id	sid	tid	token	lemma	pos
ap-942	1	1	ap07_2-3.vp	ap07_2-3.vp	VERB
ap-942	1	2	in	in	ADP
ap-942	1	3	[	[	X
ap-942	1	4	1	1	NUM
ap-942	1	5	]	]	PUNCT
ap-942	1	6	,	,	PUNCT
ap-942	1	7	the	the	DET
ap-942	1	8	authors	author	NOUN
ap-942	1	9	study	study	VERB
ap-942	1	10	matrices	matrix	NOUN
ap-942	1	11	of	of	ADP
ap-942	1	12	morphisms	morphism	NOUN
ap-942	1	13	preserving	preserve	VERB
ap-942	1	14	the	the	DET
ap-942	1	15	family	family	NOUN
ap-942	1	16	of	of	ADP
ap-942	1	17	words	word	NOUN
ap-942	1	18	coding	code	VERB
ap-942	1	19	3	3	NUM
ap-942	1	20	-	-	PUNCT
ap-942	1	21	interval	interval	NOUN
ap-942	1	22	exchange	exchange	NOUN
ap-942	1	23	transformations	transformation	NOUN
ap-942	1	24	.	.	PUNCT
ap-942	2	1	it	it	PRON
ap-942	2	2	is	be	AUX
ap-942	2	3	well	well	ADV
ap-942	2	4	known	known	ADJ
ap-942	2	5	[	[	X
ap-942	2	6	2–4	2–4	NUM
ap-942	2	7	]	]	X
ap-942	2	8	that	that	SCONJ
ap-942	2	9	matrices	matrix	NOUN
ap-942	2	10	of	of	ADP
ap-942	2	11	morphisms	morphism	NOUN
ap-942	2	12	preserving	preserve	VERB
ap-942	2	13	sturmian	sturmian	NOUN
ap-942	2	14	words	word	NOUN
ap-942	2	15	(	(	PUNCT
ap-942	2	16	i.e.	i.e.	X
ap-942	2	17	words	word	NOUN
ap-942	2	18	coding	code	VERB
ap-942	2	19	2	2	NUM
ap-942	2	20	-	-	PUNCT
ap-942	2	21	interval	interval	NOUN
ap-942	2	22	exchange	exchange	NOUN
ap-942	2	23	transformations	transformation	NOUN
ap-942	2	24	with	with	ADP
ap-942	2	25	the	the	DET
ap-942	2	26	maximal	maximal	ADJ
ap-942	2	27	possible	possible	ADJ
ap-942	2	28	subword	subword	PROPN
ap-942	2	29	complexity	complexity	NOUN
ap-942	2	30	)	)	PUNCT
ap-942	2	31	form	form	VERB
ap-942	2	32	the	the	DET
ap-942	2	33	monoid	monoid	PROPN
ap-942	2	34	�	�	PROPN
ap-942	2	35	�	�	PROPN
ap-942	2	36	�	�	PROPN
ap-942	2	37	�	�	PROPN
ap-942	2	38	m	m	PROPN
ap-942	2	39	m	m	VERB
ap-942	2	40	m	m	VERB
ap-942	2	41	mem	mem	ADJ
ap-942	2	42	e	e	NOUN
ap-942	2	43	�	�	PROPN
ap-942	2	44	�	�	PROPN
ap-942	2	45	�	�	PROPN
ap-942	2	46	�	�	PROPN
ap-942	2	47	�	�	PROPN
ap-942	2	48	�	�	PROPN
ap-942	2	49	�	�	PROPN
ap-942	2	50	�	�	PROPN
ap-942	2	51	�	�	PROPN
ap-942	2	52	�	�	PROPN
ap-942	2	53	�	�	PROPN
ap-942	2	54	2	2	NUM
ap-942	2	55	2	2	NUM
ap-942	2	56	2	2	NUM
ap-942	2	57	21det	21det	NOUN
ap-942	2	58	,	,	PUNCT
ap-942	2	59	where	where	SCONJ
ap-942	2	60	e	e	X
ap-942	2	61	�	�	PROPN
ap-942	2	62	�	�	PROPN
ap-942	2	63	�	�	PROPN
ap-942	2	64	�	�	PROPN
ap-942	2	65	�	�	PROPN
ap-942	2	66	�	�	PROPN
ap-942	2	67	�	�	PROPN
ap-942	2	68	0	0	NUM
ap-942	2	69	1	1	NUM
ap-942	2	70	1	1	NUM
ap-942	2	71	0	0	NUM
ap-942	2	72	.	.	PUNCT
ap-942	3	1	the	the	DET
ap-942	3	2	result	result	NOUN
ap-942	3	3	of	of	ADP
ap-942	3	4	[	[	X
ap-942	3	5	1	1	NUM
ap-942	3	6	]	]	PUNCT
ap-942	3	7	states	state	VERB
ap-942	3	8	that	that	SCONJ
ap-942	3	9	in	in	ADP
ap-942	3	10	the	the	DET
ap-942	3	11	case	case	NOUN
ap-942	3	12	of	of	ADP
ap-942	3	13	3	3	NUM
ap-942	3	14	-	-	PUNCT
ap-942	3	15	interval	interval	NOUN
ap-942	3	16	exchange	exchange	NOUN
ap-942	3	17	transformations	transformation	VERB
ap-942	3	18	the	the	DET
ap-942	3	19	matrices	matrix	NOUN
ap-942	3	20	preserving	preserve	VERB
ap-942	3	21	words	word	NOUN
ap-942	3	22	coding	code	VERB
ap-942	3	23	these	these	DET
ap-942	3	24	transformations	transformation	NOUN
ap-942	3	25	and	and	CCONJ
ap-942	3	26	having	have	VERB
ap-942	3	27	the	the	DET
ap-942	3	28	maximal	maximal	ADJ
ap-942	3	29	possible	possible	ADJ
ap-942	3	30	subword	subword	PROPN
ap-942	3	31	complexity	complexity	NOUN
ap-942	3	32	belong	belong	VERB
ap-942	3	33	to	to	ADP
ap-942	3	34	the	the	DET
ap-942	3	35	monoid	monoid	PROPN
ap-942	3	36	�	�	PROPN
ap-942	3	37	�	�	PROPN
ap-942	3	38	m	m	PART
ap-942	3	39	mem	mem	ADJ
ap-942	3	40	e	e	PROPN
ap-942	3	41	m	m	PROPN
ap-942	3	42	�	�	PROPN
ap-942	3	43	�	�	PROPN
ap-942	3	44	�	�	PROPN
ap-942	3	45	�	�	PROPN
ap-942	3	46	�	�	PROPN
ap-942	3	47	�	�	PROPN
ap-942	3	48	�	�	PROPN
ap-942	3	49	3	3	NUM
ap-942	3	50	3	3	NUM
ap-942	3	51	1anddet	1anddet	NUM
ap-942	3	52	,	,	PUNCT
ap-942	3	53	where	where	SCONJ
ap-942	3	54	e	e	X
ap-942	3	55	�	�	PROPN
ap-942	3	56	�	�	PROPN
ap-942	3	57	�	�	PROPN
ap-942	3	58	�	�	PROPN
ap-942	3	59	�	�	PROPN
ap-942	3	60	�	�	PROPN
ap-942	3	61	�	�	PROPN
ap-942	3	62	�	�	PROPN
ap-942	3	63	�	�	PROPN
ap-942	3	64	�	�	PROPN
ap-942	3	65	�	�	PROPN
ap-942	3	66	0	0	NUM
ap-942	3	67	1	1	NUM
ap-942	3	68	1	1	NUM
ap-942	3	69	1	1	NUM
ap-942	3	70	0	0	NUM
ap-942	3	71	1	1	NUM
ap-942	3	72	1	1	NUM
ap-942	3	73	1	1	NUM
ap-942	3	74	0	0	NUM
ap-942	3	75	.	.	PUNCT
ap-942	4	1	we	we	PRON
ap-942	4	2	say	say	VERB
ap-942	4	3	that	that	SCONJ
ap-942	4	4	a	a	DET
ap-942	4	5	matrix	matrix	NOUN
ap-942	4	6	fulfilling	fulfil	VERB
ap-942	4	7	the	the	DET
ap-942	4	8	first	first	ADJ
ap-942	4	9	condition	condition	NOUN
ap-942	4	10	has	have	VERB
ap-942	4	11	the	the	DET
ap-942	4	12	so	so	ADV
ap-942	4	13	-	-	PUNCT
ap-942	4	14	called	call	VERB
ap-942	4	15	meme	meme	NOUN
ap-942	4	16	property	property	NOUN
ap-942	4	17	.	.	PUNCT
ap-942	5	1	definition	definition	NOUN
ap-942	5	2	1	1	NUM
ap-942	5	3	let	let	VERB
ap-942	5	4	m	m	PROPN
ap-942	5	5	�	�	PROPN
ap-942	5	6	�	�	PROPN
ap-942	5	7	�	�	PROPN
ap-942	5	8	3	3	NUM
ap-942	5	9	3	3	NUM
ap-942	5	10	.	.	PUNCT
ap-942	6	1	m	m	PROPN
ap-942	6	2	is	be	AUX
ap-942	6	3	said	say	VERB
ap-942	6	4	to	to	PART
ap-942	6	5	have	have	VERB
ap-942	6	6	the	the	DET
ap-942	6	7	meme	meme	NOUN
ap-942	6	8	property	property	NOUN
ap-942	6	9	if	if	SCONJ
ap-942	6	10	mem	mem	X
ap-942	6	11	et	et	PROPN
ap-942	6	12	�	�	PROPN
ap-942	6	13	�	�	PROPN
ap-942	6	14	,	,	PUNCT
ap-942	6	15	where	where	SCONJ
ap-942	6	16	e	e	X
ap-942	6	17	�	�	PROPN
ap-942	6	18	�	�	PROPN
ap-942	6	19	�	�	PROPN
ap-942	6	20	�	�	PROPN
ap-942	6	21	�	�	PROPN
ap-942	6	22	�	�	PROPN
ap-942	6	23	�	�	PROPN
ap-942	6	24	�	�	PROPN
ap-942	6	25	�	�	PROPN
ap-942	6	26	�	�	PROPN
ap-942	6	27	�	�	PROPN
ap-942	6	28	0	0	NUM
ap-942	6	29	1	1	NUM
ap-942	6	30	1	1	NUM
ap-942	6	31	1	1	NUM
ap-942	6	32	0	0	NUM
ap-942	6	33	1	1	NUM
ap-942	6	34	1	1	NUM
ap-942	6	35	1	1	NUM
ap-942	6	36	0	0	NUM
ap-942	6	37	.	.	PUNCT
ap-942	7	1	the	the	DET
ap-942	7	2	aim	aim	NOUN
ap-942	7	3	of	of	ADP
ap-942	7	4	this	this	DET
ap-942	7	5	paper	paper	NOUN
ap-942	7	6	is	be	AUX
ap-942	7	7	to	to	PART
ap-942	7	8	provide	provide	VERB
ap-942	7	9	a	a	DET
ap-942	7	10	stand	stand	VERB
ap-942	7	11	-	-	PUNCT
ap-942	7	12	alone	alone	ADJ
ap-942	7	13	result	result	NOUN
ap-942	7	14	connected	connect	VERB
ap-942	7	15	with	with	ADP
ap-942	7	16	this	this	DET
ap-942	7	17	property	property	NOUN
ap-942	7	18	.	.	PUNCT
ap-942	8	1	strictly	strictly	ADV
ap-942	8	2	speaking	speak	VERB
ap-942	8	3	,	,	PUNCT
ap-942	8	4	we	we	PRON
ap-942	8	5	prove	prove	VERB
ap-942	8	6	another	another	DET
ap-942	8	7	algebraic	algebraic	ADJ
ap-942	8	8	characterization	characterization	NOUN
ap-942	8	9	of	of	ADP
ap-942	8	10	matrices	matrix	NOUN
ap-942	8	11	having	have	VERB
ap-942	8	12	this	this	DET
ap-942	8	13	property	property	NOUN
ap-942	8	14	.	.	PUNCT
ap-942	9	1	before	before	SCONJ
ap-942	9	2	we	we	PRON
ap-942	9	3	give	give	VERB
ap-942	9	4	the	the	DET
ap-942	9	5	above	above	ADJ
ap-942	9	6	mentioned	mention	VERB
ap-942	9	7	characterization	characterization	NOUN
ap-942	9	8	,	,	PUNCT
ap-942	9	9	we	we	PRON
ap-942	9	10	need	need	VERB
ap-942	9	11	to	to	PART
ap-942	9	12	prove	prove	VERB
ap-942	9	13	the	the	DET
ap-942	9	14	following	follow	VERB
ap-942	9	15	technical	technical	ADJ
ap-942	9	16	lemma	lemma	PROPN
ap-942	9	17	.	.	PUNCT
ap-942	10	1	lemma	lemma	PROPN
ap-942	10	2	2	2	NUM
ap-942	10	3	let	let	VERB
ap-942	10	4	m	m	PROPN
ap-942	10	5	�	�	PROPN
ap-942	10	6	�	�	PROPN
ap-942	10	7	�	�	PROPN
ap-942	10	8	3	3	NUM
ap-942	10	9	3	3	NUM
ap-942	10	10	,	,	PUNCT
ap-942	10	11	m	m	PROPN
ap-942	10	12	�	�	PROPN
ap-942	10	13	�	�	PROPN
ap-942	10	14	�	�	PROPN
ap-942	10	15	(	(	PUNCT
ap-942	10	16	)	)	PUNCT
ap-942	10	17	,	,	PUNCT
ap-942	10	18	mij	mij	INTJ
ap-942	10	19	i	i	NOUN
ap-942	10	20	j1	j1	PROPN
ap-942	10	21	3	3	NUM
ap-942	10	22	be	be	AUX
ap-942	10	23	a	a	DET
ap-942	10	24	matrix	matrix	NOUN
ap-942	10	25	.	.	PUNCT
ap-942	11	1	then	then	ADV
ap-942	11	2	m	m	PROPN
ap-942	11	3	has	have	VERB
ap-942	11	4	the	the	DET
ap-942	11	5	meme	meme	NOUN
ap-942	11	6	property	property	NOUN
ap-942	11	7	if	if	SCONJ
ap-942	11	8	and	and	CCONJ
ap-942	11	9	only	only	ADV
ap-942	11	10	if	if	SCONJ
ap-942	11	11	there	there	PRON
ap-942	11	12	exists	exist	VERB
ap-942	11	13	�	�	PROPN
ap-942	11	14	�	�	PROPN
ap-942	11	15	�	�	PROPN
ap-942	11	16	�	�	PROPN
ap-942	11	17	�	�	PROPN
ap-942	11	18	1	1	NUM
ap-942	11	19	1	1	NUM
ap-942	11	20	,	,	PUNCT
ap-942	11	21	such	such	ADJ
ap-942	11	22	that	that	PRON
ap-942	11	23	det	det	NOUN
ap-942	11	24	1	1	NUM
ap-942	11	25	1	1	NUM
ap-942	11	26	1	1	NUM
ap-942	11	27	21	21	NUM
ap-942	11	28	22	22	NUM
ap-942	11	29	23	23	NUM
ap-942	11	30	31	31	NUM
ap-942	11	31	32	32	NUM
ap-942	11	32	33	33	NUM
ap-942	11	33	�	�	PROPN
ap-942	11	34	�	�	PROPN
ap-942	11	35	�	�	PROPN
ap-942	11	36	�	�	PROPN
ap-942	11	37	�	�	PROPN
ap-942	11	38	�	�	PROPN
ap-942	11	39	�	�	PROPN
ap-942	11	40	�	�	PROPN
ap-942	11	41	�	�	PROPN
ap-942	11	42	m	m	NOUN
ap-942	11	43	m	m	VERB
ap-942	11	44	m	m	VERB
ap-942	11	45	m	m	VERB
ap-942	11	46	m	m	VERB
ap-942	11	47	m	m	VERB
ap-942	11	48	�	�	PROPN
ap-942	11	49	,	,	PUNCT
ap-942	11	50	(	(	PUNCT
ap-942	11	51	1	1	X
ap-942	11	52	)	)	PUNCT
ap-942	11	53	det	det	PROPN
ap-942	11	54	m	m	PROPN
ap-942	11	55	m	m	VERB
ap-942	11	56	m	m	VERB
ap-942	11	57	m	m	VERB
ap-942	11	58	m	m	VERB
ap-942	11	59	m	m	VERB
ap-942	11	60	11	11	NUM
ap-942	11	61	12	12	NUM
ap-942	11	62	13	13	NUM
ap-942	11	63	31	31	NUM
ap-942	11	64	32	32	NUM
ap-942	11	65	32	32	NUM
ap-942	11	66	1	1	NUM
ap-942	11	67	1	1	NUM
ap-942	11	68	1	1	NUM
ap-942	11	69	�	�	PROPN
ap-942	11	70	�	�	PROPN
ap-942	11	71	�	�	PROPN
ap-942	11	72	�	�	PROPN
ap-942	11	73	�	�	PROPN
ap-942	11	74	�	�	PROPN
ap-942	11	75	�	�	PROPN
ap-942	11	76	�	�	PROPN
ap-942	11	77	�	�	PROPN
ap-942	11	78	�	�	PROPN
ap-942	11	79	�	�	PROPN
ap-942	11	80	,	,	PUNCT
ap-942	11	81	(	(	PUNCT
ap-942	11	82	2	2	X
ap-942	11	83	)	)	PUNCT
ap-942	11	84	det	det	NOUN
ap-942	11	85	m	m	PROPN
ap-942	11	86	m	m	VERB
ap-942	11	87	m	m	VERB
ap-942	11	88	m	m	VERB
ap-942	11	89	m	m	VERB
ap-942	11	90	m	m	VERB
ap-942	11	91	11	11	NUM
ap-942	11	92	12	12	NUM
ap-942	11	93	13	13	NUM
ap-942	11	94	21	21	NUM
ap-942	11	95	22	22	NUM
ap-942	11	96	23	23	NUM
ap-942	11	97	1	1	NUM
ap-942	11	98	1	1	NUM
ap-942	11	99	1	1	NUM
ap-942	11	100	�	�	PROPN
ap-942	11	101	�	�	PROPN
ap-942	11	102	�	�	PROPN
ap-942	11	103	�	�	PROPN
ap-942	11	104	�	�	PROPN
ap-942	11	105	�	�	PROPN
ap-942	11	106	�	�	PROPN
ap-942	11	107	�	�	PROPN
ap-942	11	108	�	�	PROPN
ap-942	11	109	�	�	PROPN
ap-942	11	110	.	.	PUNCT
ap-942	12	1	(	(	PUNCT
ap-942	12	2	3	3	X
ap-942	12	3	)	)	PUNCT
ap-942	12	4	proof	proof	NOUN
ap-942	12	5	.	.	PUNCT
ap-942	13	1	let	let	VERB
ap-942	13	2	us	we	PRON
ap-942	13	3	denote	denote	VERB
ap-942	13	4	k	k	PROPN
ap-942	13	5	mem	mem	PROPN
ap-942	13	6	�	�	PROPN
ap-942	13	7	t	t	PROPN
ap-942	13	8	.	.	PUNCT
ap-942	14	1	the	the	DET
ap-942	14	2	transpose	transpose	NOUN
ap-942	14	3	of	of	ADP
ap-942	14	4	k	k	PROPN
ap-942	14	5	is	be	AUX
ap-942	14	6	k	k	PROPN
ap-942	14	7	m	m	PROPN
ap-942	14	8	e	e	NOUN
ap-942	14	9	m	m	PROPN
ap-942	14	10	kt	kt	PROPN
ap-942	14	11	t	t	PROPN
ap-942	14	12	�	�	PROPN
ap-942	14	13	�	�	PROPN
ap-942	14	14	�	�	PROPN
ap-942	14	15	�	�	PROPN
ap-942	14	16	(	(	PUNCT
ap-942	14	17	)	)	PUNCT
ap-942	14	18	and	and	CCONJ
ap-942	14	19	hence	hence	ADV
ap-942	14	20	k	k	PROPN
ap-942	14	21	is	be	AUX
ap-942	14	22	an	an	DET
ap-942	14	23	anti	anti	ADJ
ap-942	14	24	-	-	ADJ
ap-942	14	25	symmetric	symmetric	ADJ
ap-942	14	26	matrix	matrix	NOUN
ap-942	14	27	.	.	PUNCT
ap-942	15	1	to	to	PART
ap-942	15	2	investigate	investigate	VERB
ap-942	15	3	equalities	equality	NOUN
ap-942	15	4	of	of	ADP
ap-942	15	5	anti	anti	ADJ
ap-942	15	6	-	-	ADJ
ap-942	15	7	symmetric	symmetric	ADJ
ap-942	15	8	matrices	matrix	NOUN
ap-942	15	9	it	it	PRON
ap-942	15	10	suffices	suffice	VERB
ap-942	15	11	to	to	PART
ap-942	15	12	consider	consider	VERB
ap-942	15	13	elements	element	NOUN
ap-942	15	14	k12	k12	NOUN
ap-942	15	15	,	,	PUNCT
ap-942	15	16	k13	k13	PROPN
ap-942	15	17	,	,	PUNCT
ap-942	15	18	k23	k23	PROPN
ap-942	15	19	.	.	PUNCT
ap-942	16	1	let	let	VERB
ap-942	16	2	us	we	PRON
ap-942	16	3	compute	compute	VERB
ap-942	16	4	these	these	DET
ap-942	16	5	relevant	relevant	ADJ
ap-942	16	6	elements	element	NOUN
ap-942	16	7	of	of	ADP
ap-942	16	8	k.	k.	PROPN
ap-942	16	9	k	k	PROPN
ap-942	17	1	k	k	PROPN
ap-942	18	1	k	k	PROPN
ap-942	19	1	k	k	PROPN
ap-942	19	2	k	k	PROPN
ap-942	20	1	k	k	PROPN
ap-942	20	2	k	k	PROPN
ap-942	20	3	m	m	VERB
ap-942	20	4	m	m	VERB
ap-942	20	5	m	m	VERB
ap-942	20	6	t	t	PROPN
ap-942	20	7	�	�	PROPN
ap-942	20	8	�	�	PROPN
ap-942	20	9	�	�	PROPN
ap-942	20	10	�	�	PROPN
ap-942	20	11	�	�	PROPN
ap-942	20	12	�	�	PROPN
ap-942	20	13	�	�	PROPN
ap-942	20	14	�	�	PROPN
ap-942	20	15	�	�	PROPN
ap-942	20	16	�	�	PROPN
ap-942	20	17	�	�	PROPN
ap-942	20	18	�	�	PROPN
ap-942	20	19	�	�	PROPN
ap-942	20	20	0	0	NUM
ap-942	20	21	0	0	NUM
ap-942	20	22	0	0	NUM
ap-942	20	23	12	12	NUM
ap-942	20	24	13	13	NUM
ap-942	20	25	12	12	NUM
ap-942	20	26	23	23	NUM
ap-942	20	27	13	13	NUM
ap-942	20	28	23	23	NUM
ap-942	20	29	11	11	NUM
ap-942	20	30	12	12	NUM
ap-942	20	31	1	1	NUM
ap-942	20	32	mem	mem	NOUN
ap-942	20	33	3	3	NUM
ap-942	20	34	21	21	NUM
ap-942	20	35	22	22	NUM
ap-942	20	36	23	23	NUM
ap-942	20	37	31	31	NUM
ap-942	20	38	32	32	NUM
ap-942	20	39	33	33	NUM
ap-942	20	40	0	0	NUM
ap-942	20	41	1	1	NUM
ap-942	20	42	1	1	NUM
ap-942	20	43	1	1	NUM
ap-942	20	44	0	0	NUM
ap-942	20	45	1	1	NUM
ap-942	20	46	1	1	NUM
ap-942	20	47	1	1	NUM
ap-942	20	48	0	0	NUM
ap-942	20	49	m	m	VERB
ap-942	20	50	m	m	VERB
ap-942	20	51	m	m	VERB
ap-942	20	52	m	m	VERB
ap-942	20	53	m	m	VERB
ap-942	20	54	m	m	PROPN
ap-942	20	55	�	�	PROPN
ap-942	20	56	�	�	PROPN
ap-942	20	57	�	�	PROPN
ap-942	20	58	�	�	PROPN
ap-942	20	59	�	�	PROPN
ap-942	20	60	�	�	PROPN
ap-942	20	61	�	�	PROPN
ap-942	20	62	�	�	PROPN
ap-942	20	63	�	�	PROPN
ap-942	20	64	�	�	PROPN
ap-942	20	65	�	�	PROPN
ap-942	20	66	�	�	PROPN
ap-942	20	67	�	�	PROPN
ap-942	20	68	�	�	PROPN
ap-942	20	69	�	�	PROPN
ap-942	20	70	�	�	PROPN
ap-942	20	71	�	�	PROPN
ap-942	20	72	�	�	PROPN
ap-942	20	73	�	�	PROPN
ap-942	20	74	�	�	PROPN
ap-942	20	75	�	�	PROPN
ap-942	20	76	�	�	PROPN
ap-942	20	77	�	�	PROPN
ap-942	20	78	�	�	PROPN
ap-942	20	79	�	�	PROPN
ap-942	20	80	�	�	PROPN
ap-942	20	81	�	�	PROPN
ap-942	20	82	m	m	VERB
ap-942	20	83	m	m	VERB
ap-942	20	84	m	m	VERB
ap-942	20	85	m	m	VERB
ap-942	20	86	m	m	VERB
ap-942	20	87	m	m	VERB
ap-942	20	88	m	m	VERB
ap-942	20	89	m	m	VERB
ap-942	20	90	m	m	VERB
ap-942	20	91	m	m	VERB
ap-942	20	92	m	m	VERB
ap-942	20	93	m	m	VERB
ap-942	20	94	11	11	NUM
ap-942	20	95	21	21	NUM
ap-942	20	96	31	31	NUM
ap-942	20	97	12	12	NUM
ap-942	20	98	22	22	NUM
ap-942	20	99	32	32	NUM
ap-942	20	100	13	13	NUM
ap-942	20	101	23	23	NUM
ap-942	20	102	33	33	NUM
ap-942	20	103	12	12	NUM
ap-942	20	104	13	13	NUM
ap-942	20	105	11	11	NUM
ap-942	20	106	�	�	PROPN
ap-942	20	107	�	�	PROPN
ap-942	20	108	�	�	PROPN
ap-942	20	109	�	�	PROPN
ap-942	20	110	�	�	PROPN
ap-942	20	111	�	�	PROPN
ap-942	20	112	�	�	PROPN
ap-942	20	113	�	�	PROPN
ap-942	20	114	�	�	PROPN
ap-942	20	115	m	m	VERB
ap-942	20	116	m	m	VERB
ap-942	20	117	m	m	VERB
ap-942	20	118	m	m	VERB
ap-942	20	119	m	m	VERB
ap-942	20	120	m	m	VERB
ap-942	20	121	m	m	VERB
ap-942	20	122	m	m	VERB
ap-942	20	123	m	m	VERB
ap-942	20	124	m	m	VERB
ap-942	20	125	m	m	VERB
ap-942	20	126	m	m	VERB
ap-942	20	127	m	m	VERB
ap-942	20	128	m	m	VERB
ap-942	20	129	13	13	NUM
ap-942	20	130	11	11	NUM
ap-942	20	131	12	12	NUM
ap-942	20	132	22	22	NUM
ap-942	20	133	23	23	NUM
ap-942	20	134	21	21	NUM
ap-942	20	135	23	23	NUM
ap-942	20	136	21	21	NUM
ap-942	20	137	22	22	NUM
ap-942	20	138	32	32	NUM
ap-942	20	139	33	33	NUM
ap-942	20	140	32	32	NUM
ap-942	20	141	33	33	NUM
ap-942	20	142	31	31	NUM
ap-942	20	143	32	32	NUM
ap-942	20	144	11	11	NUM
ap-942	20	145	21	21	NUM
ap-942	20	146	31	31	NUM
ap-942	20	147	12	12	NUM
ap-942	20	148	22	22	NUM
ap-942	20	149	32	32	NUM
ap-942	20	150	13	13	NUM
ap-942	20	151	23	23	NUM
ap-942	20	152	33	33	NUM
ap-942	20	153	�	�	PROPN
ap-942	20	154	�	�	PROPN
ap-942	20	155	�	�	PROPN
ap-942	20	156	�	�	PROPN
ap-942	20	157	�	�	PROPN
ap-942	20	158	�	�	PROPN
ap-942	20	159	�	�	PROPN
ap-942	20	160	�	�	PROPN
ap-942	20	161	�	�	PROPN
ap-942	20	162	�	�	PROPN
ap-942	20	163	�	�	PROPN
ap-942	20	164	�	�	PROPN
ap-942	20	165	�	�	PROPN
ap-942	20	166	m	m	VERB
ap-942	20	167	m	m	VERB
ap-942	20	168	m	m	VERB
ap-942	20	169	m	m	VERB
ap-942	20	170	m	m	VERB
ap-942	20	171	m	m	VERB
ap-942	20	172	m	m	VERB
ap-942	20	173	m	m	VERB
ap-942	20	174	m	m	VERB
ap-942	20	175	m	m	PROPN
ap-942	20	176	�	�	PROPN
ap-942	20	177	�	�	PROPN
ap-942	20	178	,	,	PUNCT
ap-942	20	179	and	and	CCONJ
ap-942	20	180	hence	hence	ADV
ap-942	20	181	k	k	PROPN
ap-942	20	182	m	m	VERB
ap-942	20	183	m	m	VERB
ap-942	20	184	m	m	VERB
ap-942	20	185	m	m	VERB
ap-942	20	186	m	m	VERB
ap-942	20	187	m	m	VERB
ap-942	20	188	m	m	VERB
ap-942	20	189	m	m	VERB
ap-942	20	190	m	m	VERB
ap-942	20	191	k	k	ADJ
ap-942	20	192	12	12	NUM
ap-942	20	193	12	12	NUM
ap-942	20	194	13	13	NUM
ap-942	20	195	21	21	NUM
ap-942	20	196	11	11	NUM
ap-942	20	197	13	13	NUM
ap-942	20	198	22	22	NUM
ap-942	20	199	11	11	NUM
ap-942	20	200	12	12	NUM
ap-942	20	201	23	23	NUM
ap-942	20	202	13	13	NUM
ap-942	20	203	�	�	PROPN
ap-942	20	204	�	�	PROPN
ap-942	20	205	�	�	PROPN
ap-942	20	206	�	�	PROPN
ap-942	20	207	�	�	PROPN
ap-942	20	208	�	�	PROPN
ap-942	20	209	�	�	PROPN
ap-942	20	210	�	�	PROPN
ap-942	20	211	�	�	PROPN
ap-942	20	212	(	(	PUNCT
ap-942	20	213	)	)	PUNCT
ap-942	20	214	(	(	PUNCT
ap-942	20	215	)	)	PUNCT
ap-942	20	216	(	(	PUNCT
ap-942	20	217	)	)	PUNCT
ap-942	20	218	,	,	PUNCT
ap-942	20	219	(	(	PUNCT
ap-942	20	220	m	m	VERB
ap-942	20	221	m	m	VERB
ap-942	20	222	m	m	VERB
ap-942	20	223	m	m	VERB
ap-942	20	224	m	m	VERB
ap-942	20	225	m	m	VERB
ap-942	20	226	m	m	VERB
ap-942	20	227	m	m	VERB
ap-942	20	228	m	m	VERB
ap-942	20	229	k	k	NOUN
ap-942	20	230	m	m	VERB
ap-942	20	231	m	m	VERB
ap-942	20	232	12	12	NUM
ap-942	20	233	13	13	NUM
ap-942	20	234	31	31	NUM
ap-942	20	235	11	11	NUM
ap-942	20	236	13	13	NUM
ap-942	20	237	32	32	NUM
ap-942	20	238	11	11	NUM
ap-942	20	239	12	12	NUM
ap-942	20	240	33	33	NUM
ap-942	20	241	23	23	NUM
ap-942	20	242	22	22	NUM
ap-942	20	243	2	2	NUM
ap-942	20	244	�	�	PROPN
ap-942	20	245	�	�	PROPN
ap-942	20	246	�	�	PROPN
ap-942	20	247	�	�	PROPN
ap-942	20	248	�	�	PROPN
ap-942	20	249	�	�	PROPN
ap-942	20	250	�	�	PROPN
ap-942	20	251	�	�	PROPN
ap-942	20	252	)	)	PUNCT
ap-942	20	253	(	(	PUNCT
ap-942	20	254	)	)	PUNCT
ap-942	20	255	(	(	PUNCT
ap-942	20	256	)	)	PUNCT
ap-942	20	257	,	,	PUNCT
ap-942	20	258	(	(	PUNCT
ap-942	20	259	3	3	NUM
ap-942	20	260	31	31	NUM
ap-942	20	261	21	21	NUM
ap-942	20	262	23	23	NUM
ap-942	20	263	32	32	NUM
ap-942	20	264	21	21	NUM
ap-942	20	265	22	22	NUM
ap-942	20	266	33	33	NUM
ap-942	20	267	)	)	PUNCT
ap-942	20	268	(	(	PUNCT
ap-942	20	269	)	)	PUNCT
ap-942	20	270	(	(	PUNCT
ap-942	20	271	)	)	PUNCT
ap-942	20	272	.m	.m	PROPN
ap-942	21	1	m	m	VERB
ap-942	21	2	m	m	VERB
ap-942	21	3	m	m	VERB
ap-942	21	4	m	m	VERB
ap-942	21	5	m	m	NOUN
ap-942	21	6	m	m	PROPN
ap-942	21	7	�	�	PROPN
ap-942	21	8	�	�	PROPN
ap-942	21	9	�	�	PROPN
ap-942	21	10	�	�	PROPN
ap-942	21	11	by	by	ADP
ap-942	21	12	definition	definition	NOUN
ap-942	21	13	of	of	ADP
ap-942	21	14	the	the	DET
ap-942	21	15	determinant	determinant	ADJ
ap-942	21	16	,	,	PUNCT
ap-942	21	17	k12	k12	PROPN
ap-942	21	18	is	be	AUX
ap-942	21	19	equal	equal	ADJ
ap-942	21	20	to	to	ADP
ap-942	21	21	the	the	DET
ap-942	21	22	left	left	ADJ
ap-942	21	23	-	-	PUNCT
ap-942	21	24	hand	hand	NOUN
ap-942	21	25	side	side	NOUN
ap-942	21	26	of	of	ADP
ap-942	21	27	(	(	PUNCT
ap-942	21	28	1	1	NUM
ap-942	21	29	)	)	PUNCT
ap-942	21	30	,	,	PUNCT
ap-942	21	31	�	�	PROPN
ap-942	21	32	k13	k13	PROPN
ap-942	21	33	is	be	AUX
ap-942	21	34	equal	equal	ADJ
ap-942	21	35	to	to	ADP
ap-942	21	36	the	the	DET
ap-942	21	37	left	left	ADJ
ap-942	21	38	-	-	PUNCT
ap-942	21	39	hand	hand	NOUN
ap-942	21	40	side	side	NOUN
ap-942	21	41	of	of	ADP
ap-942	21	42	(	(	PUNCT
ap-942	21	43	2	2	NUM
ap-942	21	44	)	)	PUNCT
ap-942	21	45	,	,	PUNCT
ap-942	21	46	and	and	CCONJ
ap-942	21	47	k23	k23	PROPN
ap-942	21	48	is	be	AUX
ap-942	21	49	equal	equal	ADJ
ap-942	21	50	to	to	ADP
ap-942	21	51	the	the	DET
ap-942	21	52	left	left	ADJ
ap-942	21	53	-	-	PUNCT
ap-942	21	54	hand	hand	NOUN
ap-942	21	55	side	side	NOUN
ap-942	21	56	of	of	ADP
ap-942	21	57	(	(	PUNCT
ap-942	21	58	3	3	NUM
ap-942	21	59	)	)	PUNCT
ap-942	21	60	.	.	PUNCT
ap-942	22	1	this	this	PRON
ap-942	22	2	implies	imply	VERB
ap-942	22	3	k	k	PROPN
ap-942	22	4	e	e	PROPN
ap-942	22	5	�	�	PROPN
ap-942	22	6	�	�	PROPN
ap-942	22	7	if	if	SCONJ
ap-942	23	1	and	and	CCONJ
ap-942	23	2	only	only	ADV
ap-942	23	3	if	if	SCONJ
ap-942	23	4	equations	equation	NOUN
ap-942	23	5	(	(	PUNCT
ap-942	23	6	1)–(3	1)–(3	NUM
ap-942	23	7	)	)	PUNCT
ap-942	23	8	hold	hold	NOUN
ap-942	23	9	.	.	PUNCT
ap-942	24	1	�	�	PROPN
ap-942	24	2	now	now	ADV
ap-942	24	3	we	we	PRON
ap-942	24	4	can	can	AUX
ap-942	24	5	prove	prove	VERB
ap-942	24	6	the	the	DET
ap-942	24	7	two	two	NUM
ap-942	24	8	main	main	ADJ
ap-942	24	9	theorems	theorem	NOUN
ap-942	24	10	–	–	PUNCT
ap-942	24	11	one	one	NUM
ap-942	24	12	providing	provide	VERB
ap-942	24	13	the	the	DET
ap-942	24	14	desired	desire	VERB
ap-942	24	15	characterization	characterization	NOUN
ap-942	24	16	in	in	ADP
ap-942	24	17	the	the	DET
ap-942	24	18	regular	regular	ADJ
ap-942	24	19	case	case	NOUN
ap-942	24	20	and	and	CCONJ
ap-942	24	21	the	the	DET
ap-942	24	22	other	other	ADJ
ap-942	24	23	in	in	ADP
ap-942	24	24	the	the	DET
ap-942	24	25	singular	singular	ADJ
ap-942	24	26	case	case	NOUN
ap-942	24	27	.	.	PUNCT
ap-942	25	1	68	68	NUM
ap-942	25	2	©	©	PROPN
ap-942	25	3	czech	czech	PROPN
ap-942	25	4	technical	technical	PROPN
ap-942	25	5	university	university	PROPN
ap-942	25	6	publishing	publishing	NOUN
ap-942	25	7	house	house	NOUN
ap-942	25	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-942	25	9	acta	acta	PROPN
ap-942	25	10	polytechnica	polytechnica	PROPN
ap-942	25	11	vol	vol	NOUN
ap-942	25	12	.	.	PUNCT
ap-942	26	1	47	47	NUM
ap-942	26	2	no	no	NOUN
ap-942	26	3	.	.	PUNCT
ap-942	27	1	2–3/2007	2–3/2007	NUM
ap-942	27	2	matrices	matrix	NOUN
ap-942	27	3	associated	associate	VERB
ap-942	27	4	to	to	ADP
ap-942	27	5	3	3	NUM
ap-942	27	6	-	-	PUNCT
ap-942	27	7	interval	interval	NOUN
ap-942	27	8	exchange	exchange	NOUN
ap-942	27	9	transformation	transformation	NOUN
ap-942	27	10	and	and	CCONJ
ap-942	27	11	their	their	PRON
ap-942	27	12	spectra	spectra	ADJ
ap-942	27	13	p.	p.	NOUN
ap-942	27	14	ambrož	ambrož	NOUN
ap-942	27	15	a	a	DET
ap-942	27	16	three	three	NUM
ap-942	27	17	by	by	ADP
ap-942	27	18	three	three	NUM
ap-942	27	19	integer	integer	NOUN
ap-942	27	20	matrix	matrix	NOUN
ap-942	27	21	m	m	VERB
ap-942	27	22	is	be	AUX
ap-942	27	23	said	say	VERB
ap-942	27	24	to	to	PART
ap-942	27	25	have	have	VERB
ap-942	27	26	the	the	DET
ap-942	27	27	meme	meme	NOUN
ap-942	27	28	property	property	NOUN
ap-942	27	29	if	if	SCONJ
ap-942	27	30	mem	mem	X
ap-942	27	31	et	et	PROPN
ap-942	27	32	�	�	PROPN
ap-942	27	33	�	�	PROPN
ap-942	27	34	,	,	PUNCT
ap-942	27	35	where	where	SCONJ
ap-942	27	36	e	e	X
ap-942	27	37	�	�	PROPN
ap-942	27	38	�	�	PROPN
ap-942	27	39	�	�	PROPN
ap-942	27	40	�	�	PROPN
ap-942	27	41	�	�	PROPN
ap-942	27	42	�	�	PROPN
ap-942	27	43	�	�	PROPN
ap-942	27	44	�	�	PROPN
ap-942	27	45	�	�	PROPN
ap-942	27	46	�	�	PROPN
ap-942	27	47	�	�	PROPN
ap-942	27	48	0	0	NUM
ap-942	27	49	1	1	NUM
ap-942	27	50	1	1	NUM
ap-942	27	51	1	1	NUM
ap-942	27	52	0	0	NUM
ap-942	27	53	1	1	NUM
ap-942	27	54	1	1	NUM
ap-942	27	55	1	1	NUM
ap-942	27	56	0	0	NUM
ap-942	27	57	.	.	PUNCT
ap-942	28	1	we	we	PRON
ap-942	28	2	characterize	characterize	VERB
ap-942	28	3	such	such	ADJ
ap-942	28	4	matrices	matrix	NOUN
ap-942	28	5	in	in	ADP
ap-942	28	6	terms	term	NOUN
ap-942	28	7	of	of	ADP
ap-942	28	8	their	their	PRON
ap-942	28	9	spectra	spectra	NOUN
ap-942	28	10	.	.	PUNCT
ap-942	29	1	keywords	keyword	NOUN
ap-942	29	2	:	:	PUNCT
ap-942	29	3	integer	integer	NOUN
ap-942	29	4	matrix	matrix	NOUN
ap-942	29	5	,	,	PUNCT
ap-942	29	6	meme	meme	NOUN
ap-942	29	7	property	property	NOUN
ap-942	29	8	,	,	PUNCT
ap-942	29	9	spectrum	spectrum	NOUN
ap-942	29	10	.	.	PUNCT
ap-942	30	1	theorem	theorem	VERB
ap-942	30	2	3	3	NUM
ap-942	30	3	let	let	VERB
ap-942	30	4	m	m	PROPN
ap-942	30	5	�	�	PROPN
ap-942	30	6	�	�	PROPN
ap-942	30	7	�	�	PROPN
ap-942	30	8	3	3	NUM
ap-942	30	9	3	3	NUM
ap-942	30	10	be	be	AUX
ap-942	30	11	a	a	DET
ap-942	30	12	regular	regular	ADJ
ap-942	30	13	matrix	matrix	NOUN
ap-942	30	14	.	.	PUNCT
ap-942	31	1	then	then	ADV
ap-942	31	2	m	m	PROPN
ap-942	31	3	has	have	VERB
ap-942	31	4	meme	meme	NOUN
ap-942	31	5	if	if	SCONJ
ap-942	32	1	and	and	CCONJ
ap-942	32	2	only	only	ADV
ap-942	32	3	if	if	SCONJ
ap-942	32	4	the	the	DET
ap-942	32	5	number	number	NOUN
ap-942	32	6	det	det	PROPN
ap-942	32	7	m	m	PROPN
ap-942	32	8	or	or	CCONJ
ap-942	32	9	�	�	PROPN
ap-942	32	10	det	det	PROPN
ap-942	32	11	m	m	PROPN
ap-942	32	12	is	be	AUX
ap-942	32	13	an	an	DET
ap-942	32	14	eigenvalue	eigenvalue	NOUN
ap-942	32	15	of	of	ADP
ap-942	32	16	m	m	PROPN
ap-942	32	17	with	with	ADP
ap-942	32	18	(	(	PUNCT
ap-942	32	19	1	1	NUM
ap-942	32	20	,	,	PUNCT
ap-942	32	21	�	�	PROPN
ap-942	32	22	1	1	NUM
ap-942	32	23	,	,	PUNCT
ap-942	32	24	1	1	NUM
ap-942	32	25	)	)	PUNCT
ap-942	32	26	being	be	AUX
ap-942	32	27	an	an	DET
ap-942	32	28	associated	associated	ADJ
ap-942	32	29	left	leave	VERB
ap-942	32	30	eigenvector	eigenvector	NOUN
ap-942	32	31	.	.	PUNCT
ap-942	33	1	proof	proof	NOUN
ap-942	33	2	.	.	PUNCT
ap-942	34	1	�	�	PROPN
ap-942	34	2	:	:	PUNCT
ap-942	34	3	denote	denote	PROPN
ap-942	34	4	�	�	PROPN
ap-942	34	5	:	:	PUNCT
ap-942	34	6	det	det	PROPN
ap-942	34	7	�	�	PROPN
ap-942	34	8	m	m	PROPN
ap-942	34	9	and	and	CCONJ
ap-942	34	10	let	let	VERB
ap-942	34	11	�	�	PROPN
ap-942	34	12	�	�	PROPN
ap-942	34	13	,	,	PUNCT
ap-942	34	14	�	�	PROPN
ap-942	34	15	�	�	PROPN
ap-942	34	16	�	�	PROPN
ap-942	34	17	�	�	PROPN
ap-942	34	18	�	�	PROPN
ap-942	34	19	1	1	NUM
ap-942	34	20	1	1	NUM
ap-942	34	21	,	,	PUNCT
ap-942	34	22	be	be	AUX
ap-942	34	23	an	an	DET
ap-942	34	24	eigenvalue	eigenvalue	NOUN
ap-942	34	25	of	of	ADP
ap-942	34	26	m.	m.	NOUN
ap-942	34	27	if	if	SCONJ
ap-942	34	28	(	(	PUNCT
ap-942	34	29	1	1	NUM
ap-942	34	30	,	,	PUNCT
ap-942	34	31	�	�	PROPN
ap-942	34	32	1	1	NUM
ap-942	34	33	,	,	PUNCT
ap-942	34	34	1	1	NUM
ap-942	34	35	)	)	PUNCT
ap-942	34	36	is	be	AUX
ap-942	34	37	a	a	DET
ap-942	34	38	left	left	ADJ
ap-942	34	39	eigenvector	eigenvector	NOUN
ap-942	34	40	of	of	ADP
ap-942	34	41	m	m	PROPN
ap-942	34	42	associated	associate	VERB
ap-942	34	43	to	to	ADP
ap-942	34	44	�	�	PROPN
ap-942	34	45	then	then	ADV
ap-942	34	46	we	we	PRON
ap-942	34	47	have	have	VERB
ap-942	34	48	the	the	DET
ap-942	34	49	following	follow	VERB
ap-942	34	50	dependence	dependence	NOUN
ap-942	34	51	between	between	ADP
ap-942	34	52	rows	row	NOUN
ap-942	34	53	of	of	ADP
ap-942	34	54	m	m	PRON
ap-942	34	55	,	,	PUNCT
ap-942	34	56	denoted	denote	VERB
ap-942	34	57	by	by	ADP
ap-942	34	58	m	m	PROPN
ap-942	34	59	m	m	PROPN
ap-942	34	60	m1	m1	NOUN
ap-942	34	61	2	2	NUM
ap-942	34	62	3	3	NUM
ap-942	34	63	�	�	PROPN
ap-942	34	64	�	�	PROPN
ap-942	34	65	�	�	PROPN
ap-942	34	66	,	,	PUNCT
ap-942	34	67	,	,	PUNCT
ap-942	34	68	(	(	PUNCT
ap-942	34	69	,	,	PUNCT
ap-942	34	70	,	,	PUNCT
ap-942	34	71	)	)	PUNCT
ap-942	34	72	(	(	PUNCT
ap-942	34	73	,	,	PUNCT
ap-942	34	74	,	,	PUNCT
ap-942	34	75	)	)	PUNCT
ap-942	35	1	1	1	NUM
ap-942	35	2	1	1	NUM
ap-942	35	3	1	1	NUM
ap-942	35	4	1	1	NUM
ap-942	35	5	1	1	NUM
ap-942	35	6	11	11	NUM
ap-942	35	7	2	2	NUM
ap-942	35	8	3	3	NUM
ap-942	35	9	�	�	PROPN
ap-942	35	10	�	�	PROPN
ap-942	35	11	�	�	PROPN
ap-942	35	12	�	�	PROPN
ap-942	35	13	�	�	PROPN
ap-942	35	14	�	�	PROPN
ap-942	35	15	�	�	PROPN
ap-942	35	16	�	�	PROPN
ap-942	35	17	�	�	PROPN
ap-942	35	18	m	m	NOUN
ap-942	35	19	m	m	VERB
ap-942	35	20	m	m	VERB
ap-942	35	21	m	m	NOUN
ap-942	35	22	�	�	NOUN
ap-942	35	23	�	�	PROPN
ap-942	35	24	.	.	PUNCT
ap-942	36	1	(	(	PUNCT
ap-942	36	2	4	4	X
ap-942	36	3	)	)	PUNCT
ap-942	36	4	using	use	VERB
ap-942	36	5	(	(	PUNCT
ap-942	36	6	4	4	X
ap-942	36	7	)	)	PUNCT
ap-942	36	8	we	we	PRON
ap-942	36	9	have	have	VERB
ap-942	36	10	�	�	PROPN
ap-942	36	11	�	�	PROPN
ap-942	36	12	�	�	PROPN
ap-942	36	13	�	�	PROPN
ap-942	36	14	�	�	PROPN
ap-942	36	15	�	�	PROPN
ap-942	36	16	�	�	PROPN
ap-942	36	17	�	�	PROPN
ap-942	36	18	�	�	PROPN
ap-942	36	19	�	�	PROPN
ap-942	36	20	�	�	PROPN
ap-942	36	21	�	�	PROPN
ap-942	36	22	�	�	PROPN
ap-942	36	23	�	�	PROPN
ap-942	36	24	�	�	PROPN
ap-942	36	25	�	�	PROPN
ap-942	36	26	�	�	PROPN
ap-942	36	27	�	�	PROPN
ap-942	36	28	�	�	PROPN
ap-942	36	29	�	�	PROPN
ap-942	36	30	det	det	PROPN
ap-942	36	31	det	det	PROPN
ap-942	36	32	(	(	PUNCT
ap-942	36	33	,	,	PUNCT
ap-942	36	34	,	,	PUNCT
ap-942	36	35	)	)	PUNCT
ap-942	36	36	m	m	VERB
ap-942	36	37	m	m	VERB
ap-942	36	38	m	m	VERB
ap-942	36	39	m	m	VERB
ap-942	36	40	m	m	VERB
ap-942	36	41	m	m	VERB
ap-942	36	42	m	m	VERB
ap-942	36	43	1	1	NUM
ap-942	36	44	2	2	NUM
ap-942	36	45	3	3	NUM
ap-942	36	46	1	1	NUM
ap-942	36	47	1	1	NUM
ap-942	36	48	3	3	NUM
ap-942	36	49	1	1	NUM
ap-942	36	50	1	1	NUM
ap-942	36	51	1	1	NUM
ap-942	36	52	�	�	PROPN
ap-942	36	53	3	3	NUM
ap-942	36	54	�	�	PROPN
ap-942	36	55	�	�	PROPN
ap-942	36	56	�	�	PROPN
ap-942	36	57	�	�	PROPN
ap-942	36	58	�	�	PROPN
ap-942	36	59	�	�	PROPN
ap-942	36	60	�	�	PROPN
ap-942	36	61	�	�	PROPN
ap-942	36	62	,	,	PUNCT
ap-942	36	63	by	by	ADP
ap-942	36	64	subtracting	subtract	VERB
ap-942	36	65	the	the	DET
ap-942	36	66	first	first	ADJ
ap-942	36	67	and	and	CCONJ
ap-942	36	68	the	the	DET
ap-942	36	69	third	third	ADJ
ap-942	36	70	row	row	NOUN
ap-942	36	71	from	from	ADP
ap-942	36	72	the	the	DET
ap-942	36	73	second	second	ADJ
ap-942	36	74	row	row	NOUN
ap-942	36	75	and	and	CCONJ
ap-942	36	76	by	by	ADP
ap-942	36	77	factoring	factor	VERB
ap-942	36	78	�	�	PROPN
ap-942	36	79	�	�	PROPN
ap-942	36	80	out	out	ADP
ap-942	36	81	from	from	ADP
ap-942	36	82	the	the	DET
ap-942	36	83	second	second	ADJ
ap-942	36	84	row	row	NOUN
ap-942	36	85	we	we	PRON
ap-942	36	86	obtain	obtain	VERB
ap-942	36	87	�	�	PROPN
ap-942	36	88	�	�	PROPN
ap-942	36	89	�	�	PROPN
ap-942	36	90	�	�	PROPN
ap-942	36	91	�	�	PROPN
ap-942	36	92	�	�	PROPN
ap-942	36	93	�	�	PROPN
ap-942	36	94	�	�	PROPN
ap-942	36	95	�	�	PROPN
ap-942	36	96	�	�	PROPN
ap-942	36	97	�	�	PROPN
ap-942	36	98	�	�	PROPN
ap-942	36	99	�	�	PROPN
ap-942	36	100	�	�	PROPN
ap-942	36	101	�	�	PROPN
ap-942	36	102	det	det	PROPN
ap-942	36	103	(	(	PUNCT
ap-942	36	104	,	,	PUNCT
ap-942	36	105	,	,	PUNCT
ap-942	36	106	)	)	PUNCT
ap-942	36	107	m	m	VERB
ap-942	36	108	m	m	VERB
ap-942	36	109	1	1	NUM
ap-942	36	110	3	3	NUM
ap-942	36	111	1	1	NUM
ap-942	36	112	1	1	NUM
ap-942	36	113	1	1	NUM
ap-942	36	114	,	,	PUNCT
ap-942	36	115	which	which	PRON
ap-942	36	116	gives	give	VERB
ap-942	36	117	(	(	PUNCT
ap-942	36	118	2	2	NUM
ap-942	36	119	)	)	PUNCT
ap-942	36	120	.	.	PUNCT
ap-942	37	1	similarly	similarly	ADV
ap-942	37	2	,	,	PUNCT
ap-942	37	3	using	use	VERB
ap-942	37	4	the	the	DET
ap-942	37	5	row	row	NOUN
ap-942	37	6	dependence	dependence	NOUN
ap-942	37	7	(	(	PUNCT
ap-942	37	8	4	4	NUM
ap-942	37	9	)	)	PUNCT
ap-942	37	10	in	in	ADP
ap-942	37	11	the	the	DET
ap-942	37	12	first	first	ADJ
ap-942	37	13	and	and	CCONJ
ap-942	37	14	in	in	ADP
ap-942	37	15	the	the	DET
ap-942	37	16	third	third	ADJ
ap-942	37	17	row	row	NOUN
ap-942	37	18	of	of	ADP
ap-942	37	19	m	m	VERB
ap-942	37	20	provides	provide	VERB
ap-942	37	21	the	the	DET
ap-942	37	22	equalities	equality	NOUN
ap-942	37	23	(	(	PUNCT
ap-942	37	24	1	1	NUM
ap-942	37	25	)	)	PUNCT
ap-942	37	26	and	and	CCONJ
ap-942	37	27	(	(	PUNCT
ap-942	37	28	3	3	NUM
ap-942	37	29	)	)	PUNCT
ap-942	37	30	.	.	PUNCT
ap-942	38	1	therefore	therefore	ADV
ap-942	38	2	by	by	ADP
ap-942	38	3	lemma	lemma	PROPN
ap-942	38	4	2	2	NUM
ap-942	38	5	the	the	DET
ap-942	38	6	matrix	matrix	NOUN
ap-942	38	7	m	m	AUX
ap-942	38	8	has	have	VERB
ap-942	38	9	meme	meme	NOUN
ap-942	38	10	.	.	PUNCT
ap-942	39	1	�	�	PROPN
ap-942	39	2	:	:	PUNCT
ap-942	39	3	let	let	VERB
ap-942	39	4	mt	mt	PROPN
ap-942	39	5	x	x	PUNCT
ap-942	39	6	x	x	PUNCT
ap-942	39	7	x	x	SYM
ap-942	39	8	1	1	NUM
ap-942	39	9	2	2	NUM
ap-942	39	10	3	3	NUM
ap-942	39	11	1	1	NUM
ap-942	39	12	1	1	NUM
ap-942	39	13	1	1	NUM
ap-942	39	14	�	�	PROPN
ap-942	39	15	�	�	PROPN
ap-942	39	16	�	�	PROPN
ap-942	39	17	�	�	PROPN
ap-942	39	18	�	�	PROPN
ap-942	39	19	�	�	PROPN
ap-942	39	20	�	�	PROPN
ap-942	39	21	�	�	PROPN
ap-942	39	22	�	�	PROPN
ap-942	39	23	�	�	PROPN
ap-942	39	24	�	�	PROPN
ap-942	39	25	�	�	PROPN
ap-942	39	26	�	�	PROPN
ap-942	39	27	�	�	PROPN
ap-942	39	28	�	�	PROPN
ap-942	39	29	�	�	PROPN
ap-942	39	30	.	.	PUNCT
ap-942	40	1	(	(	PUNCT
ap-942	40	2	5	5	X
ap-942	40	3	)	)	PUNCT
ap-942	40	4	we	we	PRON
ap-942	40	5	will	will	AUX
ap-942	40	6	compute	compute	VERB
ap-942	40	7	the	the	DET
ap-942	40	8	components	component	NOUN
ap-942	40	9	x1	x1	PROPN
ap-942	40	10	,	,	PUNCT
ap-942	40	11	x2	x2	PROPN
ap-942	40	12	,	,	PUNCT
ap-942	40	13	x3	x3	ADV
ap-942	40	14	using	use	VERB
ap-942	40	15	cramer	cramer	PROPN
ap-942	40	16	’s	’s	PART
ap-942	40	17	rule	rule	NOUN
ap-942	40	18	.	.	PUNCT
ap-942	41	1	x	x	X
ap-942	41	2	m	m	VERB
ap-942	41	3	m	m	VERB
ap-942	41	4	m	m	VERB
ap-942	41	5	m	m	VERB
ap-942	41	6	m	m	VERB
ap-942	41	7	m	m	VERB
ap-942	41	8	t1	t1	NOUN
ap-942	41	9	21	21	NUM
ap-942	41	10	31	31	NUM
ap-942	41	11	22	22	NUM
ap-942	41	12	32	32	NUM
ap-942	41	13	23	23	NUM
ap-942	41	14	33	33	NUM
ap-942	41	15	1	1	NUM
ap-942	41	16	1	1	NUM
ap-942	41	17	1	1	NUM
ap-942	41	18	1	1	NUM
ap-942	41	19	�	�	PROPN
ap-942	41	20	�	�	PROPN
ap-942	41	21	�	�	PROPN
ap-942	41	22	�	�	PROPN
ap-942	41	23	�	�	PROPN
ap-942	41	24	�	�	PROPN
ap-942	41	25	�	�	PROPN
ap-942	41	26	�	�	PROPN
ap-942	41	27	�	�	PROPN
ap-942	41	28	�	�	PROPN
ap-942	41	29	det	det	PROPN
ap-942	41	30	det	det	PROPN
ap-942	41	31	det	det	PROPN
ap-942	41	32	(	(	PUNCT
ap-942	41	33	,	,	PUNCT
ap-942	41	34	m	m	PROPN
ap-942	41	35	�	�	PROPN
ap-942	41	36	�	�	PROPN
ap-942	41	37	�	�	PROPN
ap-942	41	38	�	�	PROPN
ap-942	41	39	�	�	PROPN
ap-942	41	40	�	�	PROPN
ap-942	41	41	�	�	PROPN
ap-942	41	42	�	�	PROPN
ap-942	41	43	�	�	PROPN
ap-942	41	44	�	�	PROPN
ap-942	41	45	�	�	PROPN
ap-942	41	46	1	1	NUM
ap-942	41	47	1	1	NUM
ap-942	41	48	2	2	NUM
ap-942	41	49	3	3	NUM
ap-942	41	50	,	,	PUNCT
ap-942	41	51	)	)	PUNCT
ap-942	41	52	det	det	PROPN
ap-942	41	53	det	det	PROPN
ap-942	41	54	m	m	PROPN
ap-942	41	55	m	m	VERB
ap-942	41	56	m	m	VERB
ap-942	41	57	m	m	VERB
ap-942	41	58	�	�	PROPN
ap-942	41	59	,	,	PUNCT
ap-942	41	60	where	where	SCONJ
ap-942	41	61	the	the	DET
ap-942	41	62	last	last	ADJ
ap-942	41	63	equality	equality	NOUN
ap-942	41	64	comes	come	VERB
ap-942	41	65	by	by	ADP
ap-942	41	66	lemma	lemma	PROPN
ap-942	41	67	2	2	NUM
ap-942	41	68	from	from	ADP
ap-942	41	69	the	the	DET
ap-942	41	70	fact	fact	NOUN
ap-942	41	71	that	that	SCONJ
ap-942	41	72	m	m	PROPN
ap-942	41	73	has	have	AUX
ap-942	41	74	meme	meme	NOUN
ap-942	41	75	.	.	PUNCT
ap-942	42	1	similarly	similarly	ADV
ap-942	42	2	,	,	PUNCT
ap-942	42	3	one	one	PRON
ap-942	42	4	can	can	AUX
ap-942	42	5	compute	compute	VERB
ap-942	42	6	x2	x2	PROPN
ap-942	42	7	�	�	PROPN
ap-942	42	8	�	�	PROPN
ap-942	42	9	�	�	PROPN
ap-942	42	10	det	det	PROPN
ap-942	42	11	m	m	PROPN
ap-942	42	12	and	and	CCONJ
ap-942	42	13	x3	x3	PROPN
ap-942	42	14	�	�	PROPN
ap-942	42	15	�	�	PROPN
ap-942	42	16	det	det	PROPN
ap-942	42	17	m	m	PROPN
ap-942	42	18	.	.	PUNCT
ap-942	43	1	hence	hence	ADV
ap-942	43	2	x	x	X
ap-942	43	3	x	x	SYM
ap-942	43	4	x	x	SYM
ap-942	43	5	1	1	NUM
ap-942	43	6	2	2	NUM
ap-942	43	7	3	3	NUM
ap-942	43	8	1	1	NUM
ap-942	43	9	1	1	NUM
ap-942	43	10	1	1	NUM
ap-942	43	11	�	�	PROPN
ap-942	43	12	�	�	PROPN
ap-942	43	13	�	�	PROPN
ap-942	43	14	�	�	PROPN
ap-942	43	15	�	�	PROPN
ap-942	43	16	�	�	PROPN
ap-942	43	17	�	�	PROPN
ap-942	43	18	�	�	PROPN
ap-942	43	19	�	�	PROPN
ap-942	43	20	�	�	PROPN
ap-942	43	21	�	�	PROPN
ap-942	43	22	�	�	PROPN
ap-942	43	23	�	�	PROPN
ap-942	43	24	�	�	PROPN
ap-942	43	25	�	�	PROPN
ap-942	43	26	�	�	PROPN
ap-942	43	27	�	�	PROPN
ap-942	43	28	det	det	PROPN
ap-942	43	29	m	m	PROPN
ap-942	43	30	.	.	PUNCT
ap-942	44	1	(	(	PUNCT
ap-942	44	2	6	6	X
ap-942	44	3	)	)	PUNCT
ap-942	44	4	substituting	substitute	VERB
ap-942	44	5	(	(	PUNCT
ap-942	44	6	6	6	NUM
ap-942	44	7	)	)	PUNCT
ap-942	44	8	in	in	ADP
ap-942	44	9	(	(	PUNCT
ap-942	44	10	5	5	NUM
ap-942	44	11	)	)	PUNCT
ap-942	44	12	and	and	CCONJ
ap-942	44	13	multiplying	multiply	VERB
ap-942	44	14	by	by	ADP
ap-942	44	15	�	�	PROPN
ap-942	44	16	detm	detm	NOUN
ap-942	44	17	,	,	PUNCT
ap-942	44	18	which	which	PRON
ap-942	44	19	is	be	AUX
ap-942	44	20	non	non	ADJ
ap-942	44	21	-	-	ADJ
ap-942	44	22	zero	zero	NUM
ap-942	44	23	due	due	ADP
ap-942	44	24	to	to	ADP
ap-942	44	25	the	the	DET
ap-942	44	26	regularity	regularity	NOUN
ap-942	44	27	of	of	ADP
ap-942	44	28	m	m	PROPN
ap-942	44	29	,	,	PUNCT
ap-942	44	30	we	we	PRON
ap-942	44	31	obtain	obtain	VERB
ap-942	44	32	(	(	PUNCT
ap-942	44	33	,	,	PUNCT
ap-942	44	34	,	,	PUNCT
ap-942	44	35	)	)	PUNCT
ap-942	44	36	det	det	PROPN
ap-942	44	37	(	(	PUNCT
ap-942	44	38	,	,	PUNCT
ap-942	44	39	,	,	PUNCT
ap-942	44	40	)	)	PUNCT
ap-942	44	41	1	1	NUM
ap-942	44	42	1	1	NUM
ap-942	44	43	1	1	NUM
ap-942	44	44	1	1	NUM
ap-942	44	45	1	1	NUM
ap-942	44	46	1	1	NUM
ap-942	44	47	�	�	PROPN
ap-942	44	48	�	�	PROPN
ap-942	44	49	�	�	PROPN
ap-942	44	50	m	m	PROPN
ap-942	44	51	m	m	NOUN
ap-942	44	52	�	�	PROPN
ap-942	44	53	,	,	PUNCT
ap-942	44	54	that	that	ADV
ap-942	44	55	is	is	ADV
ap-942	44	56	,	,	PUNCT
ap-942	44	57	�	�	PROPN
ap-942	44	58	det	det	PROPN
ap-942	44	59	m	m	PROPN
ap-942	44	60	is	be	AUX
ap-942	44	61	an	an	DET
ap-942	44	62	eigenvalue	eigenvalue	NOUN
ap-942	44	63	of	of	ADP
ap-942	44	64	m	m	PRON
ap-942	44	65	,	,	PUNCT
ap-942	44	66	(	(	PUNCT
ap-942	44	67	,	,	PUNCT
ap-942	44	68	,	,	PUNCT
ap-942	44	69	)	)	PUNCT
ap-942	44	70	1	1	NUM
ap-942	44	71	1	1	NUM
ap-942	44	72	1	1	NUM
ap-942	44	73	�	�	NOUN
ap-942	44	74	is	be	AUX
ap-942	44	75	an	an	DET
ap-942	44	76	associated	associated	ADJ
ap-942	44	77	left	leave	VERB
ap-942	44	78	eigenvector	eigenvector	PROPN
ap-942	44	79	.	.	PUNCT
ap-942	44	80	�	�	PROPN
ap-942	44	81	theorem	theorem	VERB
ap-942	44	82	4	4	NUM
ap-942	44	83	.	.	PUNCT
ap-942	44	84	letm	letm	PROPN
ap-942	44	85	�	�	PROPN
ap-942	44	86	�	�	PROPN
ap-942	44	87	�	�	PROPN
ap-942	44	88	3	3	NUM
ap-942	44	89	3	3	NUM
ap-942	44	90	be	be	AUX
ap-942	44	91	a	a	DET
ap-942	44	92	singular	singular	ADJ
ap-942	44	93	matrix	matrix	NOUN
ap-942	44	94	.	.	PUNCT
ap-942	45	1	then	then	ADV
ap-942	45	2	m	m	PROPN
ap-942	45	3	has	have	VERB
ap-942	45	4	meme	meme	NOUN
ap-942	45	5	if	if	SCONJ
ap-942	46	1	and	and	CCONJ
ap-942	46	2	only	only	ADV
ap-942	46	3	if	if	SCONJ
ap-942	46	4	�	�	PROPN
ap-942	46	5	�	�	PROPN
ap-942	46	6	�	�	PROPN
ap-942	46	7	�	�	PROPN
ap-942	46	8	�	�	PROPN
ap-942	46	9	�	�	PROPN
ap-942	46	10	�	�	PROPN
ap-942	46	11	(	(	PUNCT
ap-942	46	12	)	)	PUNCT
ap-942	46	13	,	,	PUNCT
ap-942	46	14	,	,	PUNCT
ap-942	46	15	,	,	PUNCT
ap-942	46	16	m	m	PROPN
ap-942	46	17	�	�	PROPN
ap-942	46	18	�	�	PROPN
ap-942	46	19	�	�	PROPN
ap-942	46	20	0	0	NUM
ap-942	46	21	12	12	NUM
ap-942	46	22	3	3	NUM
ap-942	46	23	2	2	NUM
ap-942	46	24	3	3	NUM
ap-942	46	25	and	and	CCONJ
ap-942	46	26	(	(	PUNCT
ap-942	46	27	,	,	PUNCT
ap-942	46	28	,	,	PUNCT
ap-942	46	29	)	)	PUNCT
ap-942	46	30	1	1	NUM
ap-942	46	31	1	1	NUM
ap-942	46	32	1	1	NUM
ap-942	46	33	�	�	NOUN
ap-942	46	34	is	be	AUX
ap-942	46	35	a	a	DET
ap-942	46	36	left	left	ADJ
ap-942	46	37	eigenvector	eigenvector	NOUN
ap-942	46	38	associated	associate	VERB
ap-942	46	39	with	with	ADP
ap-942	46	40	the	the	DET
ap-942	46	41	eigenvalue	eigenvalue	PROPN
ap-942	46	42	0	0	NUM
ap-942	46	43	.	.	PUNCT
ap-942	47	1	proof	proof	NOUN
ap-942	47	2	.	.	PUNCT
ap-942	48	1	�	�	PROPN
ap-942	48	2	:	:	PUNCT
ap-942	48	3	since	since	SCONJ
ap-942	48	4	det	det	PROPN
ap-942	48	5	m	m	PROPN
ap-942	48	6	�	�	PROPN
ap-942	48	7	0	0	NUM
ap-942	48	8	we	we	PRON
ap-942	48	9	have	have	VERB
ap-942	48	10	0	0	NUM
ap-942	48	11	�	�	PROPN
ap-942	48	12	�	�	PROPN
ap-942	48	13	(	(	PUNCT
ap-942	48	14	)	)	PUNCT
ap-942	48	15	m	m	VERB
ap-942	48	16	.	.	PUNCT
ap-942	49	1	let	let	VERB
ap-942	49	2	x	x	PRON
ap-942	49	3	be	be	AUX
ap-942	49	4	a	a	DET
ap-942	49	5	left	left	ADJ
ap-942	49	6	eigenvector	eigenvector	NOUN
ap-942	49	7	of	of	ADP
ap-942	49	8	m	m	PRON
ap-942	49	9	to	to	ADP
ap-942	49	10	the	the	DET
ap-942	49	11	eigenvalue	eigenvalue	PROPN
ap-942	49	12	0	0	NUM
ap-942	49	13	,	,	PUNCT
ap-942	49	14	i.e.	i.e.	X
ap-942	49	15	xm	xm	PROPN
ap-942	49	16	�	�	PROPN
ap-942	49	17	0	0	PUNCT
ap-942	50	1	and	and	CCONJ
ap-942	50	2	hence	hence	ADV
ap-942	50	3	x	x	X
ap-942	50	4	x	x	X
ap-942	50	5	te	te	ADP
ap-942	50	6	mem	mem	PROPN
ap-942	50	7	�	�	PROPN
ap-942	50	8	�	�	PROPN
ap-942	50	9	0	0	NUM
ap-942	50	10	,	,	PUNCT
ap-942	50	11	that	that	ADV
ap-942	50	12	is	is	ADV
ap-942	50	13	,	,	PUNCT
ap-942	50	14	x	x	X
ap-942	50	15	is	be	AUX
ap-942	50	16	also	also	ADV
ap-942	50	17	a	a	DET
ap-942	50	18	left	left	ADJ
ap-942	50	19	eigenvector	eigenvector	NOUN
ap-942	50	20	of	of	ADP
ap-942	50	21	e	e	PROPN
ap-942	50	22	,	,	PUNCT
ap-942	50	23	associated	associate	VERB
ap-942	50	24	to	to	ADP
ap-942	50	25	0	0	NUM
ap-942	50	26	.	.	PUNCT
ap-942	51	1	obviously	obviously	ADV
ap-942	51	2	,	,	PUNCT
ap-942	51	3	x	x	PROPN
ap-942	51	4	�	�	PROPN
ap-942	51	5	�	�	PROPN
ap-942	51	6	(	(	PUNCT
ap-942	51	7	,	,	PUNCT
ap-942	51	8	,	,	PUNCT
ap-942	51	9	)	)	PUNCT
ap-942	51	10	1	1	NUM
ap-942	51	11	1	1	NUM
ap-942	51	12	1	1	NUM
ap-942	51	13	.	.	PUNCT
ap-942	52	1	concerning	concern	VERB
ap-942	52	2	the	the	DET
ap-942	52	3	other	other	ADJ
ap-942	52	4	eigenvalues	eigenvalue	NOUN
ap-942	52	5	of	of	ADP
ap-942	52	6	m	m	PRON
ap-942	52	7	,	,	PUNCT
ap-942	52	8	since	since	SCONJ
ap-942	52	9	the	the	DET
ap-942	52	10	equality	equality	NOUN
ap-942	52	11	(	(	PUNCT
ap-942	52	12	4	4	NUM
ap-942	52	13	)	)	PUNCT
ap-942	52	14	for	for	ADP
ap-942	52	15	a	a	DET
ap-942	52	16	singular	singular	NOUN
ap-942	52	17	m	m	AUX
ap-942	52	18	has	have	VERB
ap-942	52	19	the	the	DET
ap-942	52	20	following	follow	VERB
ap-942	52	21	form	form	NOUN
ap-942	52	22	(	(	PUNCT
ap-942	52	23	,	,	PUNCT
ap-942	52	24	,	,	PUNCT
ap-942	52	25	)	)	PUNCT
ap-942	52	26	1	1	NUM
ap-942	52	27	1	1	NUM
ap-942	52	28	1	1	NUM
ap-942	52	29	01	01	NUM
ap-942	52	30	2	2	NUM
ap-942	52	31	3	3	NUM
ap-942	52	32	�	�	PROPN
ap-942	52	33	�	�	PROPN
ap-942	52	34	�	�	PROPN
ap-942	52	35	�	�	PROPN
ap-942	52	36	�	�	PROPN
ap-942	52	37	�	�	PROPN
ap-942	52	38	�	�	PROPN
ap-942	52	39	�	�	PROPN
ap-942	52	40	m	m	NOUN
ap-942	52	41	m	m	VERB
ap-942	52	42	m	m	VERB
ap-942	52	43	m	m	VERB
ap-942	52	44	(	(	PUNCT
ap-942	52	45	7	7	NUM
ap-942	52	46	)	)	PUNCT
ap-942	52	47	the	the	DET
ap-942	52	48	characteristic	characteristic	ADJ
ap-942	52	49	polynomial	polynomial	PROPN
ap-942	52	50	�	�	PROPN
ap-942	52	51	�	�	PROPN
ap-942	52	52	m	m	PROPN
ap-942	52	53	(	(	PUNCT
ap-942	52	54	)	)	PUNCT
ap-942	52	55	will	will	AUX
ap-942	52	56	be	be	AUX
ap-942	52	57	given	give	VERB
ap-942	52	58	by	by	ADP
ap-942	52	59	the	the	DET
ap-942	52	60	matrix	matrix	NOUN
ap-942	52	61	(	(	PUNCT
ap-942	52	62	)	)	PUNCT
ap-942	52	63	m	m	VERB
ap-942	52	64	i	i	PROPN
ap-942	52	65	�	�	PROPN
ap-942	52	66	�	�	PROPN
ap-942	52	67	�	�	PROPN
ap-942	52	68	�	�	PROPN
ap-942	52	69	�	�	PROPN
ap-942	52	70	�	�	PROPN
ap-942	52	71	�	�	PROPN
ap-942	52	72	�	�	PROPN
ap-942	52	73	�	�	PROPN
ap-942	52	74	�	�	PROPN
ap-942	52	75	m	m	VERB
ap-942	52	76	m	m	VERB
ap-942	52	77	m	m	VERB
ap-942	52	78	m	m	VERB
ap-942	52	79	m	m	VERB
ap-942	52	80	m	m	VERB
ap-942	52	81	m	m	VERB
ap-942	52	82	m	m	VERB
ap-942	52	83	m	m	VERB
ap-942	52	84	m	m	VERB
ap-942	52	85	m	m	VERB
ap-942	52	86	m	m	VERB
ap-942	52	87	11	11	NUM
ap-942	52	88	12	12	NUM
ap-942	52	89	13	13	NUM
ap-942	52	90	11	11	NUM
ap-942	52	91	31	31	NUM
ap-942	52	92	12	12	NUM
ap-942	52	93	32	32	NUM
ap-942	52	94	13	13	NUM
ap-942	52	95	33	33	NUM
ap-942	52	96	31	31	NUM
ap-942	52	97	32	32	NUM
ap-942	52	98	33	33	NUM
ap-942	52	99	�	�	PROPN
ap-942	52	100	�	�	PROPN
ap-942	52	101	�	�	PROPN
ap-942	52	102	�	�	PROPN
ap-942	52	103	�	�	PROPN
ap-942	52	104	�	�	PROPN
ap-942	52	105	�	�	PROPN
ap-942	52	106	�	�	PROPN
ap-942	52	107	�	�	PROPN
ap-942	52	108	.	.	PUNCT
ap-942	53	1	computing	compute	VERB
ap-942	53	2	its	its	PRON
ap-942	53	3	determinant	determinant	ADJ
ap-942	53	4	,	,	PUNCT
ap-942	53	5	the	the	DET
ap-942	53	6	linear	linear	ADJ
ap-942	53	7	component	component	NOUN
ap-942	53	8	of	of	ADP
ap-942	53	9	�	�	PROPN
ap-942	53	10	�	�	PROPN
ap-942	53	11	m	m	PROPN
ap-942	53	12	(	(	PUNCT
ap-942	53	13	)	)	PUNCT
ap-942	53	14	is	be	AUX
ap-942	53	15	�	�	PROPN
ap-942	53	16	�	�	PROPN
ap-942	53	17	�	�	PROPN
ap-942	53	18	�	�	PROPN
ap-942	53	19	�	�	PROPN
ap-942	53	20	�	�	PROPN
ap-942	53	21	�	�	PROPN
ap-942	53	22	�	�	PROPN
ap-942	53	23	�	�	PROPN
ap-942	53	24	�	�	PROPN
ap-942	53	25	�	�	PROPN
ap-942	53	26	�	�	PROPN
ap-942	53	27	m	m	VERB
ap-942	53	28	m	m	VERB
ap-942	53	29	m	m	VERB
ap-942	53	30	m	m	VERB
ap-942	53	31	m	m	VERB
ap-942	53	32	m	m	VERB
ap-942	53	33	m	m	VERB
ap-942	53	34	m	m	VERB
ap-942	53	35	m	m	VERB
ap-942	53	36	m	m	VERB
ap-942	53	37	m	m	VERB
ap-942	53	38	m	m	VERB
ap-942	53	39	33	33	NUM
ap-942	53	40	12	12	NUM
ap-942	53	41	11	11	NUM
ap-942	53	42	33	33	NUM
ap-942	53	43	11	11	NUM
ap-942	53	44	32	32	NUM
ap-942	53	45	13	13	NUM
ap-942	53	46	32	32	NUM
ap-942	53	47	13	13	NUM
ap-942	53	48	31	31	NUM
ap-942	53	49	12	12	NUM
ap-942	53	50	31	31	NUM
ap-942	53	51	,	,	PUNCT
ap-942	53	52	which	which	PRON
ap-942	53	53	is	be	AUX
ap-942	53	54	exactly	exactly	ADV
ap-942	53	55	the	the	DET
ap-942	53	56	left	left	ADJ
ap-942	53	57	hand	hand	NOUN
ap-942	53	58	side	side	NOUN
ap-942	53	59	of	of	ADP
ap-942	53	60	(	(	PUNCT
ap-942	53	61	2	2	NUM
ap-942	53	62	)	)	PUNCT
ap-942	53	63	,	,	PUNCT
ap-942	53	64	and	and	CCONJ
ap-942	53	65	hence	hence	ADV
ap-942	53	66	it	it	PRON
ap-942	53	67	is	be	AUX
ap-942	53	68	equal	equal	ADJ
ap-942	53	69	to	to	ADP
ap-942	53	70	�	�	PROPN
ap-942	53	71	1	1	NUM
ap-942	53	72	.	.	PUNCT
ap-942	54	1	on	on	ADP
ap-942	54	2	the	the	DET
ap-942	54	3	other	other	ADJ
ap-942	54	4	hand	hand	NOUN
ap-942	54	5	,	,	PUNCT
ap-942	54	6	since	since	SCONJ
ap-942	54	7	the	the	DET
ap-942	54	8	characteristic	characteristic	ADJ
ap-942	54	9	polynomial	polynomial	NOUN
ap-942	54	10	can	can	AUX
ap-942	54	11	be	be	AUX
ap-942	54	12	written	write	VERB
ap-942	54	13	in	in	ADP
ap-942	54	14	the	the	DET
ap-942	54	15	form	form	NOUN
ap-942	54	16	�	�	PROPN
ap-942	54	17	�	�	PROPN
ap-942	54	18	�	�	PROPN
ap-942	54	19	�	�	PROPN
ap-942	54	20	�	�	PROPN
ap-942	54	21	�	�	PROPN
ap-942	54	22	�	�	PROPN
ap-942	54	23	�	�	PROPN
ap-942	54	24	�	�	PROPN
ap-942	54	25	�	�	PROPN
ap-942	54	26	�	�	PROPN
ap-942	54	27	�	�	PROPN
ap-942	54	28	�	�	PROPN
ap-942	54	29	�	�	PROPN
ap-942	54	30	�	�	PROPN
ap-942	54	31	�	�	PROPN
ap-942	54	32	�	�	PROPN
ap-942	54	33	m	m	PROPN
ap-942	54	34	(	(	PUNCT
ap-942	54	35	)	)	PUNCT
ap-942	54	36	(	(	PUNCT
ap-942	54	37	)	)	PUNCT
ap-942	54	38	(	(	PUNCT
ap-942	54	39	)	)	PUNCT
ap-942	54	40	(	(	PUNCT
ap-942	54	41	)	)	PUNCT
ap-942	54	42	(	(	PUNCT
ap-942	54	43	)	)	PUNCT
ap-942	54	44	(	(	PUNCT
ap-942	54	45	�	�	PROPN
ap-942	54	46	�	�	PROPN
ap-942	54	47	�	�	PROPN
ap-942	54	48	�	�	PROPN
ap-942	54	49	�	�	PROPN
ap-942	54	50	�	�	PROPN
ap-942	54	51	�	�	PROPN
ap-942	54	52	�	�	PROPN
ap-942	54	53	�	�	PROPN
ap-942	54	54	�	�	PROPN
ap-942	54	55	1	1	NUM
ap-942	54	56	2	2	NUM
ap-942	54	57	3	3	NUM
ap-942	54	58	3	3	NUM
ap-942	54	59	1	1	NUM
ap-942	54	60	2	2	NUM
ap-942	54	61	3	3	NUM
ap-942	54	62	2	2	NUM
ap-942	54	63	1	1	NUM
ap-942	54	64	2	2	NUM
ap-942	54	65	2	2	NUM
ap-942	54	66	3	3	NUM
ap-942	54	67	1	1	NUM
ap-942	54	68	3	3	NUM
ap-942	54	69	1	1	NUM
ap-942	54	70	2	2	NUM
ap-942	54	71	3	3	NUM
ap-942	54	72	�	�	PROPN
ap-942	54	73	�	�	PROPN
ap-942	54	74	�	�	PROPN
ap-942	54	75	�	�	PROPN
ap-942	54	76	�	�	PROPN
ap-942	54	77	�	�	PROPN
ap-942	54	78	�	�	PROPN
ap-942	54	79	)	)	PUNCT
ap-942	54	80	,	,	PUNCT
ap-942	54	81	x	x	PUNCT
ap-942	54	82	and	and	CCONJ
ap-942	54	83	,	,	PUNCT
ap-942	54	84	moreover	moreover	ADV
ap-942	54	85	,	,	PUNCT
ap-942	54	86	�	�	PROPN
ap-942	54	87	1	1	NUM
ap-942	54	88	0	0	NUM
ap-942	54	89	�	�	PROPN
ap-942	54	90	�	�	PROPN
ap-942	54	91	det	det	PROPN
ap-942	54	92	m	m	PROPN
ap-942	54	93	,	,	PUNCT
ap-942	54	94	the	the	DET
ap-942	54	95	linear	linear	ADJ
ap-942	54	96	component	component	NOUN
ap-942	54	97	of	of	ADP
ap-942	54	98	�	�	PROPN
ap-942	54	99	�	�	PROPN
ap-942	54	100	m	m	PROPN
ap-942	54	101	(	(	PUNCT
ap-942	54	102	)	)	PUNCT
ap-942	54	103	is	be	AUX
ap-942	54	104	also	also	ADV
ap-942	54	105	equal	equal	ADJ
ap-942	54	106	to	to	ADP
ap-942	54	107	(	(	PUNCT
ap-942	54	108	)	)	PUNCT
ap-942	54	109	�	�	PROPN
ap-942	54	110	�	�	PROPN
ap-942	54	111	2	2	NUM
ap-942	54	112	3	3	NUM
ap-942	54	113	x	x	NOUN
ap-942	54	114	.	.	PUNCT
ap-942	55	1	this	this	PRON
ap-942	55	2	implies	imply	VERB
ap-942	55	3	�	�	PROPN
ap-942	55	4	�	�	PROPN
ap-942	55	5	2	2	NUM
ap-942	55	6	3	3	NUM
ap-942	55	7	1	1	NUM
ap-942	55	8	�	�	PROPN
ap-942	55	9	�	�	PROPN
ap-942	55	10	.	.	PUNCT
ap-942	56	1	�	�	PROPN
ap-942	56	2	:	:	PUNCT
ap-942	56	3	due	due	ADP
ap-942	56	4	to	to	ADP
ap-942	56	5	the	the	DET
ap-942	56	6	row	row	NOUN
ap-942	56	7	dependency	dependency	NOUN
ap-942	56	8	(	(	PUNCT
ap-942	56	9	7	7	X
ap-942	56	10	)	)	PUNCT
ap-942	56	11	we	we	PRON
ap-942	56	12	have	have	VERB
ap-942	56	13	for	for	ADP
ap-942	56	14	the	the	DET
ap-942	56	15	left	left	ADJ
ap-942	56	16	hand	hand	NOUN
ap-942	56	17	side	side	NOUN
ap-942	56	18	of	of	ADP
ap-942	56	19	(	(	PUNCT
ap-942	56	20	1	1	NUM
ap-942	56	21	)	)	PUNCT
ap-942	56	22	det	det	PROPN
ap-942	56	23	det	det	PROPN
ap-942	56	24	1	1	NUM
ap-942	56	25	1	1	NUM
ap-942	56	26	1	1	NUM
ap-942	56	27	1	1	NUM
ap-942	56	28	1	1	NUM
ap-942	56	29	1	1	NUM
ap-942	56	30	21	21	NUM
ap-942	56	31	22	22	NUM
ap-942	56	32	23	23	NUM
ap-942	56	33	31	31	NUM
ap-942	56	34	32	32	NUM
ap-942	56	35	33	33	NUM
ap-942	56	36	11	11	NUM
ap-942	56	37	31	31	NUM
ap-942	56	38	�	�	PROPN
ap-942	56	39	�	�	PROPN
ap-942	56	40	�	�	PROPN
ap-942	56	41	�	�	PROPN
ap-942	56	42	�	�	PROPN
ap-942	56	43	�	�	PROPN
ap-942	56	44	�	�	PROPN
ap-942	56	45	�	�	PROPN
ap-942	56	46	�	�	PROPN
ap-942	56	47	�	�	PROPN
ap-942	56	48	�	�	PROPN
ap-942	56	49	m	m	VERB
ap-942	56	50	m	m	VERB
ap-942	56	51	m	m	VERB
ap-942	56	52	m	m	VERB
ap-942	56	53	m	m	VERB
ap-942	56	54	m	m	VERB
ap-942	56	55	m	m	VERB
ap-942	56	56	m	m	VERB
ap-942	56	57	m	m	VERB
ap-942	56	58	m	m	VERB
ap-942	56	59	m	m	VERB
ap-942	56	60	m	m	VERB
ap-942	56	61	m	m	VERB
ap-942	56	62	m	m	VERB
ap-942	56	63	m	m	VERB
ap-942	56	64	m	m	VERB
ap-942	56	65	m	m	VERB
ap-942	56	66	m	m	VERB
ap-942	56	67	12	12	NUM
ap-942	56	68	32	32	NUM
ap-942	56	69	13	13	NUM
ap-942	56	70	33	33	NUM
ap-942	56	71	31	31	NUM
ap-942	56	72	32	32	NUM
ap-942	56	73	33	33	NUM
ap-942	56	74	11	11	NUM
ap-942	56	75	12	12	NUM
ap-942	56	76	13	13	NUM
ap-942	56	77	1	1	NUM
ap-942	56	78	1	1	NUM
ap-942	56	79	1	1	NUM
ap-942	56	80	�	�	PROPN
ap-942	56	81	�	�	PROPN
ap-942	56	82	�	�	PROPN
ap-942	56	83	�	�	PROPN
ap-942	56	84	�	�	PROPN
ap-942	56	85	�	�	PROPN
ap-942	56	86	�	�	PROPN
ap-942	56	87	�	�	PROPN
ap-942	56	88	�	�	PROPN
ap-942	56	89	�	�	PROPN
ap-942	56	90	�	�	PROPN
ap-942	56	91	det	det	PROPN
ap-942	56	92	m	m	PROPN
ap-942	56	93	m	m	VERB
ap-942	56	94	m	m	VERB
ap-942	56	95	m	m	VERB
ap-942	56	96	m	m	VERB
ap-942	56	97	m	m	VERB
ap-942	56	98	m	m	VERB
ap-942	56	99	m	m	NOUN
ap-942	56	100	m31	m31	NOUN
ap-942	56	101	32	32	NUM
ap-942	56	102	33	33	NUM
ap-942	56	103	11	11	NUM
ap-942	56	104	12	12	NUM
ap-942	56	105	13	13	NUM
ap-942	56	106	31	31	NUM
ap-942	56	107	32	32	NUM
ap-942	56	108	33	33	NUM
ap-942	56	109	1	1	NUM
ap-942	56	110	1	1	NUM
ap-942	56	111	1	1	NUM
ap-942	56	112	�	�	PROPN
ap-942	56	113	�	�	PROPN
ap-942	56	114	�	�	PROPN
ap-942	56	115	�	�	PROPN
ap-942	56	116	�	�	PROPN
ap-942	56	117	�	�	PROPN
ap-942	56	118	�	�	PROPN
ap-942	56	119	�	�	PROPN
ap-942	56	120	�	�	PROPN
ap-942	56	121	�	�	PROPN
ap-942	56	122	�	�	PROPN
ap-942	56	123	�	�	PROPN
ap-942	56	124	det	det	PROPN
ap-942	56	125	�	�	PROPN
ap-942	56	126	�	�	PROPN
ap-942	56	127	�	�	PROPN
ap-942	56	128	�	�	PROPN
ap-942	56	129	�	�	PROPN
ap-942	56	130	,	,	PUNCT
ap-942	56	131	and	and	CCONJ
ap-942	56	132	similarly	similarly	ADV
ap-942	56	133	for	for	ADP
ap-942	56	134	(	(	PUNCT
ap-942	56	135	3	3	X
ap-942	56	136	)	)	PUNCT
ap-942	56	137	det	det	PROPN
ap-942	56	138	det	det	PROPN
ap-942	56	139	m	m	PROPN
ap-942	56	140	m	m	VERB
ap-942	56	141	m	m	VERB
ap-942	56	142	m	m	VERB
ap-942	56	143	m	m	VERB
ap-942	56	144	m	m	VERB
ap-942	56	145	m	m	VERB
ap-942	56	146	m	m	VERB
ap-942	56	147	m	m	VERB
ap-942	56	148	m	m	VERB
ap-942	56	149	11	11	NUM
ap-942	56	150	12	12	NUM
ap-942	56	151	13	13	NUM
ap-942	56	152	21	21	NUM
ap-942	56	153	22	22	NUM
ap-942	56	154	23	23	NUM
ap-942	56	155	11	11	NUM
ap-942	56	156	12	12	NUM
ap-942	56	157	13	13	NUM
ap-942	56	158	1	1	NUM
ap-942	56	159	1	1	NUM
ap-942	56	160	1	1	NUM
ap-942	56	161	1	1	NUM
ap-942	56	162	�	�	PROPN
ap-942	56	163	�	�	PROPN
ap-942	56	164	�	�	PROPN
ap-942	56	165	�	�	PROPN
ap-942	56	166	�	�	PROPN
ap-942	56	167	�	�	PROPN
ap-942	56	168	�	�	PROPN
ap-942	56	169	�	�	PROPN
ap-942	56	170	�	�	PROPN
ap-942	56	171	1	1	NUM
ap-942	56	172	31	31	NUM
ap-942	56	173	12	12	NUM
ap-942	56	174	32	32	NUM
ap-942	56	175	13	13	NUM
ap-942	56	176	33	33	NUM
ap-942	56	177	11	11	NUM
ap-942	56	178	12	12	NUM
ap-942	56	179	13	13	NUM
ap-942	56	180	31	31	NUM
ap-942	56	181	1	1	NUM
ap-942	56	182	1	1	NUM
ap-942	56	183	1	1	NUM
ap-942	56	184	�	�	PROPN
ap-942	56	185	�	�	PROPN
ap-942	56	186	�	�	PROPN
ap-942	56	187	�	�	PROPN
ap-942	56	188	�	�	PROPN
ap-942	56	189	�	�	PROPN
ap-942	56	190	�	�	PROPN
ap-942	56	191	�	�	PROPN
ap-942	56	192	�	�	PROPN
ap-942	56	193	�	�	PROPN
ap-942	56	194	�	�	PROPN
ap-942	56	195	�	�	PROPN
ap-942	56	196	m	m	VERB
ap-942	56	197	m	m	VERB
ap-942	56	198	m	m	VERB
ap-942	56	199	m	m	VERB
ap-942	56	200	m	m	VERB
ap-942	56	201	m	m	VERB
ap-942	56	202	m	m	VERB
ap-942	56	203	m	m	VERB
ap-942	56	204	m	m	NOUN
ap-942	56	205	mdet	mdet	NOUN
ap-942	56	206	32	32	NUM
ap-942	57	1	33	33	NUM
ap-942	57	2	11	11	NUM
ap-942	57	3	12	12	NUM
ap-942	57	4	13	13	NUM
ap-942	57	5	31	31	NUM
ap-942	57	6	32	32	NUM
ap-942	57	7	331	331	NUM
ap-942	57	8	1	1	NUM
ap-942	57	9	1	1	NUM
ap-942	57	10	1	1	NUM
ap-942	57	11	1	1	NUM
ap-942	57	12	1	1	NUM
ap-942	57	13	m	m	NOUN
ap-942	57	14	m	m	VERB
ap-942	57	15	m	m	VERB
ap-942	57	16	m	m	VERB
ap-942	57	17	m	m	VERB
ap-942	57	18	m	m	NOUN
ap-942	57	19	m	m	PROPN
ap-942	57	20	�	�	PROPN
ap-942	57	21	�	�	PROPN
ap-942	57	22	�	�	PROPN
ap-942	57	23	�	�	PROPN
ap-942	57	24	�	�	PROPN
ap-942	57	25	�	�	PROPN
ap-942	57	26	�	�	PROPN
ap-942	57	27	�	�	PROPN
ap-942	57	28	�	�	PROPN
ap-942	57	29	�	�	PROPN
ap-942	57	30	�	�	PROPN
ap-942	57	31	�	�	PROPN
ap-942	57	32	�	�	PROPN
ap-942	57	33	det	det	PROPN
ap-942	57	34	�	�	PROPN
ap-942	57	35	�	�	PROPN
ap-942	57	36	�	�	PROPN
ap-942	57	37	�	�	PROPN
ap-942	57	38	�	�	PROPN
ap-942	57	39	.	.	PUNCT
ap-942	58	1	therefore	therefore	ADV
ap-942	58	2	the	the	DET
ap-942	58	3	conditions	condition	NOUN
ap-942	58	4	(	(	PUNCT
ap-942	58	5	1)–(3	1)–(3	NUM
ap-942	58	6	)	)	PUNCT
ap-942	58	7	are	be	AUX
ap-942	58	8	equivalent	equivalent	ADJ
ap-942	58	9	for	for	ADP
ap-942	58	10	singular	singular	ADJ
ap-942	58	11	matrices	matrix	NOUN
ap-942	58	12	.	.	PUNCT
ap-942	59	1	using	use	VERB
ap-942	59	2	the	the	DET
ap-942	59	3	same	same	ADJ
ap-942	59	4	argument	argument	NOUN
ap-942	59	5	concerning	concern	VERB
ap-942	59	6	the	the	DET
ap-942	59	7	linear	linear	ADJ
ap-942	59	8	component	component	NOUN
ap-942	59	9	of	of	ADP
ap-942	59	10	�	�	PROPN
ap-942	59	11	�	�	PROPN
ap-942	59	12	m	m	PROPN
ap-942	59	13	(	(	PUNCT
ap-942	59	14	)	)	PUNCT
ap-942	59	15	as	as	ADP
ap-942	59	16	in	in	ADP
ap-942	59	17	the	the	DET
ap-942	59	18	previous	previous	ADJ
ap-942	59	19	part	part	NOUN
ap-942	59	20	of	of	ADP
ap-942	59	21	the	the	DET
ap-942	59	22	proof	proof	NOUN
ap-942	59	23	one	one	PRON
ap-942	59	24	can	can	AUX
ap-942	59	25	show	show	VERB
ap-942	59	26	that	that	SCONJ
ap-942	59	27	the	the	DET
ap-942	59	28	conditions	condition	NOUN
ap-942	59	29	�	�	PROPN
ap-942	59	30	�	�	PROPN
ap-942	59	31	�	�	PROPN
ap-942	59	32	�	�	PROPN
ap-942	59	33	�	�	PROPN
ap-942	59	34	�	�	PROPN
ap-942	59	35	�	�	PROPN
ap-942	59	36	(	(	PUNCT
ap-942	59	37	)	)	PUNCT
ap-942	59	38	,	,	PUNCT
ap-942	59	39	,	,	PUNCT
ap-942	59	40	,	,	PUNCT
ap-942	59	41	m	m	PROPN
ap-942	59	42	�	�	PROPN
ap-942	59	43	�	�	PROPN
ap-942	59	44	�	�	PROPN
ap-942	59	45	0	0	NUM
ap-942	59	46	12	12	NUM
ap-942	59	47	3	3	NUM
ap-942	59	48	2	2	NUM
ap-942	59	49	3and	3and	NUM
ap-942	59	50	imply	imply	VERB
ap-942	59	51	the	the	DET
ap-942	59	52	equality	equality	NOUN
ap-942	59	53	(	(	PUNCT
ap-942	59	54	2	2	NUM
ap-942	59	55	)	)	PUNCT
ap-942	59	56	and	and	CCONJ
ap-942	59	57	hence	hence	ADV
ap-942	59	58	m	m	AUX
ap-942	59	59	has	have	VERB
ap-942	59	60	meme	meme	NOUN
ap-942	59	61	.	.	PUNCT
ap-942	60	1	�	�	PROPN
ap-942	61	1	in	in	ADP
ap-942	61	2	addition	addition	NOUN
ap-942	61	3	to	to	ADP
ap-942	61	4	the	the	DET
ap-942	61	5	above	above	ADJ
ap-942	61	6	stated	state	VERB
ap-942	61	7	algebraic	algebraic	ADJ
ap-942	61	8	characterizations	characterization	NOUN
ap-942	61	9	of	of	ADP
ap-942	61	10	matrices	matrix	NOUN
ap-942	61	11	having	have	VERB
ap-942	61	12	the	the	DET
ap-942	61	13	meme	meme	NOUN
ap-942	61	14	property	property	NOUN
ap-942	61	15	,	,	PUNCT
ap-942	61	16	there	there	PRON
ap-942	61	17	is	be	VERB
ap-942	61	18	also	also	ADV
ap-942	61	19	a	a	DET
ap-942	61	20	nice	nice	ADJ
ap-942	61	21	relation	relation	NOUN
ap-942	61	22	between	between	ADP
ap-942	61	23	the	the	DET
ap-942	61	24	singular	singular	NOUN
ap-942	61	25	and	and	CCONJ
ap-942	61	26	the	the	DET
ap-942	61	27	non	non	ADJ
ap-942	61	28	-	-	ADJ
ap-942	61	29	singular	singular	ADJ
ap-942	61	30	case	case	NOUN
ap-942	61	31	.	.	PUNCT
ap-942	62	1	let	let	VERB
ap-942	62	2	©	©	PROPN
ap-942	62	3	czech	czech	PROPN
ap-942	62	4	technical	technical	PROPN
ap-942	62	5	university	university	PROPN
ap-942	62	6	publishing	publishing	NOUN
ap-942	62	7	house	house	NOUN
ap-942	62	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-942	62	9	69	69	NUM
ap-942	62	10	acta	acta	PROPN
ap-942	62	11	polytechnica	polytechnica	PROPN
ap-942	62	12	vol	vol	NOUN
ap-942	62	13	.	.	PUNCT
ap-942	63	1	47	47	NUM
ap-942	63	2	no	no	NOUN
ap-942	63	3	.	.	PUNCT
ap-942	64	1	2–3/2007	2–3/2007	NUM
ap-942	64	2	m	m	PROPN
ap-942	64	3	�	�	PROPN
ap-942	64	4	�	�	PROPN
ap-942	64	5	�	�	PROPN
ap-942	64	6	3	3	NUM
ap-942	64	7	3	3	NUM
ap-942	64	8	be	be	AUX
ap-942	64	9	a	a	DET
ap-942	64	10	singular	singular	ADJ
ap-942	64	11	matrix	matrix	NOUN
ap-942	64	12	having	have	VERB
ap-942	64	13	meme	meme	NOUN
ap-942	64	14	and	and	CCONJ
ap-942	64	15	let	let	VERB
ap-942	64	16	us	we	PRON
ap-942	64	17	consider	consider	VERB
ap-942	64	18	a	a	DET
ap-942	64	19	matrix	matrix	NOUN
ap-942	64	20	m	m	ADP
ap-942	64	21	,	,	PUNCT
ap-942	64	22	given	give	VERB
ap-942	64	23	by	by	ADP
ap-942	64	24	m	m	PROPN
ap-942	64	25	m	m	PROPN
ap-942	64	26	:	:	PUNCT
ap-942	64	27	,	,	PUNCT
ap-942	64	28	�	�	PROPN
ap-942	64	29	�	�	PROPN
ap-942	64	30	�	�	PROPN
ap-942	64	31	�	�	PROPN
ap-942	64	32	�	�	PROPN
ap-942	64	33	�	�	PROPN
ap-942	64	34	�	�	PROPN
ap-942	64	35	�	�	PROPN
ap-942	64	36	�	�	PROPN
ap-942	64	37	�	�	PROPN
ap-942	64	38	�	�	PROPN
ap-942	64	39	k	k	PROPN
ap-942	64	40	0	0	NUM
ap-942	64	41	0	0	NUM
ap-942	64	42	0	0	NUM
ap-942	64	43	1	1	NUM
ap-942	64	44	d	d	SYM
ap-942	64	45	1	1	NUM
ap-942	64	46	1	1	NUM
ap-942	64	47	0	0	NUM
ap-942	64	48	0	0	NUM
ap-942	64	49	0	0	NUM
ap-942	64	50	�	�	PROPN
ap-942	64	51	�	�	PROPN
ap-942	64	52	�	�	PROPN
ap-942	64	53	�	�	PROPN
ap-942	64	54	�	�	PROPN
ap-942	64	55	�	�	PROPN
ap-942	64	56	�	�	PROPN
ap-942	64	57	where	where	SCONJ
ap-942	64	58	k	k	PROPN
ap-942	64	59	�	�	PROPN
ap-942	64	60	�	�	PROPN
ap-942	64	61	.	.	PUNCT
ap-942	65	1	since	since	SCONJ
ap-942	65	2	de	de	PROPN
ap-942	65	3	ed	ed	PROPN
ap-942	65	4	�	�	PROPN
ap-942	65	5	�	�	PROPN
ap-942	65	6	t	t	PROPN
ap-942	65	7	0	0	NUM
ap-942	65	8	,	,	PUNCT
ap-942	65	9	we	we	PRON
ap-942	65	10	have	have	VERB
ap-942	65	11	mem	mem	VERB
ap-942	65	12	m	m	NOUN
ap-942	65	13	d	d	NOUN
ap-942	65	14	e	e	NOUN
ap-942	65	15	m	m	PROPN
ap-942	65	16	d	d	X
ap-942	65	17	mem	mem	X
ap-942	65	18	dem	dem	PROPN
ap-942	65	19	med	med	PROPN
ap-942	65	20	ded	de	VERB
ap-942	65	21	mem	mem	PROPN
ap-942	65	22	t	t	PROPN
ap-942	65	23	t	t	PROPN
ap-942	65	24	t	t	PROPN
ap-942	65	25	t	t	PROPN
ap-942	65	26	t	t	PROPN
ap-942	65	27	t	t	PROPN
ap-942	65	28	t	t	PROPN
ap-942	65	29	t	t	PROPN
ap-942	65	30	k	k	PROPN
ap-942	65	31	k	k	PROPN
ap-942	65	32	k	k	PROPN
ap-942	65	33	k	k	PROPN
ap-942	65	34	k	k	PROPN
ap-942	65	35	�	�	PROPN
ap-942	65	36	�	�	PROPN
ap-942	65	37	�	�	PROPN
ap-942	65	38	�	�	PROPN
ap-942	65	39	�	�	PROPN
ap-942	65	40	�	�	PROPN
ap-942	65	41	�	�	PROPN
ap-942	65	42	�	�	PROPN
ap-942	65	43	�	�	PROPN
ap-942	65	44	�	�	PROPN
ap-942	65	45	(	(	PUNCT
ap-942	65	46	)	)	PUNCT
ap-942	65	47	(	(	PUNCT
ap-942	65	48	)	)	PUNCT
ap-942	65	49	e	e	NOUN
ap-942	65	50	,	,	PUNCT
ap-942	65	51	hence	hence	ADV
ap-942	65	52	also	also	ADV
ap-942	65	53	the	the	DET
ap-942	65	54	regular	regular	ADJ
ap-942	65	55	matrix	matrix	NOUN
ap-942	65	56	m	m	AUX
ap-942	65	57	has	have	VERB
ap-942	65	58	meme	meme	NOUN
ap-942	65	59	.	.	PUNCT
ap-942	66	1	equivalently	equivalently	ADV
ap-942	66	2	,	,	PUNCT
ap-942	66	3	one	one	PRON
ap-942	66	4	can	can	AUX
ap-942	66	5	say	say	VERB
ap-942	66	6	that	that	SCONJ
ap-942	66	7	for	for	ADP
ap-942	66	8	each	each	DET
ap-942	66	9	singular	singular	ADJ
ap-942	66	10	matrix	matrix	NOUN
ap-942	66	11	m	m	AUX
ap-942	66	12	having	have	VERB
ap-942	66	13	meme	meme	NOUN
ap-942	66	14	there	there	PRON
ap-942	66	15	exists	exist	VERB
ap-942	66	16	a	a	DET
ap-942	66	17	regular	regular	ADJ
ap-942	66	18	matrix	matrix	NOUN
ap-942	66	19	m	m	AUX
ap-942	66	20	having	have	VERB
ap-942	66	21	meme	meme	NOUN
ap-942	66	22	such	such	ADJ
ap-942	66	23	that	that	SCONJ
ap-942	66	24	their	their	PRON
ap-942	66	25	first	first	ADJ
ap-942	66	26	and	and	CCONJ
ap-942	66	27	third	third	ADJ
ap-942	66	28	row	row	NOUN
ap-942	66	29	coincide	coincide	NOUN
ap-942	66	30	,	,	PUNCT
ap-942	66	31	that	that	ADV
ap-942	66	32	is	is	ADV
ap-942	66	33	,	,	PUNCT
ap-942	66	34	m	m	VERB
ap-942	66	35	m	m	VERB
ap-942	66	36	�	�	PROPN
ap-942	66	37	�	�	PROPN
ap-942	66	38	�	�	PROPN
ap-942	66	39	�	�	PROPN
ap-942	66	40	�	�	PROPN
ap-942	66	41	�	�	PROPN
ap-942	66	42	�	�	PROPN
ap-942	66	43	�	�	PROPN
ap-942	66	44	1	1	NUM
ap-942	66	45	0	0	NUM
ap-942	66	46	0	0	NUM
ap-942	66	47	1	1	NUM
ap-942	66	48	0	0	NUM
ap-942	66	49	1	1	NUM
ap-942	66	50	0	0	NUM
ap-942	66	51	0	0	NUM
ap-942	66	52	1	1	NUM
ap-942	66	53	.	.	PUNCT
ap-942	67	1	acknowledgment	acknowledgment	NOUN
ap-942	67	2	the	the	DET
ap-942	67	3	author	author	NOUN
ap-942	67	4	acknowledges	acknowledge	VERB
ap-942	67	5	financial	financial	ADJ
ap-942	67	6	support	support	NOUN
ap-942	67	7	from	from	ADP
ap-942	67	8	the	the	DET
ap-942	67	9	grant	grant	NOUN
ap-942	67	10	agency	agency	NOUN
ap-942	67	11	of	of	ADP
ap-942	67	12	the	the	DET
ap-942	67	13	czech	czech	PROPN
ap-942	67	14	republic	republic	PROPN
ap-942	67	15	gačr	gačr	PROPN
ap-942	67	16	201/05/0169	201/05/0169	PROPN
ap-942	67	17	,	,	PUNCT
ap-942	67	18	and	and	CCONJ
ap-942	67	19	from	from	ADP
ap-942	67	20	ministry	ministry	PROPN
ap-942	67	21	of	of	ADP
ap-942	67	22	education	education	PROPN
ap-942	67	23	,	,	PUNCT
ap-942	67	24	youth	youth	NOUN
ap-942	67	25	,	,	PUNCT
ap-942	67	26	and	and	CCONJ
ap-942	67	27	sports	sport	NOUN
ap-942	67	28	of	of	ADP
ap-942	67	29	the	the	DET
ap-942	67	30	czech	czech	PROPN
ap-942	67	31	republic	republic	NOUN
ap-942	67	32	grant	grant	PROPN
ap-942	67	33	lc	lc	PROPN
ap-942	67	34	06002	06002	NUM
ap-942	67	35	.	.	PUNCT
ap-942	68	1	references	reference	NOUN
ap-942	68	2	[	[	X
ap-942	68	3	1	1	NUM
ap-942	68	4	]	]	PUNCT
ap-942	68	5	ambrož	ambrož	NOUN
ap-942	68	6	,	,	PUNCT
ap-942	68	7	p.	p.	NOUN
ap-942	68	8	,	,	PUNCT
ap-942	68	9	masáková	masáková	PROPN
ap-942	68	10	,	,	PUNCT
ap-942	68	11	z.	z.	PROPN
ap-942	68	12	,	,	PUNCT
ap-942	68	13	pelantová	pelantová	PROPN
ap-942	68	14	,	,	PUNCT
ap-942	68	15	e.	e.	PROPN
ap-942	68	16	:	:	PUNCT
ap-942	68	17	matrices	matrix	NOUN
ap-942	68	18	of	of	ADP
ap-942	68	19	3iet	3iet	NUM
ap-942	68	20	preserving	preserve	VERB
ap-942	68	21	morphisms	morphism	NOUN
ap-942	68	22	.	.	PUNCT
ap-942	69	1	submitted	submit	VERB
ap-942	69	2	to	to	ADP
ap-942	69	3	theor	theor	PROPN
ap-942	69	4	.	.	PUNCT
ap-942	70	1	comp	comp	PROPN
ap-942	70	2	.	.	PUNCT
ap-942	71	1	sci	sci	PROPN
ap-942	71	2	.	.	PROPN
ap-942	71	3	,	,	PUNCT
ap-942	71	4	2007	2007	NUM
ap-942	71	5	.	.	PUNCT
ap-942	72	1	[	[	X
ap-942	72	2	2	2	NUM
ap-942	72	3	]	]	X
ap-942	72	4	berstel	berstel	NOUN
ap-942	72	5	,	,	PUNCT
ap-942	72	6	j.	j.	PROPN
ap-942	72	7	,	,	PUNCT
ap-942	72	8	séébold	séébold	NOUN
ap-942	72	9	,	,	PUNCT
ap-942	72	10	p.	p.	NOUN
ap-942	72	11	:	:	PUNCT
ap-942	72	12	morphismes	morphismes	PROPN
ap-942	72	13	de	de	PROPN
ap-942	72	14	sturm	sturm	PROPN
ap-942	72	15	.	.	PUNCT
ap-942	73	1	bull	bull	NOUN
ap-942	73	2	.	.	PUNCT
ap-942	74	1	belg	belg	PROPN
ap-942	74	2	.	.	PUNCT
ap-942	75	1	math	math	NOUN
ap-942	75	2	.	.	PUNCT
ap-942	76	1	soc	soc	PROPN
ap-942	76	2	.	.	PUNCT
ap-942	77	1	simon	simon	PROPN
ap-942	77	2	stevin	stevin	PROPN
ap-942	77	3	,	,	PUNCT
ap-942	77	4	vol	vol	NOUN
ap-942	77	5	.	.	PROPN
ap-942	77	6	1	1	NUM
ap-942	77	7	(	(	PUNCT
ap-942	77	8	1994	1994	NUM
ap-942	77	9	)	)	PUNCT
ap-942	77	10	,	,	PUNCT
ap-942	77	11	p.	p.	NOUN
ap-942	77	12	175–189	175–189	NUM
ap-942	77	13	.	.	PUNCT
ap-942	78	1	[	[	X
ap-942	78	2	3	3	NUM
ap-942	78	3	]	]	X
ap-942	78	4	mignosi	mignosi	NOUN
ap-942	78	5	,	,	PUNCT
ap-942	78	6	f.	f.	PROPN
ap-942	78	7	,	,	PUNCT
ap-942	78	8	séébold	séébold	NOUN
ap-942	78	9	,	,	PUNCT
ap-942	78	10	p.	p.	NOUN
ap-942	78	11	:	:	PUNCT
ap-942	78	12	morphismes	morphisme	NOUN
ap-942	78	13	sturmiens	sturmien	VERB
ap-942	78	14	et	et	NOUN
ap-942	78	15	r	r	NOUN
ap-942	78	16	gles	gle	NOUN
ap-942	78	17	de	de	ADP
ap-942	78	18	rauzy	rauzy	NOUN
ap-942	78	19	.	.	PUNCT
ap-942	79	1	j.	j.	PROPN
ap-942	79	2	théor	théor	PROPN
ap-942	79	3	.	.	PUNCT
ap-942	80	1	nombres	nombre	NOUN
ap-942	80	2	bordeaux	bordeaux	PROPN
ap-942	80	3	,	,	PUNCT
ap-942	80	4	vol	vol	NOUN
ap-942	80	5	.	.	PROPN
ap-942	80	6	5	5	NUM
ap-942	80	7	(	(	PUNCT
ap-942	80	8	1993	1993	NUM
ap-942	80	9	)	)	PUNCT
ap-942	80	10	,	,	PUNCT
ap-942	80	11	p.	p.	NOUN
ap-942	80	12	221–233	221–233	NUM
ap-942	80	13	.	.	PUNCT
ap-942	81	1	[	[	X
ap-942	81	2	4	4	NUM
ap-942	81	3	]	]	X
ap-942	81	4	séébold	séébold	NOUN
ap-942	81	5	,	,	PUNCT
ap-942	81	6	p.	p.	NOUN
ap-942	81	7	:	:	PUNCT
ap-942	82	1	fibonacci	fibonacci	NOUN
ap-942	82	2	morphisms	morphism	NOUN
ap-942	82	3	and	and	CCONJ
ap-942	82	4	sturmian	sturmian	NOUN
ap-942	82	5	words	word	NOUN
ap-942	82	6	.	.	PUNCT
ap-942	83	1	theoret	theoret	ADJ
ap-942	83	2	.	.	PUNCT
ap-942	84	1	comput	comput	NOUN
ap-942	84	2	.	.	PUNCT
ap-942	85	1	sci	sci	PROPN
ap-942	85	2	.	.	PROPN
ap-942	85	3	,	,	PUNCT
ap-942	85	4	vol	vol	NOUN
ap-942	85	5	.	.	PROPN
ap-942	85	6	88	88	NUM
ap-942	85	7	(	(	PUNCT
ap-942	85	8	1991	1991	NUM
ap-942	85	9	)	)	PUNCT
ap-942	85	10	,	,	PUNCT
ap-942	85	11	p.	p.	NOUN
ap-942	85	12	365–384	365–384	NUM
ap-942	85	13	.	.	PUNCT
ap-942	86	1	ing	ing	PROPN
ap-942	86	2	.	.	PUNCT
ap-942	87	1	petr	petr	PROPN
ap-942	87	2	ambrož	ambrož	PROPN
ap-942	87	3	,	,	PUNCT
ap-942	87	4	ph.d	ph.d	PROPN
ap-942	87	5	.	.	PUNCT
ap-942	88	1	petr.ambroz@fjfi.cvut.cz	petr.ambroz@fjfi.cvut.cz	PROPN
ap-942	88	2	department	department	PROPN
ap-942	88	3	of	of	ADP
ap-942	88	4	mathematics	mathematics	PROPN
ap-942	88	5	faculty	faculty	NOUN
ap-942	88	6	of	of	ADP
ap-942	88	7	nuclear	nuclear	ADJ
ap-942	88	8	sciences	science	NOUN
ap-942	88	9	and	and	CCONJ
ap-942	88	10	physical	physical	ADJ
ap-942	88	11	engineering	engineering	NOUN
ap-942	88	12	trojanova	trojanova	ADP
ap-942	88	13	13	13	NUM
ap-942	88	14	120	120	NUM
ap-942	88	15	00	00	NUM
ap-942	88	16	praha	praha	PROPN
ap-942	88	17	2	2	NUM
ap-942	88	18	,	,	PUNCT
ap-942	88	19	czech	czech	PROPN
ap-942	88	20	republic	republic	NOUN
ap-942	88	21	70	70	NUM
ap-942	88	22	©	©	PROPN
ap-942	88	23	czech	czech	PROPN
ap-942	88	24	technical	technical	PROPN
ap-942	88	25	university	university	PROPN
ap-942	88	26	publishing	publishing	NOUN
ap-942	88	27	house	house	NOUN
ap-942	88	28	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-942	88	29	acta	acta	PROPN
ap-942	88	30	polytechnica	polytechnica	PROPN
ap-942	88	31	vol	vol	NOUN
ap-942	88	32	.	.	PUNCT
ap-942	89	1	47	47	NUM
ap-942	89	2	no	no	INTJ
ap-942	89	3	.	.	PUNCT
ap-942	90	1	2–3/2007	2–3/2007	NUM