158	2	<	<	X
ejpam-6417	158	3	0	0	PROPN
ejpam-6417	158	4	,	,	PUNCT
ejpam-6417	158	5	which	which	PRON
ejpam-6417	158	6	implies	imply	VERB
ejpam-6417	158	7	that	that	SCONJ
ejpam-6417	158	8	(	(	PUNCT
ejpam-6417	158	9	a1h11	a1h11	X
ejpam-6417	158	10	+	+	ADP
ejpam-6417	158	11	a2h	a2h	NOUN
ejpam-6417	158	12	t	t	PROPN
ejpam-6417	158	13	12	12	NUM
ejpam-6417	159	1	+	+	NOUN
ejpam-6417	159	2	a3h	a3h	X
ejpam-6417	159	3	t	t	X
ejpam-6417	159	4	13)kk	13)kk	NUM
ejpam-6417	159	5	<	<	X
ejpam-6417	159	6	0	0	X
ejpam-6417	159	7	.	.	PUNCT
ejpam-6417	160	1	it	it	PRON
ejpam-6417	160	2	follows	follow	VERB
ejpam-6417	160	3	,	,	PUNCT
ejpam-6417	160	4	from	from	ADP
ejpam-6417	160	5	theorem	theorem	NOUN
ejpam-6417	160	6	2	2	NUM
ejpam-6417	160	7	,	,	PUNCT
ejpam-6417	160	8	that	that	SCONJ
ejpam-6417	160	9	the	the	DET
ejpam-6417	160	10	triple	triple	ADJ
ejpam-6417	160	11	(	(	PUNCT
ejpam-6417	160	12	a1	a1	NOUN
ejpam-6417	160	13	,	,	PUNCT
ejpam-6417	160	14	a2	a2	PROPN
ejpam-6417	160	15	,	,	PUNCT
ejpam-6417	160	16	a3	a3	NOUN
ejpam-6417	160	17	)	)	PUNCT
ejpam-6417	160	18	admits	admit	VERB
ejpam-6417	160	19	a	a	DET
ejpam-6417	160	20	positive	positive	ADJ
ejpam-6417	160	21	diagonal	diagonal	ADJ
ejpam-6417	160	22	solution	solution	NOUN
ejpam-6417	160	23	.	.	PUNCT
ejpam-6417	161	1	now	now	ADV
ejpam-6417	161	2	,	,	PUNCT
ejpam-6417	161	3	the	the	DET
ejpam-6417	161	4	proof	proof	NOUN
ejpam-6417	161	5	is	be	AUX
ejpam-6417	161	6	complete	complete	ADJ
ejpam-6417	161	7	.	.	PUNCT
ejpam-6417	162	1	4	4	X
ejpam-6417	162	2	.	.	X
ejpam-6417	162	3	conclusions	conclusion	NOUN
ejpam-6417	162	4	we	we	PRON
ejpam-6417	162	5	have	have	AUX
ejpam-6417	162	6	characterized	characterize	VERB
ejpam-6417	162	7	the	the	DET
ejpam-6417	162	8	existence	existence	NOUN
ejpam-6417	162	9	of	of	ADP
ejpam-6417	162	10	positive	positive	ADJ
ejpam-6417	162	11	diagonal	diagonal	ADJ
ejpam-6417	162	12	solutions	solution	NOUN
ejpam-6417	162	13	for	for	ADP
ejpam-6417	162	14	a	a	DET
ejpam-6417	162	15	class	class	NOUN
ejpam-6417	162	16	of	of	ADP
ejpam-6417	162	17	lmis	lmis	ADJ
ejpam-6417	162	18	,	,	PUNCT
ejpam-6417	162	19	providing	provide	VERB
ejpam-6417	162	20	equivalent	equivalent	ADJ
ejpam-6417	162	21	conditions	condition	NOUN
ejpam-6417	162	22	via	via	ADP
ejpam-6417	162	23	test	test	NOUN
ejpam-6417	162	24	matrices	matrix	NOUN
ejpam-6417	162	25	(	(	PUNCT
ejpam-6417	162	26	theorems	theorem	NOUN
ejpam-6417	162	27	1	1	NUM
ejpam-6417	162	28	,	,	PUNCT
ejpam-6417	162	29	2	2	NUM
ejpam-6417	162	30	)	)	PUNCT
ejpam-6417	162	31	and	and	CCONJ
ejpam-6417	162	32	hadamard	hadamard	ADJ
ejpam-6417	162	33	product	product	NOUN
ejpam-6417	162	34	transformations	transformation	NOUN
ejpam-6417	162	35	(	(	PUNCT
ejpam-6417	162	36	theorems	theorem	NOUN
ejpam-6417	162	37	3	3	NUM
ejpam-6417	162	38	,	,	PUNCT
ejpam-6417	162	39	4	4	NUM
ejpam-6417	162	40	)	)	PUNCT
ejpam-6417	162	41	.	.	PUNCT
ejpam-6417	163	1	these	these	DET
ejpam-6417	163	2	results	result	NOUN
ejpam-6417	163	3	generalize	generalize	VERB
ejpam-6417	163	4	classical	classical	ADJ
ejpam-6417	163	5	stability	stability	NOUN
ejpam-6417	163	6	criteria	criterion	NOUN
ejpam-6417	163	7	and	and	CCONJ
ejpam-6417	163	8	offer	offer	VERB
ejpam-6417	163	9	tools	tool	NOUN
ejpam-6417	163	10	for	for	ADP
ejpam-6417	163	11	analyzing	analyze	VERB
ejpam-6417	163	12	multi	multi	ADJ
ejpam-6417	163	13	-	-	ADJ
ejpam-6417	163	14	matrix	matrix	ADJ
ejpam-6417	163	15	systems	system	NOUN
ejpam-6417	163	16	in	in	ADP
ejpam-6417	163	17	control	control	NOUN
ejpam-6417	163	18	and	and	CCONJ
ejpam-6417	163	19	dynamics	dynamic	NOUN
ejpam-6417	163	20	.	.	PUNCT
ejpam-6417	164	1	5	5	X
ejpam-6417	164	2	.	.	X
ejpam-6417	164	3	conclusions	conclusion	NOUN
ejpam-6417	164	4	in	in	ADP
ejpam-6417	164	5	this	this	DET
ejpam-6417	164	6	paper	paper	NOUN
ejpam-6417	164	7	,	,	PUNCT
ejpam-6417	164	8	we	we	PRON
ejpam-6417	164	9	have	have	AUX
ejpam-6417	164	10	investigated	investigate	VERB
ejpam-6417	164	11	the	the	DET
ejpam-6417	164	12	existence	existence	NOUN
ejpam-6417	164	13	of	of	ADP
ejpam-6417	164	14	positive	positive	ADJ
ejpam-6417	164	15	diagonal	diagonal	ADJ
ejpam-6417	164	16	solutions	solution	NOUN
ejpam-6417	164	17	for	for	ADP
ejpam-6417	164	18	a	a	DET
ejpam-6417	164	19	class	class	NOUN
ejpam-6417	164	20	of	of	ADP
ejpam-6417	164	21	linear	linear	ADJ
ejpam-6417	164	22	matrix	matrix	NOUN
ejpam-6417	164	23	inequalities	inequality	NOUN
ejpam-6417	164	24	involving	involve	VERB
ejpam-6417	164	25	a	a	DET
ejpam-6417	164	26	structured	structured	ADJ
ejpam-6417	164	27	block	block	NOUN
ejpam-6417	164	28	matrix	matrix	NOUN
ejpam-6417	164	29	defined	define	VERB
ejpam-6417	164	30	by	by	ADP
ejpam-6417	164	31	a	a	DET
ejpam-6417	164	32	triple	triple	NOUN
ejpam-6417	164	33	of	of	ADP
ejpam-6417	164	34	matrices	matrix	NOUN
ejpam-6417	164	35	(	(	PUNCT
ejpam-6417	164	36	a1	a1	NOUN
ejpam-6417	164	37	,	,	PUNCT
ejpam-6417	164	38	a2	a2	PROPN
ejpam-6417	164	39	,	,	PUNCT
ejpam-6417	164	40	a3	a3	NOUN
ejpam-6417	164	41	)	)	PUNCT
ejpam-6417	164	42	.	.	PUNCT
ejpam-6417	165	1	we	we	PRON
ejpam-6417	165	2	established	establish	VERB
ejpam-6417	165	3	several	several	ADJ
ejpam-6417	165	4	equivalent	equivalent	ADJ
ejpam-6417	165	5	conditions	condition	NOUN
ejpam-6417	165	6	that	that	PRON
ejpam-6417	165	7	characterize	characterize	VERB
ejpam-6417	165	8	such	such	ADJ
ejpam-6417	165	9	solutions	solution	NOUN
ejpam-6417	165	10	,	,	PUNCT
ejpam-6417	165	11	linking	link	VERB
ejpam-6417	165	12	the	the	DET
ejpam-6417	165	13	negative	negative	ADJ
ejpam-6417	165	14	definiteness	definiteness	NOUN
ejpam-6417	165	15	of	of	ADP
ejpam-6417	165	16	the	the	DET
ejpam-6417	165	17	block	block	NOUN
ejpam-6417	165	18	matrix	matrix	NOUN
ejpam-6417	165	19	to	to	ADP
ejpam-6417	165	20	properties	property	NOUN
ejpam-6417	165	21	of	of	ADP
ejpam-6417	165	22	positive	positive	ADJ
ejpam-6417	165	23	semidefinite	semidefinite	NOUN
ejpam-6417	165	24	test	test	NOUN
ejpam-6417	165	25	matrices	matrix	NOUN
ejpam-6417	165	26	and	and	CCONJ
ejpam-6417	165	27	to	to	ADP
ejpam-6417	165	28	the	the	DET
ejpam-6417	165	29	p	p	NOUN
ejpam-6417	165	30	-	-	PUNCT
ejpam-6417	165	31	matrix	matrix	NOUN
ejpam-6417	165	32	property	property	NOUN
ejpam-6417	165	33	of	of	ADP
ejpam-6417	165	34	transformed	transform	VERB
ejpam-6417	165	35	matrices	matrix	NOUN
ejpam-6417	165	36	under	under	ADP
ejpam-6417	165	37	hadamard	hadamard	ADJ
ejpam-6417	165	38	products	product	NOUN
ejpam-6417	165	39	.	.	PUNCT
ejpam-6417	166	1	these	these	DET
ejpam-6417	166	2	results	result	NOUN
ejpam-6417	166	3	generalize	generalize	VERB
ejpam-6417	166	4	classical	classical	ADJ
ejpam-6417	166	5	lyapunov	lyapunov	ADJ
ejpam-6417	166	6	diagonal	diagonal	ADJ
ejpam-6417	166	7	stability	stability	NOUN
ejpam-6417	166	8	conditions	condition	NOUN
ejpam-6417	166	9	to	to	ADP
ejpam-6417	166	10	a	a	DET
ejpam-6417	166	11	multimatrix	multimatrix	NOUN
ejpam-6417	166	12	setting	setting	NOUN
ejpam-6417	166	13	,	,	PUNCT
ejpam-6417	166	14	offering	offer	VERB
ejpam-6417	166	15	new	new	ADJ
ejpam-6417	166	16	insights	insight	NOUN
ejpam-6417	166	17	and	and	CCONJ
ejpam-6417	166	18	tools	tool	NOUN
ejpam-6417	166	19	for	for	ADP
ejpam-6417	166	20	the	the	DET
ejpam-6417	166	21	stability	stability	NOUN
ejpam-6417	166	22	analysis	analysis	NOUN
ejpam-6417	166	23	of	of	ADP
ejpam-6417	166	24	complex	complex	ADJ
ejpam-6417	166	25	systems	system	NOUN
ejpam-6417	166	26	.	.	PUNCT
ejpam-6417	167	1	in	in	ADP
ejpam-6417	167	2	particular	particular	ADJ
ejpam-6417	167	3	,	,	PUNCT
ejpam-6417	167	4	the	the	DET
ejpam-6417	167	5	characterizations	characterization	NOUN
ejpam-6417	167	6	provided	provide	VERB
ejpam-6417	167	7	in	in	ADP
ejpam-6417	167	8	this	this	DET
ejpam-6417	167	9	paper	paper	NOUN
ejpam-6417	167	10	contribute	contribute	NOUN
ejpam-6417	167	11	to	to	ADP
ejpam-6417	167	12	the	the	DET
ejpam-6417	167	13	understanding	understanding	NOUN
ejpam-6417	167	14	of	of	ADP
ejpam-6417	167	15	how	how	SCONJ
ejpam-6417	167	16	structural	structural	ADJ
ejpam-6417	167	17	constraints	constraint	NOUN
ejpam-6417	167	18	and	and	CCONJ
ejpam-6417	167	19	matrix	matrix	NOUN
ejpam-6417	167	20	interactions	interaction	NOUN
ejpam-6417	167	21	affect	affect	VERB
ejpam-6417	167	22	stability	stability	NOUN
ejpam-6417	167	23	,	,	PUNCT
ejpam-6417	167	24	with	with	ADP
ejpam-6417	167	25	potential	potential	ADJ
ejpam-6417	167	26	applications	application	NOUN
ejpam-6417	167	27	in	in	ADP
ejpam-6417	167	28	control	control	NOUN
ejpam-6417	167	29	theory	theory	NOUN
ejpam-6417	167	30	,	,	PUNCT
ejpam-6417	167	31	networked	networked	ADJ
ejpam-6417	167	32	systems	system	NOUN
ejpam-6417	167	33	,	,	PUNCT
ejpam-6417	167	34	and	and	CCONJ
ejpam-6417	167	35	biological	biological	ADJ
ejpam-6417	167	36	models	model	NOUN
ejpam-6417	167	37	.	.	PUNCT
ejpam-6417	168	1	future	future	ADJ
ejpam-6417	168	2	work	work	NOUN
ejpam-6417	168	3	may	may	AUX
ejpam-6417	168	4	explore	explore	VERB
ejpam-6417	168	5	numerical	numerical	ADJ
ejpam-6417	168	6	algorithms	algorithm	NOUN
ejpam-6417	168	7	to	to	PART
ejpam-6417	168	8	compute	compute	VERB
ejpam-6417	168	9	such	such	ADJ
ejpam-6417	168	10	diagonal	diagonal	ADJ
ejpam-6417	168	11	solutions	solution	NOUN
ejpam-6417	168	12	efficiently	efficiently	ADV
ejpam-6417	168	13	and	and	CCONJ
ejpam-6417	168	14	investigate	investigate	VERB
ejpam-6417	168	15	extensions	extension	NOUN
ejpam-6417	168	16	to	to	ADP
ejpam-6417	168	17	nonlinear	nonlinear	ADJ
ejpam-6417	168	18	systems	system	NOUN
ejpam-6417	168	19	or	or	CCONJ
ejpam-6417	168	20	systems	system	NOUN
ejpam-6417	168	21	with	with	ADP
ejpam-6417	168	22	time	time	NOUN
ejpam-6417	168	23	-	-	PUNCT
ejpam-6417	168	24	varying	vary	VERB
ejpam-6417	168	25	parameters	parameter	NOUN
ejpam-6417	168	26	.	.	PUNCT
ejpam-6417	169	1	the	the	DET
ejpam-6417	169	2	approach	approach	NOUN
ejpam-6417	169	3	developed	develop	VERB
ejpam-6417	169	4	here	here	ADV
ejpam-6417	169	5	opens	open	VERB
ejpam-6417	169	6	avenues	avenue	NOUN
ejpam-6417	169	7	for	for	ADP
ejpam-6417	169	8	further	further	ADJ
ejpam-6417	169	9	research	research	NOUN
ejpam-6417	169	10	on	on	ADP
ejpam-6417	169	11	structured	structured	ADJ
ejpam-6417	169	12	stability	stability	NOUN
ejpam-6417	169	13	criteria	criterion	NOUN
ejpam-6417	169	14	in	in	ADP
ejpam-6417	169	15	high	high	ADV
ejpam-6417	169	16	-	-	PUNCT
ejpam-6417	169	17	dimensional	dimensional	ADJ
ejpam-6417	169	18	and	and	CCONJ
ejpam-6417	169	19	interconnected	interconnected	ADJ
ejpam-6417	169	20	dynamical	dynamical	ADJ
ejpam-6417	169	21	systems	system	NOUN
ejpam-6417	169	22	.	.	PUNCT
ejpam-6417	170	1	a.	a.	PROPN
ejpam-6417	170	2	algefary	algefary	PROPN
ejpam-6417	170	3	,	,	PUNCT
ejpam-6417	170	4	t.	t.	PROPN
ejpam-6417	170	5	alhumaidan	alhumaidan	PROPN
ejpam-6417	170	6	/	/	SYM
ejpam-6417	170	7	eur	eur	PROPN
ejpam-6417	170	8	.	.	PUNCT
ejpam-6417	171	1	j.	j.	PROPN
ejpam-6417	171	2	pure	pure	PROPN
ejpam-6417	171	3	appl	appl	PROPN
ejpam-6417	171	4	.	.	PROPN
ejpam-6417	171	5	math	math	PROPN
ejpam-6417	171	6	,	,	PUNCT
ejpam-6417	171	7	18	18	NUM
ejpam-6417	171	8	(	(	PUNCT
ejpam-6417	171	9	3	3	NUM
ejpam-6417	171	10	)	)	PUNCT
ejpam-6417	171	11	(	(	PUNCT
ejpam-6417	171	12	2025	2025	NUM
ejpam-6417	171	13	)	)	PUNCT
ejpam-6417	171	14	,	,	PUNCT
ejpam-6417	171	15	6417	6417	NUM
ejpam-6417	171	16	9	9	NUM
ejpam-6417	171	17	of	of	ADP
ejpam-6417	171	18	10	10	NUM
ejpam-6417	171	19	acknowledgements	acknowledgement	NOUN
ejpam-6417	171	20	the	the	DET
ejpam-6417	171	21	authors	author	NOUN
ejpam-6417	171	22	gratefully	gratefully	ADV
ejpam-6417	171	23	acknowledge	acknowledge	VERB
ejpam-6417	171	24	qassim	qassim	PROPN
ejpam-6417	171	25	university	university	PROPN
ejpam-6417	171	26	,	,	PUNCT
ejpam-6417	171	27	represented	represent	VERB
ejpam-6417	171	28	by	by	ADP
ejpam-6417	171	29	the	the	DET
ejpam-6417	171	30	deanship	deanship	NOUN
ejpam-6417	171	31	of	of	ADP
ejpam-6417	171	32	graduate	graduate	NOUN
ejpam-6417	171	33	studies	study	NOUN
ejpam-6417	171	34	and	and	CCONJ
ejpam-6417	171	35	scientific	scientific	ADJ
ejpam-6417	171	36	research	research	NOUN
ejpam-6417	171	37	,	,	PUNCT
ejpam-6417	171	38	on	on	ADP
ejpam-6417	171	39	the	the	DET
ejpam-6417	171	40	financial	financial	ADJ
ejpam-6417	171	41	support	support	NOUN
ejpam-6417	171	42	for	for	ADP
ejpam-6417	171	43	this	this	DET
ejpam-6417	171	44	research	research	NOUN
ejpam-6417	171	45	under	under	ADP
ejpam-6417	171	46	the	the	DET
ejpam-6417	171	47	number	number	NOUN
ejpam-6417	171	48	(	(	PUNCT
ejpam-6417	171	49	qu	qu	PROPN
ejpam-6417	171	50	-	-	PROPN
ejpam-6417	171	51	j	j	NOUN
ejpam-6417	171	52	-	-	PUNCT
ejpam-6417	171	53	ug-2	ug-2	NOUN
ejpam-6417	171	54	-	-	PUNCT
ejpam-6417	171	55	2025	2025	NUM
ejpam-6417	171	56	-	-	SYM
ejpam-6417	171	57	56237	56237	NUM
ejpam-6417	171	58	)	)	PUNCT
ejpam-6417	171	59	during	during	ADP
ejpam-6417	171	60	the	the	DET
ejpam-6417	171	61	academic	academic	ADJ
ejpam-6417	171	62	year	year	NOUN
ejpam-6417	171	63	1446	1446	NUM
ejpam-6417	171	64	ah	ah	INTJ
ejpam-6417	171	65	/	/	SYM
ejpam-6417	171	66	2024	2024	NUM
ejpam-6417	171	67	ad	ad	NOUN
ejpam-6417	171	68	.	.	PUNCT
ejpam-6417	172	1	we	we	PRON
ejpam-6417	172	2	also	also	ADV
ejpam-6417	172	3	sincerely	sincerely	ADV
ejpam-6417	172	4	thank	thank	VERB
ejpam-6417	172	5	the	the	DET
ejpam-6417	172	6	reviewers	reviewer	NOUN
ejpam-6417	172	7	for	for	ADP
ejpam-6417	172	8	their	their	PRON
ejpam-6417	172	9	valuable	valuable	ADJ
ejpam-6417	172	10	feedback	feedback	NOUN
ejpam-6417	172	11	and	and	CCONJ
ejpam-6417	172	12	constructive	constructive	ADJ
ejpam-6417	172	13	comments	comment	NOUN
ejpam-6417	172	14	,	,	PUNCT
ejpam-6417	172	15	which	which	PRON
ejpam-6417	172	16	have	have	AUX
ejpam-6417	172	17	significantly	significantly	ADV
ejpam-6417	172	18	contributed	contribute	VERB
ejpam-6417	172	19	to	to	ADP
ejpam-6417	172	20	enhancing	enhance	VERB
ejpam-6417	172	21	the	the	DET
ejpam-6417	172	22	quality	quality	NOUN
ejpam-6417	172	23	of	of	ADP
ejpam-6417	172	24	this	this	DET
ejpam-6417	172	25	paper	paper	NOUN
ejpam-6417	172	26	.	.	PUNCT
ejpam-6417	173	1	references	reference	NOUN
ejpam-6417	173	2	[	[	X
ejpam-6417	173	3	1	1	NUM
ejpam-6417	173	4	]	]	PUNCT
ejpam-6417	173	5	stephen	stephen	PROPN
ejpam-6417	173	6	boyd	boyd	PROPN
ejpam-6417	173	7	,	,	PUNCT
ejpam-6417	173	8	laurent	laurent	PROPN
ejpam-6417	173	9	el	el	PROPN
ejpam-6417	173	10	ghaoui	ghaoui	PROPN
ejpam-6417	173	11	,	,	PUNCT
ejpam-6417	173	12	eric	eric	PROPN
ejpam-6417	173	13	feron	feron	PROPN
ejpam-6417	173	14	,	,	PUNCT
ejpam-6417	173	15	and	and	CCONJ
ejpam-6417	173	16	venkataramanan	venkataramanan	PROPN
ejpam-6417	173	17	balakrishnan	balakrishnan	PROPN
ejpam-6417	173	18	.	.	PUNCT
ejpam-6417	174	1	linear	linear	ADJ
ejpam-6417	174	2	matrix	matrix	NOUN
ejpam-6417	174	3	inequalities	inequality	NOUN
ejpam-6417	174	4	in	in	ADP
ejpam-6417	174	5	system	system	NOUN
ejpam-6417	174	6	and	and	CCONJ
ejpam-6417	174	7	control	control	NOUN
ejpam-6417	174	8	theory	theory	NOUN
ejpam-6417	174	9	.	.	PUNCT
ejpam-6417	175	1	siam	siam	PROPN
ejpam-6417	175	2	,	,	PUNCT
ejpam-6417	175	3	1994	1994	NUM
ejpam-6417	175	4	.	.	PUNCT
ejpam-6417	176	1	[	[	X
ejpam-6417	176	2	2	2	NUM
ejpam-6417	176	3	]	]	X
ejpam-6417	176	4	pascal	pascal	ADJ
ejpam-6417	176	5	gahinet	gahinet	NOUN
ejpam-6417	176	6	and	and	CCONJ
ejpam-6417	176	7	pierre	pierre	PROPN
ejpam-6417	176	8	apkarian	apkarian	PROPN
ejpam-6417	176	9	.	.	PUNCT
ejpam-6417	177	1	a	a	DET
ejpam-6417	177	2	linear	linear	ADJ
ejpam-6417	177	3	matrix	matrix	NOUN
ejpam-6417	177	4	inequality	inequality	NOUN
ejpam-6417	177	5	approach	approach	NOUN
ejpam-6417	177	6	to	to	ADP
ejpam-6417	177	7	h∞	h∞	PROPN
ejpam-6417	177	8	control	control	PROPN
ejpam-6417	177	9	.	.	PUNCT
ejpam-6417	178	1	international	international	ADJ
ejpam-6417	178	2	journal	journal	NOUN
ejpam-6417	178	3	of	of	ADP
ejpam-6417	178	4	robust	robust	ADJ
ejpam-6417	178	5	and	and	CCONJ
ejpam-6417	178	6	nonlinear	nonlinear	ADJ
ejpam-6417	178	7	control	control	NOUN
ejpam-6417	178	8	,	,	PUNCT
ejpam-6417	178	9	4(4):421–448	4(4):421–448	NUM
ejpam-6417	178	10	,	,	PUNCT
ejpam-6417	178	11	1994	1994	NUM
ejpam-6417	178	12	.	.	PUNCT
ejpam-6417	179	1	[	[	X
ejpam-6417	179	2	3	3	X
ejpam-6417	179	3	]	]	X
ejpam-6417	179	4	lakhlifa	lakhlifa	PROPN
ejpam-6417	179	5	sadek	sadek	PROPN
ejpam-6417	179	6	,	,	PUNCT
ejpam-6417	179	7	el	el	PROPN
ejpam-6417	179	8	mostafa	mostafa	PROPN
ejpam-6417	179	9	sadek	sadek	PROPN
ejpam-6417	179	10	,	,	PUNCT
ejpam-6417	179	11	and	and	CCONJ
ejpam-6417	179	12	hamad	hamad	PROPN
ejpam-6417	179	13	talibi	talibi	PROPN
ejpam-6417	179	14	alaoui	alaoui	PROPN
ejpam-6417	179	15	.	.	PUNCT
ejpam-6417	180	1	on	on	ADP
ejpam-6417	180	2	some	some	DET
ejpam-6417	180	3	numerical	numerical	ADJ
ejpam-6417	180	4	methods	method	NOUN
ejpam-6417	180	5	for	for	ADP
ejpam-6417	180	6	solving	solve	VERB
ejpam-6417	180	7	large	large	ADJ
ejpam-6417	180	8	differential	differential	ADJ
ejpam-6417	180	9	nonsymmetric	nonsymmetric	PROPN
ejpam-6417	180	10	stein	stein	PROPN
ejpam-6417	180	11	matrix	matrix	PROPN
ejpam-6417	180	12	equations	equation	NOUN
ejpam-6417	180	13	.	.	PUNCT
ejpam-6417	181	1	mathematical	mathematical	ADJ
ejpam-6417	181	2	and	and	CCONJ
ejpam-6417	181	3	computational	computational	ADJ
ejpam-6417	181	4	applications	application	NOUN
ejpam-6417	181	5	,	,	PUNCT
ejpam-6417	181	6	27(4):69	27(4):69	NUM
ejpam-6417	181	7	,	,	PUNCT
ejpam-6417	181	8	2022	2022	NUM
ejpam-6417	181	9	.	.	PUNCT
ejpam-6417	182	1	[	[	X
ejpam-6417	182	2	4	4	NUM
ejpam-6417	182	3	]	]	PUNCT
ejpam-6417	182	4	lieven	lieven	VERB
ejpam-6417	182	5	vandenberghe	vandenberghe	PROPN
ejpam-6417	182	6	and	and	CCONJ
ejpam-6417	182	7	stephen	stephen	PROPN
ejpam-6417	182	8	boyd	boyd	PROPN
ejpam-6417	182	9	.	.	PUNCT
ejpam-6417	183	1	semidefinite	semidefinite	PROPN
ejpam-6417	183	2	programming	programming	PROPN
ejpam-6417	183	3	.	.	PUNCT
ejpam-6417	184	1	siam	siam	PROPN
ejpam-6417	184	2	review	review	PROPN
ejpam-6417	184	3	,	,	PUNCT
ejpam-6417	184	4	38(1):49–95	38(1):49–95	NUM
ejpam-6417	184	5	,	,	PUNCT
ejpam-6417	184	6	1996	1996	NUM
ejpam-6417	184	7	.	.	PUNCT
ejpam-6417	185	1	[	[	X
ejpam-6417	185	2	5	5	NUM
ejpam-6417	185	3	]	]	X
ejpam-6417	185	4	hassan	hassan	PROPN
ejpam-6417	185	5	k	k	PROPN
ejpam-6417	185	6	khalil	khalil	PROPN
ejpam-6417	185	7	and	and	CCONJ
ejpam-6417	185	8	jessy	jessy	PROPN
ejpam-6417	185	9	w	w	PROPN
ejpam-6417	185	10	grizzle	grizzle	PROPN
ejpam-6417	185	11	.	.	PUNCT
ejpam-6417	186	1	nonlinear	nonlinear	ADJ
ejpam-6417	186	2	systems	system	NOUN
ejpam-6417	186	3	,	,	PUNCT
ejpam-6417	186	4	volume	volume	NOUN
ejpam-6417	186	5	3	3	NUM
ejpam-6417	186	6	.	.	PUNCT
ejpam-6417	186	7	prentice	prentice	PROPN
ejpam-6417	186	8	hall	hall	PROPN
ejpam-6417	186	9	upper	upper	PROPN
ejpam-6417	186	10	saddle	saddle	PROPN
ejpam-6417	186	11	river	river	PROPN
ejpam-6417	186	12	,	,	PUNCT
ejpam-6417	186	13	nj	nj	PROPN
ejpam-6417	186	14	,	,	PUNCT
ejpam-6417	186	15	2002	2002	NUM
ejpam-6417	186	16	.	.	PUNCT
ejpam-6417	187	1	[	[	X
ejpam-6417	187	2	6	6	NUM
ejpam-6417	187	3	]	]	X
ejpam-6417	187	4	reza	reza	PROPN
ejpam-6417	187	5	olfati	olfati	PROPN
ejpam-6417	187	6	-	-	PUNCT
ejpam-6417	187	7	saber	saber	NOUN
ejpam-6417	187	8	,	,	PUNCT
ejpam-6417	187	9	j	j	PROPN
ejpam-6417	187	10	alex	alex	PROPN
ejpam-6417	187	11	fax	fax	PROPN
ejpam-6417	187	12	,	,	PUNCT
ejpam-6417	187	13	and	and	CCONJ
ejpam-6417	187	14	richard	richard	PROPN
ejpam-6417	187	15	m	m	PROPN
ejpam-6417	187	16	murray	murray	PROPN
ejpam-6417	187	17	.	.	PUNCT
ejpam-6417	188	1	consensus	consensus	NOUN
ejpam-6417	188	2	and	and	CCONJ
ejpam-6417	188	3	cooperation	cooperation	NOUN
ejpam-6417	188	4	in	in	ADP
ejpam-6417	188	5	networked	networked	ADJ
ejpam-6417	188	6	multi	multi	ADJ
ejpam-6417	188	7	-	-	ADJ
ejpam-6417	188	8	agent	agent	ADJ
ejpam-6417	188	9	systems	system	NOUN
ejpam-6417	188	10	.	.	PUNCT
ejpam-6417	189	1	proceedings	proceeding	NOUN
ejpam-6417	189	2	of	of	ADP
ejpam-6417	189	3	the	the	DET
ejpam-6417	189	4	ieee	ieee	NOUN
ejpam-6417	189	5	,	,	PUNCT
ejpam-6417	189	6	95(1):215–233	95(1):215–233	NUM
ejpam-6417	189	7	,	,	PUNCT
ejpam-6417	189	8	2007	2007	NUM
ejpam-6417	189	9	.	.	PUNCT
ejpam-6417	190	1	[	[	X
ejpam-6417	190	2	7	7	X
ejpam-6417	190	3	]	]	X
ejpam-6417	190	4	lakhlifa	lakhlifa	PROPN
ejpam-6417	190	5	sadek	sadek	PROPN
ejpam-6417	190	6	,	,	PUNCT
ejpam-6417	190	7	hamad	hamad	PROPN
ejpam-6417	190	8	talibi	talibi	PROPN
ejpam-6417	190	9	alaoui	alaoui	PROPN
ejpam-6417	190	10	,	,	PUNCT
ejpam-6417	190	11	et	et	PROPN
ejpam-6417	190	12	al	al	PROPN
ejpam-6417	190	13	.	.	PUNCT
ejpam-6417	191	1	the	the	DET
ejpam-6417	191	2	extended	extend	VERB
ejpam-6417	191	3	block	block	NOUN
ejpam-6417	191	4	arnoldi	arnoldi	ADJ
ejpam-6417	191	5	approach	approach	NOUN
ejpam-6417	191	6	for	for	ADP
ejpam-6417	191	7	solving	solve	VERB
ejpam-6417	191	8	large	large	ADJ
ejpam-6417	191	9	differential	differential	ADJ
ejpam-6417	191	10	matrix	matrix	NOUN
ejpam-6417	191	11	equations	equation	NOUN
ejpam-6417	191	12	t	t	PROPN
ejpam-6417	191	13	-	-	PUNCT
ejpam-6417	191	14	sylvester	sylvester	NOUN
ejpam-6417	191	15	and	and	CCONJ
ejpam-6417	191	16	nonsymmetric	nonsymmetric	PROPN
ejpam-6417	191	17	t	t	PROPN
ejpam-6417	191	18	-	-	PUNCT
ejpam-6417	191	19	riccati	riccati	NOUN
ejpam-6417	191	20	.	.	PUNCT
ejpam-6417	192	1	in	in	ADP
ejpam-6417	192	2	international	international	ADJ
ejpam-6417	192	3	conference	conference	NOUN
ejpam-6417	192	4	on	on	ADP
ejpam-6417	192	5	research	research	NOUN
ejpam-6417	192	6	in	in	ADP
ejpam-6417	192	7	applied	apply	VERB
ejpam-6417	192	8	mathematics	mathematic	NOUN
ejpam-6417	192	9	and	and	CCONJ
ejpam-6417	192	10	computer	computer	NOUN
ejpam-6417	192	11	science	science	NOUN
ejpam-6417	192	12	,	,	PUNCT
ejpam-6417	192	13	volume	volume	NOUN
ejpam-6417	192	14	2021	2021	NUM
ejpam-6417	192	15	.	.	PUNCT
ejpam-6417	193	1	icramcs	icramcs	ADJ
ejpam-6417	193	2	2021	2021	NUM
ejpam-6417	193	3	,	,	PUNCT
ejpam-6417	193	4	2021	2021	NUM
ejpam-6417	193	5	.	.	PUNCT
ejpam-6417	194	1	[	[	X
ejpam-6417	194	2	8	8	NUM
ejpam-6417	194	3	]	]	X
ejpam-6417	194	4	william	william	PROPN
ejpam-6417	194	5	h	h	PROPN
ejpam-6417	194	6	sandholm	sandholm	PROPN
ejpam-6417	194	7	.	.	PUNCT
ejpam-6417	195	1	population	population	NOUN
ejpam-6417	195	2	games	game	NOUN
ejpam-6417	195	3	and	and	CCONJ
ejpam-6417	195	4	evolutionary	evolutionary	ADJ
ejpam-6417	195	5	dynamics	dynamic	NOUN
ejpam-6417	195	6	.	.	PUNCT
ejpam-6417	196	1	mit	mit	PROPN
ejpam-6417	196	2	press	press	PROPN
ejpam-6417	196	3	,	,	PUNCT
ejpam-6417	196	4	2010	2010	NUM
ejpam-6417	196	5	.	.	PUNCT
ejpam-6417	197	1	[	[	X
ejpam-6417	197	2	9	9	NUM
ejpam-6417	197	3	]	]	X
ejpam-6417	197	4	aleksandr	aleksandr	PROPN
ejpam-6417	197	5	mikhailovich	mikhailovich	X
ejpam-6417	197	6	lyapunov	lyapunov	PROPN
ejpam-6417	197	7	.	.	PUNCT
ejpam-6417	198	1	the	the	DET
ejpam-6417	198	2	general	general	ADJ
ejpam-6417	198	3	problem	problem	NOUN
ejpam-6417	198	4	of	of	ADP
ejpam-6417	198	5	the	the	DET
ejpam-6417	198	6	stability	stability	NOUN
ejpam-6417	198	7	of	of	ADP
ejpam-6417	198	8	motion	motion	NOUN
ejpam-6417	198	9	.	.	PUNCT
ejpam-6417	199	1	international	international	ADJ
ejpam-6417	199	2	journal	journal	PROPN
ejpam-6417	199	3	of	of	ADP
ejpam-6417	199	4	control	control	NOUN
ejpam-6417	199	5	,	,	PUNCT
ejpam-6417	199	6	55(3):531–534	55(3):531–534	NUM
ejpam-6417	199	7	,	,	PUNCT
ejpam-6417	199	8	1992	1992	NUM
ejpam-6417	199	9	.	.	PUNCT
ejpam-6417	200	1	[	[	X
ejpam-6417	200	2	10	10	NUM
ejpam-6417	200	3	]	]	X
ejpam-6417	200	4	eugenius	eugenius	PROPN
ejpam-6417	200	5	kaszkurewicz	kaszkurewicz	PROPN
ejpam-6417	200	6	and	and	CCONJ
ejpam-6417	200	7	amit	amit	PROPN
ejpam-6417	200	8	bhaya	bhaya	PROPN
ejpam-6417	200	9	.	.	PUNCT
ejpam-6417	200	10	matrix	matrix	NOUN
ejpam-6417	200	11	diagonal	diagonal	ADJ
ejpam-6417	200	12	stability	stability	NOUN
ejpam-6417	200	13	in	in	ADP
ejpam-6417	200	14	systems	system	NOUN
ejpam-6417	200	15	and	and	CCONJ
ejpam-6417	200	16	computation	computation	NOUN
ejpam-6417	200	17	.	.	PUNCT
ejpam-6417	201	1	springer	springer	NOUN
ejpam-6417	201	2	science	science	PROPN
ejpam-6417	201	3	&	&	CCONJ
ejpam-6417	201	4	business	business	NOUN
ejpam-6417	201	5	media	medium	NOUN
ejpam-6417	201	6	,	,	PUNCT
ejpam-6417	201	7	2012	2012	NUM
ejpam-6417	201	8	.	.	PUNCT
ejpam-6417	202	1	[	[	X
ejpam-6417	202	2	11	11	NUM
ejpam-6417	202	3	]	]	PUNCT
ejpam-6417	202	4	abraham	abraham	PROPN
ejpam-6417	202	5	berman	berman	PROPN
ejpam-6417	202	6	and	and	CCONJ
ejpam-6417	202	7	robert	robert	PROPN
ejpam-6417	202	8	j	j	PROPN
ejpam-6417	202	9	plemmons	plemmon	NOUN
ejpam-6417	202	10	.	.	PUNCT
ejpam-6417	203	1	nonnegative	nonnegative	ADJ
ejpam-6417	203	2	matrices	matrix	NOUN
ejpam-6417	203	3	in	in	ADP
ejpam-6417	203	4	the	the	DET
ejpam-6417	203	5	mathematical	mathematical	ADJ
ejpam-6417	203	6	sciences	science	NOUN
ejpam-6417	203	7	.	.	PUNCT
ejpam-6417	204	1	siam	siam	PROPN
ejpam-6417	204	2	,	,	PUNCT
ejpam-6417	204	3	1994	1994	NUM
ejpam-6417	204	4	.	.	PUNCT
ejpam-6417	205	1	[	[	X
ejpam-6417	205	2	12	12	NUM
ejpam-6417	205	3	]	]	X
ejpam-6417	205	4	daniel	daniel	PROPN
ejpam-6417	205	5	hershkowitz	hershkowitz	PROPN
ejpam-6417	205	6	.	.	PUNCT
ejpam-6417	206	1	recent	recent	ADJ
ejpam-6417	206	2	directions	direction	NOUN
ejpam-6417	206	3	in	in	ADP
ejpam-6417	206	4	matrix	matrix	NOUN
ejpam-6417	206	5	stability	stability	NOUN
ejpam-6417	206	6	.	.	PUNCT
ejpam-6417	207	1	linear	linear	ADJ
ejpam-6417	207	2	algebra	algebra	NOUN
ejpam-6417	207	3	and	and	CCONJ
ejpam-6417	207	4	its	its	PRON
ejpam-6417	207	5	applications	application	NOUN
ejpam-6417	207	6	,	,	PUNCT
ejpam-6417	207	7	171:161–186	171:161–186	NUM
ejpam-6417	207	8	,	,	PUNCT
ejpam-6417	207	9	1992	1992	NUM
ejpam-6417	207	10	.	.	PUNCT
ejpam-6417	208	1	[	[	X
ejpam-6417	208	2	13	13	NUM
ejpam-6417	208	3	]	]	X
ejpam-6417	208	4	zhongkui	zhongkui	PROPN
ejpam-6417	208	5	li	li	PROPN
ejpam-6417	208	6	,	,	PUNCT
ejpam-6417	208	7	zhisheng	zhisheng	PROPN
ejpam-6417	208	8	duan	duan	PROPN
ejpam-6417	208	9	,	,	PUNCT
ejpam-6417	208	10	guanrong	guanrong	PROPN
ejpam-6417	208	11	chen	chen	PROPN
ejpam-6417	208	12	,	,	PUNCT
ejpam-6417	208	13	and	and	CCONJ
ejpam-6417	208	14	lin	lin	PROPN
ejpam-6417	208	15	huang	huang	PROPN
ejpam-6417	208	16	.	.	PUNCT
ejpam-6417	209	1	consensus	consensus	NOUN
ejpam-6417	209	2	of	of	ADP
ejpam-6417	209	3	multiagent	multiagent	NOUN
ejpam-6417	209	4	systems	system	NOUN
ejpam-6417	209	5	and	and	CCONJ
ejpam-6417	209	6	synchronization	synchronization	NOUN
ejpam-6417	209	7	of	of	ADP
ejpam-6417	209	8	complex	complex	ADJ
ejpam-6417	209	9	networks	network	NOUN
ejpam-6417	209	10	:	:	PUNCT
ejpam-6417	209	11	a	a	DET
ejpam-6417	209	12	unified	unified	ADJ
ejpam-6417	209	13	viewpoint	viewpoint	NOUN
ejpam-6417	209	14	.	.	PUNCT
ejpam-6417	210	1	ieee	ieee	NOUN
ejpam-6417	210	2	transactions	transaction	NOUN
ejpam-6417	210	3	on	on	ADP
ejpam-6417	210	4	circuits	circuit	NOUN
ejpam-6417	210	5	and	and	CCONJ
ejpam-6417	210	6	systems	system	NOUN
ejpam-6417	210	7	i	i	PRON
ejpam-6417	210	8	:	:	PUNCT
ejpam-6417	210	9	regular	regular	ADJ
ejpam-6417	210	10	papers	paper	NOUN
ejpam-6417	210	11	,	,	PUNCT
ejpam-6417	210	12	57(1):213–224	57(1):213–224	NUM
ejpam-6417	210	13	,	,	PUNCT
ejpam-6417	210	14	2009	2009	NUM
ejpam-6417	210	15	.	.	PUNCT
ejpam-6417	211	1	[	[	X
ejpam-6417	211	2	14	14	NUM
ejpam-6417	211	3	]	]	X
ejpam-6417	211	4	josef	josef	PROPN
ejpam-6417	211	5	hofbauer	hofbauer	PROPN
ejpam-6417	211	6	and	and	CCONJ
ejpam-6417	211	7	karl	karl	PROPN
ejpam-6417	211	8	sigmund	sigmund	PROPN
ejpam-6417	211	9	.	.	PUNCT
ejpam-6417	212	1	evolutionary	evolutionary	ADJ
ejpam-6417	212	2	games	game	NOUN
ejpam-6417	212	3	and	and	CCONJ
ejpam-6417	212	4	population	population	NOUN
ejpam-6417	212	5	dynamics	dynamic	NOUN
ejpam-6417	212	6	.	.	PUNCT
ejpam-6417	213	1	cambridge	cambridge	PROPN
ejpam-6417	213	2	university	university	PROPN
ejpam-6417	213	3	press	press	NOUN
ejpam-6417	213	4	,	,	PUNCT
ejpam-6417	213	5	1998	1998	NUM
ejpam-6417	213	6	.	.	PUNCT
ejpam-6417	214	1	a.	a.	PROPN
ejpam-6417	214	2	algefary	algefary	PROPN
ejpam-6417	214	3	,	,	PUNCT
ejpam-6417	214	4	t.	t.	PROPN
ejpam-6417	214	5	alhumaidan	alhumaidan	PROPN
ejpam-6417	214	6	/	/	SYM
ejpam-6417	214	7	eur	eur	PROPN
ejpam-6417	214	8	.	.	PUNCT
ejpam-6417	215	1	j.	j.	PROPN
ejpam-6417	215	2	pure	pure	PROPN
ejpam-6417	215	3	appl	appl	PROPN
ejpam-6417	215	4	.	.	PROPN
ejpam-6417	215	5	math	math	PROPN
ejpam-6417	215	6	,	,	PUNCT
ejpam-6417	215	7	18	18	NUM
ejpam-6417	215	8	(	(	PUNCT
ejpam-6417	215	9	3	3	NUM
ejpam-6417	215	10	)	)	PUNCT
ejpam-6417	215	11	(	(	PUNCT
ejpam-6417	215	12	2025	2025	NUM
ejpam-6417	215	13	)	)	PUNCT
ejpam-6417	215	14	,	,	PUNCT
ejpam-6417	215	15	6417	6417	NUM
ejpam-6417	215	16	10	10	NUM
ejpam-6417	215	17	of	of	ADP
ejpam-6417	215	18	10	10	NUM
ejpam-6417	216	1	[	[	SYM
ejpam-6417	216	2	15	15	NUM
ejpam-6417	216	3	]	]	X
ejpam-6417	216	4	gw	gw	PROPN
ejpam-6417	216	5	cross	cross	NOUN
ejpam-6417	216	6	.	.	PUNCT
ejpam-6417	217	1	three	three	NUM
ejpam-6417	217	2	types	type	NOUN
ejpam-6417	217	3	of	of	ADP
ejpam-6417	217	4	matrix	matrix	NOUN
ejpam-6417	217	5	stability	stability	NOUN
ejpam-6417	217	6	.	.	PUNCT
ejpam-6417	218	1	linear	linear	ADJ
ejpam-6417	218	2	algebra	algebra	NOUN
ejpam-6417	218	3	and	and	CCONJ
ejpam-6417	218	4	its	its	PRON
ejpam-6417	218	5	applications	application	NOUN
ejpam-6417	218	6	,	,	PUNCT
ejpam-6417	218	7	20(3):253–263	20(3):253–263	PROPN
ejpam-6417	218	8	,	,	PUNCT
ejpam-6417	218	9	1978	1978	NUM
ejpam-6417	218	10	.	.	PUNCT
ejpam-6417	219	1	[	[	X
ejpam-6417	219	2	16	16	NUM
ejpam-6417	219	3	]	]	X
ejpam-6417	219	4	roger	roger	PROPN
ejpam-6417	219	5	a	a	DET
ejpam-6417	219	6	horn	horn	NOUN
ejpam-6417	219	7	and	and	CCONJ
ejpam-6417	219	8	charles	charles	PROPN
ejpam-6417	219	9	r	r	PROPN
ejpam-6417	219	10	johnson	johnson	PROPN
ejpam-6417	219	11	.	.	PROPN
ejpam-6417	220	1	matrix	matrix	NOUN
ejpam-6417	220	2	analysis	analysis	NOUN
ejpam-6417	220	3	.	.	PUNCT
ejpam-6417	221	1	cambridge	cambridge	PROPN
ejpam-6417	221	2	university	university	PROPN
ejpam-6417	221	3	press	press	NOUN
ejpam-6417	221	4	,	,	PUNCT
ejpam-6417	221	5	2012	2012	NUM
ejpam-6417	221	6	.	.	PUNCT
ejpam-6417	222	1	[	[	X
ejpam-6417	222	2	17	17	NUM
ejpam-6417	222	3	]	]	X
ejpam-6417	222	4	george	george	PROPN
ejpam-6417	222	5	ph	ph	PROPN
ejpam-6417	222	6	styan	styan	PROPN
ejpam-6417	222	7	.	.	PUNCT
ejpam-6417	223	1	hadamard	hadamard	ADJ
ejpam-6417	223	2	products	product	NOUN
ejpam-6417	223	3	and	and	CCONJ
ejpam-6417	223	4	multivariate	multivariate	VERB
ejpam-6417	223	5	statistical	statistical	ADJ
ejpam-6417	223	6	analysis	analysis	NOUN
ejpam-6417	223	7	.	.	PUNCT
ejpam-6417	224	1	linear	linear	ADJ
ejpam-6417	224	2	algebra	algebra	NOUN
ejpam-6417	224	3	and	and	CCONJ
ejpam-6417	224	4	its	its	PRON
ejpam-6417	224	5	applications	application	NOUN
ejpam-6417	224	6	,	,	PUNCT
ejpam-6417	224	7	6:217–240	6:217–240	NUM
ejpam-6417	224	8	,	,	PUNCT
ejpam-6417	224	9	1973	1973	NUM
ejpam-6417	224	10	.	.	PUNCT
ejpam-6417	225	1	[	[	X
ejpam-6417	225	2	18	18	NUM
ejpam-6417	225	3	]	]	PUNCT
ejpam-6417	225	4	a.	a.	NOUN
ejpam-6417	225	5	algefary	algefary	PROPN
ejpam-6417	225	6	and	and	CCONJ
ejpam-6417	225	7	a.	a.	PROPN
ejpam-6417	225	8	s.	s.	PROPN
ejpam-6417	225	9	m.	m.	PROPN
ejpam-6417	225	10	al	al	PROPN
ejpam-6417	225	11	luhayb	luhayb	PROPN
ejpam-6417	225	12	.	.	PUNCT
ejpam-6417	226	1	stability	stability	NOUN
ejpam-6417	226	2	analysis	analysis	NOUN
ejpam-6417	226	3	of	of	ADP
ejpam-6417	226	4	linear	linear	ADJ
ejpam-6417	226	5	time	time	NOUN
ejpam-6417	226	6	invariant	invariant	ADJ
ejpam-6417	226	7	difference	difference	NOUN
ejpam-6417	226	8	-	-	PUNCT
ejpam-6417	226	9	differential	differential	NOUN
ejpam-6417	226	10	system	system	NOUN
ejpam-6417	226	11	with	with	ADP
ejpam-6417	226	12	constant	constant	ADJ
ejpam-6417	226	13	and	and	CCONJ
ejpam-6417	226	14	distributed	distribute	VERB
ejpam-6417	226	15	delays	delay	NOUN
ejpam-6417	226	16	.	.	PUNCT