id	sid	tid	token	lemma	pos
ejpam-2017	1	1	european	european	PROPN
ejpam-2017	1	2	journal	journal	PROPN
ejpam-2017	1	3	of	of	ADP
ejpam-2017	1	4	pure	pure	ADJ
ejpam-2017	1	5	and	and	CCONJ
ejpam-2017	1	6	applied	apply	VERB
ejpam-2017	1	7	mathematics	mathematic	NOUN
ejpam-2017	1	8	vol	vol	NOUN
ejpam-2017	1	9	.	.	PUNCT
ejpam-2017	2	1	7	7	NUM
ejpam-2017	2	2	,	,	PUNCT
ejpam-2017	2	3	no	no	INTJ
ejpam-2017	2	4	.	.	NOUN
ejpam-2017	2	5	4	4	NUM
ejpam-2017	2	6	,	,	PUNCT
ejpam-2017	2	7	2014	2014	NUM
ejpam-2017	2	8	,	,	PUNCT
ejpam-2017	2	9	405	405	NUM
ejpam-2017	2	10	-	-	SYM
ejpam-2017	2	11	411	411	NUM
ejpam-2017	2	12	issn	issn	PROPN
ejpam-2017	2	13	1307	1307	NUM
ejpam-2017	2	14	-	-	SYM
ejpam-2017	2	15	5543	5543	NUM
ejpam-2017	2	16	–	–	PUNCT
ejpam-2017	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2017	2	18	commutative	commutative	ADJ
ejpam-2017	2	19	law	law	NOUN
ejpam-2017	2	20	for	for	ADP
ejpam-2017	2	21	the	the	DET
ejpam-2017	2	22	multiplication	multiplication	NOUN
ejpam-2017	2	23	of	of	ADP
ejpam-2017	2	24	matrices	matrix	NOUN
ejpam-2017	2	25	as	as	SCONJ
ejpam-2017	2	26	viewed	view	VERB
ejpam-2017	2	27	in	in	ADP
ejpam-2017	2	28	terms	term	NOUN
ejpam-2017	2	29	of	of	ADP
ejpam-2017	2	30	hankel	hankel	NOUN
ejpam-2017	2	31	’s	’s	PART
ejpam-2017	2	32	principle	principle	PROPN
ejpam-2017	2	33	yukio	yukio	PROPN
ejpam-2017	2	34	kobayashi	kobayashi	PROPN
ejpam-2017	2	35	department	department	PROPN
ejpam-2017	2	36	of	of	ADP
ejpam-2017	2	37	information	information	NOUN
ejpam-2017	2	38	systems	system	NOUN
ejpam-2017	2	39	science	science	NOUN
ejpam-2017	2	40	,	,	PUNCT
ejpam-2017	2	41	faculty	faculty	NOUN
ejpam-2017	2	42	of	of	ADP
ejpam-2017	2	43	engineering	engineering	NOUN
ejpam-2017	2	44	,	,	PUNCT
ejpam-2017	2	45	soka	soka	PROPN
ejpam-2017	2	46	university	university	PROPN
ejpam-2017	2	47	,	,	PUNCT
ejpam-2017	2	48	tokyo	tokyo	PROPN
ejpam-2017	2	49	,	,	PUNCT
ejpam-2017	2	50	japan	japan	PROPN
ejpam-2017	2	51	abstract	abstract	PROPN
ejpam-2017	2	52	.	.	PUNCT
ejpam-2017	3	1	many	many	ADJ
ejpam-2017	3	2	rules	rule	NOUN
ejpam-2017	3	3	of	of	ADP
ejpam-2017	3	4	arithmetic	arithmetic	NOUN
ejpam-2017	3	5	for	for	ADP
ejpam-2017	3	6	real	real	ADJ
ejpam-2017	3	7	numbers	number	NOUN
ejpam-2017	3	8	also	also	ADV
ejpam-2017	3	9	hold	hold	VERB
ejpam-2017	3	10	for	for	ADP
ejpam-2017	3	11	matrices	matrix	NOUN
ejpam-2017	3	12	,	,	PUNCT
ejpam-2017	3	13	but	but	CCONJ
ejpam-2017	3	14	a	a	DET
ejpam-2017	3	15	few	few	ADJ
ejpam-2017	3	16	do	do	VERB
ejpam-2017	3	17	not	not	PART
ejpam-2017	3	18	.	.	PUNCT
ejpam-2017	4	1	the	the	DET
ejpam-2017	4	2	commutative	commutative	ADJ
ejpam-2017	4	3	law	law	NOUN
ejpam-2017	4	4	for	for	ADP
ejpam-2017	4	5	the	the	DET
ejpam-2017	4	6	multiplication	multiplication	NOUN
ejpam-2017	4	7	of	of	ADP
ejpam-2017	4	8	matrices	matrix	NOUN
ejpam-2017	4	9	,	,	PUNCT
ejpam-2017	4	10	however	however	ADV
ejpam-2017	4	11	,	,	PUNCT
ejpam-2017	4	12	can	can	AUX
ejpam-2017	4	13	be	be	AUX
ejpam-2017	4	14	also	also	ADV
ejpam-2017	4	15	considered	consider	VERB
ejpam-2017	4	16	as	as	ADP
ejpam-2017	4	17	an	an	DET
ejpam-2017	4	18	extension	extension	NOUN
ejpam-2017	4	19	of	of	ADP
ejpam-2017	4	20	the	the	DET
ejpam-2017	4	21	law	law	NOUN
ejpam-2017	4	22	for	for	ADP
ejpam-2017	4	23	real	real	ADJ
ejpam-2017	4	24	numbers	number	NOUN
ejpam-2017	4	25	.	.	PUNCT
ejpam-2017	5	1	the	the	DET
ejpam-2017	5	2	transpose	transpose	NOUN
ejpam-2017	5	3	of	of	ADP
ejpam-2017	5	4	a	a	DET
ejpam-2017	5	5	matrix	matrix	NOUN
ejpam-2017	5	6	conserves	conserve	VERB
ejpam-2017	5	7	“	"	PUNCT
ejpam-2017	5	8	the	the	DET
ejpam-2017	5	9	principle	principle	NOUN
ejpam-2017	5	10	of	of	ADP
ejpam-2017	5	11	the	the	DET
ejpam-2017	5	12	permanence	permanence	NOUN
ejpam-2017	5	13	of	of	ADP
ejpam-2017	5	14	form	form	NOUN
ejpam-2017	5	15	and	and	CCONJ
ejpam-2017	5	16	its	its	PRON
ejpam-2017	5	17	transition	transition	NOUN
ejpam-2017	5	18	”	"	PUNCT
ejpam-2017	5	19	for	for	ADP
ejpam-2017	5	20	the	the	DET
ejpam-2017	5	21	commutative	commutative	ADJ
ejpam-2017	5	22	law	law	NOUN
ejpam-2017	5	23	for	for	ADP
ejpam-2017	5	24	multiplication	multiplication	NOUN
ejpam-2017	5	25	.	.	PUNCT
ejpam-2017	6	1	2010	2010	NUM
ejpam-2017	6	2	mathematics	mathematic	NOUN
ejpam-2017	6	3	subject	subject	NOUN
ejpam-2017	6	4	classifications	classification	NOUN
ejpam-2017	6	5	:	:	PUNCT
ejpam-2017	6	6	15a30	15a30	NUM
ejpam-2017	6	7	,	,	PUNCT
ejpam-2017	6	8	97h60	97h60	NUM
ejpam-2017	6	9	key	key	ADJ
ejpam-2017	6	10	words	word	NOUN
ejpam-2017	6	11	and	and	CCONJ
ejpam-2017	6	12	phrases	phrase	NOUN
ejpam-2017	6	13	:	:	PUNCT
ejpam-2017	6	14	hankel	hankel	PROPN
ejpam-2017	6	15	’s	’s	PART
ejpam-2017	6	16	principle	principle	NOUN
ejpam-2017	6	17	,	,	PUNCT
ejpam-2017	6	18	the	the	DET
ejpam-2017	6	19	principle	principle	NOUN
ejpam-2017	6	20	of	of	ADP
ejpam-2017	6	21	the	the	DET
ejpam-2017	6	22	permanence	permanence	NOUN
ejpam-2017	6	23	of	of	ADP
ejpam-2017	6	24	form	form	NOUN
ejpam-2017	6	25	and	and	CCONJ
ejpam-2017	6	26	its	its	PRON
ejpam-2017	6	27	transition	transition	NOUN
ejpam-2017	6	28	,	,	PUNCT
ejpam-2017	6	29	homothety	homothety	NOUN
ejpam-2017	6	30	,	,	PUNCT
ejpam-2017	6	31	matrix	matrix	NOUN
ejpam-2017	6	32	,	,	PUNCT
ejpam-2017	6	33	commutative	commutative	ADJ
ejpam-2017	6	34	law	law	NOUN
ejpam-2017	6	35	for	for	ADP
ejpam-2017	6	36	multiplication	multiplication	NOUN
ejpam-2017	6	37	,	,	PUNCT
ejpam-2017	6	38	composite	composite	ADJ
ejpam-2017	6	39	mapping	mapping	NOUN
ejpam-2017	6	40	1	1	NUM
ejpam-2017	6	41	.	.	PUNCT
ejpam-2017	6	42	introduction	introduction	NOUN
ejpam-2017	6	43	any	any	DET
ejpam-2017	6	44	rule	rule	NOUN
ejpam-2017	6	45	of	of	ADP
ejpam-2017	6	46	numerical	numerical	ADJ
ejpam-2017	6	47	operations	operation	NOUN
ejpam-2017	6	48	should	should	AUX
ejpam-2017	6	49	be	be	AUX
ejpam-2017	6	50	extended	extend	VERB
ejpam-2017	6	51	in	in	ADP
ejpam-2017	6	52	accordance	accordance	NOUN
ejpam-2017	6	53	with	with	ADP
ejpam-2017	6	54	hankel	hankel	NOUN
ejpam-2017	6	55	’s	’s	PART
ejpam-2017	6	56	principle	principle	NOUN
ejpam-2017	6	57	,	,	PUNCT
ejpam-2017	6	58	that	that	ADV
ejpam-2017	6	59	is	is	ADV
ejpam-2017	6	60	,	,	PUNCT
ejpam-2017	6	61	“	"	PUNCT
ejpam-2017	6	62	the	the	DET
ejpam-2017	6	63	principle	principle	NOUN
ejpam-2017	6	64	of	of	ADP
ejpam-2017	6	65	the	the	DET
ejpam-2017	6	66	permanence	permanence	NOUN
ejpam-2017	6	67	of	of	ADP
ejpam-2017	6	68	form	form	NOUN
ejpam-2017	6	69	and	and	CCONJ
ejpam-2017	6	70	its	its	PRON
ejpam-2017	6	71	transition	transition	NOUN
ejpam-2017	6	72	”	"	PUNCT
ejpam-2017	7	1	[	[	X
ejpam-2017	7	2	2	2	NUM
ejpam-2017	7	3	,	,	PUNCT
ejpam-2017	7	4	3	3	NUM
ejpam-2017	7	5	]	]	PUNCT
ejpam-2017	7	6	.	.	PUNCT
ejpam-2017	8	1	the	the	DET
ejpam-2017	8	2	standard	standard	ADJ
ejpam-2017	8	3	algebraic	algebraic	ADJ
ejpam-2017	8	4	properties	property	NOUN
ejpam-2017	8	5	of	of	ADP
ejpam-2017	8	6	addition	addition	NOUN
ejpam-2017	8	7	and	and	CCONJ
ejpam-2017	8	8	multiplication	multiplication	NOUN
ejpam-2017	8	9	are	be	AUX
ejpam-2017	8	10	commutativity	commutativity	NOUN
ejpam-2017	8	11	,	,	PUNCT
ejpam-2017	8	12	associativity	associativity	NOUN
ejpam-2017	8	13	,	,	PUNCT
ejpam-2017	8	14	and	and	CCONJ
ejpam-2017	8	15	distributivity	distributivity	NOUN
ejpam-2017	8	16	.	.	PUNCT
ejpam-2017	9	1	the	the	DET
ejpam-2017	9	2	definitions	definition	NOUN
ejpam-2017	9	3	of	of	ADP
ejpam-2017	9	4	addition	addition	NOUN
ejpam-2017	9	5	and	and	CCONJ
ejpam-2017	9	6	multiplication	multiplication	NOUN
ejpam-2017	9	7	for	for	ADP
ejpam-2017	9	8	vectors	vector	NOUN
ejpam-2017	9	9	and	and	CCONJ
ejpam-2017	9	10	matrices	matrix	NOUN
ejpam-2017	9	11	should	should	AUX
ejpam-2017	9	12	be	be	AUX
ejpam-2017	9	13	extended	extend	VERB
ejpam-2017	9	14	in	in	ADP
ejpam-2017	9	15	such	such	DET
ejpam-2017	9	16	a	a	DET
ejpam-2017	9	17	way	way	NOUN
ejpam-2017	9	18	as	as	SCONJ
ejpam-2017	9	19	to	to	PART
ejpam-2017	9	20	conserve	conserve	VERB
ejpam-2017	9	21	the	the	DET
ejpam-2017	9	22	standard	standard	ADJ
ejpam-2017	9	23	algebraic	algebraic	ADJ
ejpam-2017	9	24	properties	property	NOUN
ejpam-2017	9	25	of	of	ADP
ejpam-2017	9	26	these	these	DET
ejpam-2017	9	27	numerical	numerical	ADJ
ejpam-2017	9	28	operations	operation	NOUN
ejpam-2017	9	29	.	.	PUNCT
ejpam-2017	10	1	the	the	DET
ejpam-2017	10	2	commutative	commutative	ADJ
ejpam-2017	10	3	law	law	NOUN
ejpam-2017	10	4	for	for	ADP
ejpam-2017	10	5	multiplication	multiplication	NOUN
ejpam-2017	10	6	,	,	PUNCT
ejpam-2017	10	7	ab	ab	PROPN
ejpam-2017	10	8	=	=	SYM
ejpam-2017	10	9	ba	ba	PROPN
ejpam-2017	10	10	,	,	PUNCT
ejpam-2017	10	11	holds	hold	VERB
ejpam-2017	10	12	for	for	ADP
ejpam-2017	10	13	any	any	DET
ejpam-2017	10	14	real	real	ADJ
ejpam-2017	10	15	numbers	number	NOUN
ejpam-2017	10	16	a	a	PRON
ejpam-2017	10	17	and	and	CCONJ
ejpam-2017	10	18	b.	b.	PROPN
ejpam-2017	10	19	however	however	ADV
ejpam-2017	10	20	,	,	PUNCT
ejpam-2017	10	21	ab	ab	PROPN
ejpam-2017	10	22	=	=	SYM
ejpam-2017	10	23	ba	ba	PROPN
ejpam-2017	10	24	need	need	AUX
ejpam-2017	10	25	not	not	PART
ejpam-2017	10	26	hold	hold	VERB
ejpam-2017	10	27	for	for	ADP
ejpam-2017	10	28	matrices	matrix	NOUN
ejpam-2017	10	29	a	a	PRON
ejpam-2017	10	30	and	and	CCONJ
ejpam-2017	10	31	b	b	NOUN
ejpam-2017	11	1	[	[	X
ejpam-2017	11	2	1	1	NUM
ejpam-2017	11	3	]	]	PUNCT
ejpam-2017	11	4	.	.	PUNCT
ejpam-2017	12	1	it	it	PRON
ejpam-2017	12	2	seems	seem	VERB
ejpam-2017	12	3	that	that	SCONJ
ejpam-2017	12	4	the	the	DET
ejpam-2017	12	5	commutative	commutative	ADJ
ejpam-2017	12	6	law	law	NOUN
ejpam-2017	12	7	for	for	ADP
ejpam-2017	12	8	multiplication	multiplication	NOUN
ejpam-2017	12	9	does	do	AUX
ejpam-2017	12	10	not	not	PART
ejpam-2017	12	11	follow	follow	VERB
ejpam-2017	12	12	“	"	PUNCT
ejpam-2017	12	13	the	the	DET
ejpam-2017	12	14	principle	principle	NOUN
ejpam-2017	12	15	of	of	ADP
ejpam-2017	12	16	the	the	DET
ejpam-2017	12	17	permanence	permanence	NOUN
ejpam-2017	12	18	of	of	ADP
ejpam-2017	12	19	form	form	NOUN
ejpam-2017	12	20	and	and	CCONJ
ejpam-2017	12	21	its	its	PRON
ejpam-2017	12	22	transition	transition	NOUN
ejpam-2017	12	23	”	"	PUNCT
ejpam-2017	12	24	.	.	PUNCT
ejpam-2017	13	1	the	the	DET
ejpam-2017	13	2	purpose	purpose	NOUN
ejpam-2017	13	3	of	of	ADP
ejpam-2017	13	4	the	the	DET
ejpam-2017	13	5	present	present	ADJ
ejpam-2017	13	6	article	article	NOUN
ejpam-2017	13	7	is	be	AUX
ejpam-2017	13	8	to	to	PART
ejpam-2017	13	9	show	show	VERB
ejpam-2017	13	10	another	another	DET
ejpam-2017	13	11	view	view	NOUN
ejpam-2017	13	12	that	that	SCONJ
ejpam-2017	13	13	the	the	DET
ejpam-2017	13	14	commutative	commutative	ADJ
ejpam-2017	13	15	law	law	NOUN
ejpam-2017	13	16	for	for	ADP
ejpam-2017	13	17	multiplication	multiplication	NOUN
ejpam-2017	13	18	also	also	ADV
ejpam-2017	13	19	follows	follow	VERB
ejpam-2017	13	20	this	this	DET
ejpam-2017	13	21	principle	principle	NOUN
ejpam-2017	13	22	through	through	ADP
ejpam-2017	13	23	the	the	DET
ejpam-2017	13	24	transpose	transpose	NOUN
ejpam-2017	13	25	of	of	ADP
ejpam-2017	13	26	a	a	DET
ejpam-2017	13	27	matrix	matrix	NOUN
ejpam-2017	13	28	.	.	PUNCT
ejpam-2017	14	1	2	2	X
ejpam-2017	14	2	.	.	X
ejpam-2017	14	3	composite	composite	ADJ
ejpam-2017	14	4	mapping	mapping	NOUN
ejpam-2017	14	5	as	as	ADP
ejpam-2017	14	6	an	an	DET
ejpam-2017	14	7	extension	extension	NOUN
ejpam-2017	14	8	of	of	ADP
ejpam-2017	14	9	a	a	DET
ejpam-2017	14	10	concept	concept	NOUN
ejpam-2017	14	11	of	of	ADP
ejpam-2017	14	12	proportion	proportion	NOUN
ejpam-2017	14	13	the	the	DET
ejpam-2017	14	14	theory	theory	NOUN
ejpam-2017	14	15	of	of	ADP
ejpam-2017	14	16	quantity	quantity	NOUN
ejpam-2017	14	17	originated	originate	VERB
ejpam-2017	14	18	from	from	ADP
ejpam-2017	14	19	the	the	DET
ejpam-2017	14	20	problem	problem	NOUN
ejpam-2017	14	21	of	of	ADP
ejpam-2017	14	22	proportion	proportion	NOUN
ejpam-2017	14	23	.	.	PUNCT
ejpam-2017	15	1	as	as	SCONJ
ejpam-2017	15	2	one	one	NUM
ejpam-2017	15	3	variable	variable	NOUN
ejpam-2017	15	4	x	x	NOUN
ejpam-2017	15	5	doubles	double	NOUN
ejpam-2017	15	6	,	,	PUNCT
ejpam-2017	15	7	triples	triple	NOUN
ejpam-2017	15	8	,	,	PUNCT
ejpam-2017	15	9	.	.	PUNCT
ejpam-2017	15	10	.	.	PUNCT
ejpam-2017	16	1	.	.	PUNCT
ejpam-2017	16	2	,	,	PUNCT
ejpam-2017	16	3	another	another	DET
ejpam-2017	16	4	variable	variable	ADJ
ejpam-2017	16	5	y	y	PROPN
ejpam-2017	16	6	doubles	double	VERB
ejpam-2017	16	7	,	,	PUNCT
ejpam-2017	16	8	triples	triple	NOUN
ejpam-2017	16	9	,	,	PUNCT
ejpam-2017	16	10	.	.	PUNCT
ejpam-2017	16	11	.	.	PUNCT
ejpam-2017	17	1	.	.	PUNCT
ejpam-2017	17	2	,	,	PUNCT
ejpam-2017	18	1	respectively	respectively	ADV
ejpam-2017	18	2	.	.	PUNCT
ejpam-2017	19	1	a	a	DET
ejpam-2017	19	2	proportional	proportional	ADJ
ejpam-2017	19	3	relation	relation	NOUN
ejpam-2017	19	4	is	be	AUX
ejpam-2017	19	5	expressed	express	VERB
ejpam-2017	19	6	as	as	ADP
ejpam-2017	19	7	a	a	DET
ejpam-2017	19	8	linear	linear	ADJ
ejpam-2017	19	9	equation	equation	NOUN
ejpam-2017	19	10	y	y	NOUN
ejpam-2017	19	11	=	=	PUNCT
ejpam-2017	19	12	ax	ax	NOUN
ejpam-2017	19	13	,	,	PUNCT
ejpam-2017	19	14	where	where	SCONJ
ejpam-2017	19	15	a	a	PRON
ejpam-2017	19	16	is	be	AUX
ejpam-2017	19	17	a	a	DET
ejpam-2017	19	18	constant	constant	ADJ
ejpam-2017	19	19	.	.	PUNCT
ejpam-2017	20	1	in	in	ADP
ejpam-2017	20	2	view	view	NOUN
ejpam-2017	20	3	of	of	ADP
ejpam-2017	20	4	“	"	PUNCT
ejpam-2017	20	5	the	the	DET
ejpam-2017	20	6	principle	principle	NOUN
ejpam-2017	20	7	of	of	ADP
ejpam-2017	20	8	email	email	NOUN
ejpam-2017	20	9	address	address	NOUN
ejpam-2017	20	10	:	:	PUNCT
ejpam-2017	20	11	koba@t.soka.ac.jp	koba@t.soka.ac.jp	X
ejpam-2017	20	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2017	21	1	405	405	NUM
ejpam-2017	22	1	c	c	X
ejpam-2017	22	2	©	©	NOUN
ejpam-2017	22	3	2014	2014	NUM
ejpam-2017	22	4	ejpam	ejpam	NOUN
ejpam-2017	22	5	all	all	DET
ejpam-2017	22	6	rights	right	NOUN
ejpam-2017	22	7	reserved	reserve	VERB
ejpam-2017	22	8	.	.	PUNCT
ejpam-2017	23	1	y.	y.	PROPN
ejpam-2017	23	2	kobayashi	kobayashi	PROPN
ejpam-2017	23	3	/	/	SYM
ejpam-2017	23	4	eur	eur	PROPN
ejpam-2017	23	5	.	.	PUNCT
ejpam-2017	24	1	j.	j.	PROPN
ejpam-2017	24	2	pure	pure	PROPN
ejpam-2017	24	3	appl	appl	PROPN
ejpam-2017	24	4	.	.	PROPN
ejpam-2017	24	5	math	math	PROPN
ejpam-2017	24	6	,	,	PUNCT
ejpam-2017	24	7	7	7	NUM
ejpam-2017	24	8	(	(	PUNCT
ejpam-2017	24	9	2014	2014	NUM
ejpam-2017	24	10	)	)	PUNCT
ejpam-2017	24	11	,	,	PUNCT
ejpam-2017	24	12	405	405	NUM
ejpam-2017	24	13	-	-	SYM
ejpam-2017	24	14	411	411	NUM
ejpam-2017	24	15	406	406	NUM
ejpam-2017	24	16	the	the	DET
ejpam-2017	24	17	permanence	permanence	NOUN
ejpam-2017	24	18	of	of	ADP
ejpam-2017	24	19	form	form	NOUN
ejpam-2017	24	20	and	and	CCONJ
ejpam-2017	24	21	its	its	PRON
ejpam-2017	24	22	transition	transition	NOUN
ejpam-2017	24	23	”	"	PUNCT
ejpam-2017	25	1	,	,	PUNCT
ejpam-2017	25	2	this	this	DET
ejpam-2017	25	3	relationship	relationship	NOUN
ejpam-2017	25	4	is	be	AUX
ejpam-2017	25	5	a	a	DET
ejpam-2017	25	6	special	special	ADJ
ejpam-2017	25	7	case	case	NOUN
ejpam-2017	25	8	of	of	ADP
ejpam-2017	25	9	the	the	DET
ejpam-2017	25	10	theorem	theorem	NOUN
ejpam-2017	25	11	that	that	PRON
ejpam-2017	25	12	any	any	DET
ejpam-2017	25	13	linear	linear	ADJ
ejpam-2017	25	14	mapping	mapping	NOUN
ejpam-2017	25	15	can	can	AUX
ejpam-2017	25	16	be	be	AUX
ejpam-2017	25	17	represented	represent	VERB
ejpam-2017	25	18	as	as	ADP
ejpam-2017	25	19	a	a	DET
ejpam-2017	25	20	matrix	matrix	NOUN
ejpam-2017	25	21	multiplication	multiplication	NOUN
ejpam-2017	25	22	.	.	PUNCT
ejpam-2017	26	1	y	y	NOUN
ejpam-2017	26	2	∈r	∈r	ADV
ejpam-2017	26	3	=	=	PUNCT
ejpam-2017	26	4	a	a	DET
ejpam-2017	26	5	x	x	SYM
ejpam-2017	26	6	∈r	∈r	NOUN
ejpam-2017	26	7	−→	−→	ADJ
ejpam-2017	26	8	y	y	PROPN
ejpam-2017	26	9	∈r	∈r	NOUN
ejpam-2017	26	10	=	=	PUNCT
ejpam-2017	26	11	a′	a′	NOUN
ejpam-2017	26	12	x	x	SYM
ejpam-2017	26	13	∈rn	∈rn	NOUN
ejpam-2017	26	14	−→	−→	ADJ
ejpam-2017	26	15	y	y	PROPN
ejpam-2017	26	16	∈rn	∈rn	NOUN
ejpam-2017	26	17	=	=	PUNCT
ejpam-2017	26	18	a	a	X
ejpam-2017	26	19	x	x	INTJ
ejpam-2017	26	20	∈rn	∈rn	NOUN
ejpam-2017	26	21	here	here	ADV
ejpam-2017	26	22	a′	a′	PROPN
ejpam-2017	26	23	is	be	AUX
ejpam-2017	26	24	a	a	DET
ejpam-2017	26	25	n	n	CCONJ
ejpam-2017	26	26	-	-	PUNCT
ejpam-2017	26	27	component	component	NOUN
ejpam-2017	26	28	row	row	NOUN
ejpam-2017	26	29	vector	vector	NOUN
ejpam-2017	26	30	,	,	PUNCT
ejpam-2017	26	31	x	x	PROPN
ejpam-2017	26	32	and	and	CCONJ
ejpam-2017	26	33	y	y	PROPN
ejpam-2017	26	34	are	be	AUX
ejpam-2017	26	35	n	n	CCONJ
ejpam-2017	26	36	-	-	PUNCT
ejpam-2017	26	37	component	component	NOUN
ejpam-2017	26	38	column	column	NOUN
ejpam-2017	26	39	vectors	vector	NOUN
ejpam-2017	26	40	,	,	PUNCT
ejpam-2017	26	41	and	and	CCONJ
ejpam-2017	26	42	a	a	PRON
ejpam-2017	26	43	is	be	AUX
ejpam-2017	26	44	an	an	DET
ejpam-2017	26	45	n×	n×	PRON
ejpam-2017	26	46	n	n	NOUN
ejpam-2017	26	47	matrix	matrix	NOUN
ejpam-2017	26	48	.	.	PUNCT
ejpam-2017	27	1	the	the	DET
ejpam-2017	27	2	composition	composition	NOUN
ejpam-2017	27	3	of	of	ADP
ejpam-2017	27	4	two	two	NUM
ejpam-2017	27	5	or	or	CCONJ
ejpam-2017	27	6	more	more	ADJ
ejpam-2017	27	7	mappings	mapping	NOUN
ejpam-2017	27	8	involves	involve	VERB
ejpam-2017	27	9	taking	take	VERB
ejpam-2017	27	10	the	the	DET
ejpam-2017	27	11	output	output	NOUN
ejpam-2017	27	12	of	of	ADP
ejpam-2017	27	13	one	one	NUM
ejpam-2017	27	14	or	or	CCONJ
ejpam-2017	27	15	more	more	ADJ
ejpam-2017	27	16	mappings	mapping	NOUN
ejpam-2017	27	17	as	as	ADP
ejpam-2017	27	18	the	the	DET
ejpam-2017	27	19	input	input	NOUN
ejpam-2017	27	20	of	of	ADP
ejpam-2017	27	21	other	other	ADJ
ejpam-2017	27	22	mappings	mapping	NOUN
ejpam-2017	27	23	.	.	PUNCT
ejpam-2017	28	1	the	the	DET
ejpam-2017	28	2	mappings	mapping	NOUN
ejpam-2017	28	3	f	f	X
ejpam-2017	28	4	:	:	PUNCT
ejpam-2017	28	5	x	x	X
ejpam-2017	28	6	→	→	SYM
ejpam-2017	28	7	y	y	PROPN
ejpam-2017	28	8	and	and	CCONJ
ejpam-2017	28	9	g	g	PROPN
ejpam-2017	28	10	:	:	PUNCT
ejpam-2017	28	11	y	y	PROPN
ejpam-2017	28	12	→	→	SYM
ejpam-2017	28	13	z	z	NOUN
ejpam-2017	28	14	can	can	AUX
ejpam-2017	28	15	be	be	AUX
ejpam-2017	28	16	composed	compose	VERB
ejpam-2017	28	17	by	by	ADP
ejpam-2017	28	18	first	first	ADV
ejpam-2017	28	19	applying	apply	VERB
ejpam-2017	28	20	f	f	PROPN
ejpam-2017	28	21	to	to	ADP
ejpam-2017	28	22	an	an	DET
ejpam-2017	28	23	argument	argument	NOUN
ejpam-2017	28	24	x	x	VERB
ejpam-2017	28	25	to	to	PART
ejpam-2017	28	26	obtain	obtain	VERB
ejpam-2017	28	27	y	y	NOUN
ejpam-2017	28	28	=	=	SYM
ejpam-2017	28	29	f	f	PROPN
ejpam-2017	28	30	(	(	PUNCT
ejpam-2017	28	31	x	x	NOUN
ejpam-2017	28	32	)	)	PUNCT
ejpam-2017	28	33	and	and	CCONJ
ejpam-2017	28	34	then	then	ADV
ejpam-2017	28	35	applying	apply	VERB
ejpam-2017	28	36	g	g	NOUN
ejpam-2017	28	37	to	to	ADP
ejpam-2017	28	38	y	y	PROPN
ejpam-2017	28	39	to	to	PART
ejpam-2017	28	40	obtain	obtain	VERB
ejpam-2017	28	41	z	z	NOUN
ejpam-2017	28	42	=	=	SYM
ejpam-2017	28	43	g(y	g(y	NOUN
ejpam-2017	28	44	)	)	PUNCT
ejpam-2017	28	45	.	.	PUNCT
ejpam-2017	29	1	the	the	DET
ejpam-2017	29	2	extension	extension	NOUN
ejpam-2017	29	3	of	of	ADP
ejpam-2017	29	4	the	the	DET
ejpam-2017	29	5	composition	composition	NOUN
ejpam-2017	29	6	of	of	ADP
ejpam-2017	29	7	maps	map	NOUN
ejpam-2017	29	8	can	can	AUX
ejpam-2017	29	9	be	be	AUX
ejpam-2017	29	10	expressed	express	VERB
ejpam-2017	29	11	in	in	ADP
ejpam-2017	29	12	matrix	matrix	NOUN
ejpam-2017	29	13	form	form	NOUN
ejpam-2017	29	14	.	.	PUNCT
ejpam-2017	30	1	y	y	NOUN
ejpam-2017	30	2	∈r	∈r	ADV
ejpam-2017	30	3	=	=	PUNCT
ejpam-2017	30	4	ba	ba	NOUN
ejpam-2017	30	5	x	x	PUNCT
ejpam-2017	30	6	∈r	∈r	AUX
ejpam-2017	30	7	−→	−→	ADJ
ejpam-2017	30	8	y	y	PROPN
ejpam-2017	30	9	∈rn	∈rn	NOUN
ejpam-2017	30	10	=	=	SYM
ejpam-2017	30	11	ba′	ba′	NOUN
ejpam-2017	30	12	x	x	SYM
ejpam-2017	30	13	∈rn	∈rn	NOUN
ejpam-2017	30	14	−→	−→	ADJ
ejpam-2017	30	15	y	y	PROPN
ejpam-2017	30	16	∈rn	∈rn	NOUN
ejpam-2017	30	17	=	=	SYM
ejpam-2017	30	18	ba	ba	NOUN
ejpam-2017	30	19	x	x	X
ejpam-2017	31	1	∈rn	∈rn	NOUN
ejpam-2017	31	2	here	here	ADV
ejpam-2017	31	3	b	b	NOUN
ejpam-2017	31	4	is	be	AUX
ejpam-2017	31	5	a	a	DET
ejpam-2017	31	6	constant	constant	ADJ
ejpam-2017	31	7	,	,	PUNCT
ejpam-2017	31	8	b	b	PROPN
ejpam-2017	31	9	is	be	AUX
ejpam-2017	31	10	an	an	DET
ejpam-2017	31	11	n	n	CCONJ
ejpam-2017	31	12	-	-	PUNCT
ejpam-2017	31	13	component	component	NOUN
ejpam-2017	31	14	column	column	NOUN
ejpam-2017	31	15	vector	vector	NOUN
ejpam-2017	31	16	,	,	PUNCT
ejpam-2017	31	17	and	and	CCONJ
ejpam-2017	31	18	b	b	NOUN
ejpam-2017	31	19	is	be	AUX
ejpam-2017	31	20	an	an	DET
ejpam-2017	31	21	n×	n×	PROPN
ejpam-2017	31	22	n	n	NOUN
ejpam-2017	31	23	matrix	matrix	NOUN
ejpam-2017	31	24	.	.	PUNCT
ejpam-2017	32	1	thus	thus	ADV
ejpam-2017	32	2	,	,	PUNCT
ejpam-2017	32	3	the	the	DET
ejpam-2017	32	4	above	above	ADJ
ejpam-2017	32	5	matrix	matrix	NOUN
ejpam-2017	32	6	multiplication	multiplication	NOUN
ejpam-2017	32	7	is	be	AUX
ejpam-2017	32	8	a	a	DET
ejpam-2017	32	9	representation	representation	NOUN
ejpam-2017	32	10	of	of	ADP
ejpam-2017	32	11	the	the	DET
ejpam-2017	32	12	composite	composite	ADJ
ejpam-2017	32	13	mapping	mapping	NOUN
ejpam-2017	32	14	.	.	PUNCT
ejpam-2017	33	1	remark	remark	PROPN
ejpam-2017	33	2	1	1	NUM
ejpam-2017	33	3	.	.	PUNCT
ejpam-2017	34	1	a′x	a′x	PROPN
ejpam-2017	34	2	is	be	AUX
ejpam-2017	34	3	a	a	DET
ejpam-2017	34	4	scalar	scalar	ADJ
ejpam-2017	34	5	,	,	PUNCT
ejpam-2017	34	6	and	and	CCONJ
ejpam-2017	34	7	thus	thus	ADV
ejpam-2017	34	8	it	it	PRON
ejpam-2017	34	9	might	might	AUX
ejpam-2017	34	10	seem	seem	VERB
ejpam-2017	34	11	that	that	DET
ejpam-2017	34	12	b′(a′x	b′(a′x	NOUN
ejpam-2017	34	13	)	)	PUNCT
ejpam-2017	34	14	is	be	AUX
ejpam-2017	34	15	a	a	DET
ejpam-2017	34	16	1	1	NUM
ejpam-2017	34	17	×	×	NOUN
ejpam-2017	34	18	n	n	PRON
ejpam-2017	34	19	matrix	matrix	NOUN
ejpam-2017	34	20	.	.	PUNCT
ejpam-2017	35	1	this	this	DET
ejpam-2017	35	2	view	view	NOUN
ejpam-2017	35	3	,	,	PUNCT
ejpam-2017	35	4	however	however	ADV
ejpam-2017	35	5	,	,	PUNCT
ejpam-2017	35	6	is	be	AUX
ejpam-2017	35	7	not	not	PART
ejpam-2017	35	8	correct	correct	ADJ
ejpam-2017	35	9	,	,	PUNCT
ejpam-2017	35	10	because	because	SCONJ
ejpam-2017	35	11	the	the	DET
ejpam-2017	35	12	associative	associative	ADJ
ejpam-2017	35	13	law	law	NOUN
ejpam-2017	35	14	of	of	ADP
ejpam-2017	35	15	multiplication	multiplication	NOUN
ejpam-2017	35	16	does	do	AUX
ejpam-2017	35	17	not	not	PART
ejpam-2017	35	18	hold	hold	VERB
ejpam-2017	35	19	for	for	ADP
ejpam-2017	35	20	b′a′x	b′a′x	NOUN
ejpam-2017	35	21	.	.	PUNCT
ejpam-2017	36	1	the	the	DET
ejpam-2017	36	2	multiplication	multiplication	NOUN
ejpam-2017	36	3	of	of	ADP
ejpam-2017	36	4	the	the	DET
ejpam-2017	36	5	1×n	1×n	NUM
ejpam-2017	36	6	matrices	matrix	NOUN
ejpam-2017	36	7	,	,	PUNCT
ejpam-2017	36	8	b′	b′	NUM
ejpam-2017	36	9	and	and	CCONJ
ejpam-2017	36	10	a′	a′	PROPN
ejpam-2017	36	11	,	,	PUNCT
ejpam-2017	36	12	is	be	AUX
ejpam-2017	36	13	not	not	PART
ejpam-2017	36	14	defined	define	VERB
ejpam-2017	36	15	and	and	CCONJ
ejpam-2017	36	16	thus	thus	ADV
ejpam-2017	36	17	we	we	PRON
ejpam-2017	36	18	can	can	AUX
ejpam-2017	36	19	not	not	PART
ejpam-2017	36	20	calculate	calculate	VERB
ejpam-2017	36	21	(	(	PUNCT
ejpam-2017	36	22	b′a′)x	b′a′)x	PROPN
ejpam-2017	36	23	.	.	PUNCT
ejpam-2017	37	1	the	the	DET
ejpam-2017	37	2	disagreement	disagreement	NOUN
ejpam-2017	37	3	of	of	ADP
ejpam-2017	37	4	b′(a′x	b′(a′x	NOUN
ejpam-2017	37	5	)	)	PUNCT
ejpam-2017	37	6	and	and	CCONJ
ejpam-2017	37	7	(	(	PUNCT
ejpam-2017	37	8	b′a′)x	b′a′)x	PROPN
ejpam-2017	37	9	is	be	AUX
ejpam-2017	37	10	due	due	ADJ
ejpam-2017	37	11	to	to	ADP
ejpam-2017	37	12	the	the	DET
ejpam-2017	37	13	multiplication	multiplication	NOUN
ejpam-2017	37	14	of	of	ADP
ejpam-2017	37	15	the	the	DET
ejpam-2017	37	16	1×	1×	NUM
ejpam-2017	37	17	n	n	NOUN
ejpam-2017	37	18	matrix	matrix	NOUN
ejpam-2017	37	19	b′	b′	NUM
ejpam-2017	37	20	and	and	CCONJ
ejpam-2017	37	21	the	the	DET
ejpam-2017	37	22	1×1	1×1	NUM
ejpam-2017	37	23	matrix	matrix	NOUN
ejpam-2017	37	24	a′x	a′x	NOUN
ejpam-2017	37	25	in	in	ADP
ejpam-2017	37	26	the	the	DET
ejpam-2017	37	27	order	order	NOUN
ejpam-2017	37	28	violating	violate	VERB
ejpam-2017	37	29	the	the	DET
ejpam-2017	37	30	rule	rule	NOUN
ejpam-2017	37	31	of	of	ADP
ejpam-2017	37	32	matrix	matrix	NOUN
ejpam-2017	37	33	multiplication	multiplication	NOUN
ejpam-2017	37	34	.	.	PUNCT
ejpam-2017	38	1	a	a	DET
ejpam-2017	38	2	detailed	detailed	ADJ
ejpam-2017	38	3	discussion	discussion	NOUN
ejpam-2017	38	4	is	be	AUX
ejpam-2017	38	5	given	give	VERB
ejpam-2017	38	6	later	later	ADV
ejpam-2017	38	7	(	(	PUNCT
ejpam-2017	38	8	see	see	VERB
ejpam-2017	38	9	section	section	NOUN
ejpam-2017	38	10	3	3	NUM
ejpam-2017	38	11	)	)	PUNCT
ejpam-2017	38	12	.	.	PUNCT
ejpam-2017	39	1	the	the	DET
ejpam-2017	39	2	simplest	simple	ADJ
ejpam-2017	39	3	form	form	NOUN
ejpam-2017	39	4	of	of	ADP
ejpam-2017	39	5	a	a	DET
ejpam-2017	39	6	matrix	matrix	NOUN
ejpam-2017	39	7	is	be	AUX
ejpam-2017	39	8	a	a	DET
ejpam-2017	39	9	1×	1×	NUM
ejpam-2017	39	10	1	1	NUM
ejpam-2017	39	11	matrix	matrix	NOUN
ejpam-2017	39	12	.	.	PUNCT
ejpam-2017	40	1	if	if	SCONJ
ejpam-2017	40	2	a=	a=	PROPN
ejpam-2017	40	3	(	(	PUNCT
ejpam-2017	40	4	a	a	X
ejpam-2017	40	5	)	)	PUNCT
ejpam-2017	40	6	and	and	CCONJ
ejpam-2017	40	7	b	b	X
ejpam-2017	40	8	=	=	SYM
ejpam-2017	40	9	(	(	PUNCT
ejpam-2017	40	10	b	b	NOUN
ejpam-2017	40	11	)	)	PUNCT
ejpam-2017	40	12	,	,	PUNCT
ejpam-2017	40	13	the	the	DET
ejpam-2017	40	14	following	follow	VERB
ejpam-2017	40	15	are	be	AUX
ejpam-2017	40	16	true	true	ADJ
ejpam-2017	40	17	.	.	PUNCT
ejpam-2017	41	1	(	(	PUNCT
ejpam-2017	41	2	ab)t	ab)t	PROPN
ejpam-2017	41	3	=(	=(	NOUN
ejpam-2017	41	4	(	(	PUNCT
ejpam-2017	41	5	a)(b))t	a)(b))t	ADP
ejpam-2017	41	6	=(	=(	PROPN
ejpam-2017	41	7	ab)t	ab)t	PROPN
ejpam-2017	41	8	=(	=(	PROPN
ejpam-2017	41	9	ab	ab	PROPN
ejpam-2017	41	10	)	)	PUNCT
ejpam-2017	41	11	=(	=(	NOUN
ejpam-2017	41	12	a)(b	a)(b	NUM
ejpam-2017	41	13	)	)	PUNCT
ejpam-2017	41	14	,	,	PUNCT
ejpam-2017	41	15	bt	bt	NOUN
ejpam-2017	41	16	at	at	ADP
ejpam-2017	41	17	=(	=(	ADJ
ejpam-2017	41	18	b)t	b)t	X
ejpam-2017	41	19	(	(	PUNCT
ejpam-2017	41	20	a)t	a)t	ADJ
ejpam-2017	41	21	=(	=(	NOUN
ejpam-2017	41	22	b)(a	b)(a	NOUN
ejpam-2017	41	23	)	)	PUNCT
ejpam-2017	41	24	,	,	PUNCT
ejpam-2017	41	25	where	where	SCONJ
ejpam-2017	41	26	the	the	DET
ejpam-2017	41	27	transposes	transpose	NOUN
ejpam-2017	41	28	of	of	ADP
ejpam-2017	41	29	a	a	DET
ejpam-2017	41	30	,	,	PUNCT
ejpam-2017	41	31	b	b	NOUN
ejpam-2017	41	32	,	,	PUNCT
ejpam-2017	41	33	and	and	CCONJ
ejpam-2017	41	34	ab	ab	PROPN
ejpam-2017	41	35	are	be	AUX
ejpam-2017	41	36	denoted	denote	VERB
ejpam-2017	41	37	by	by	ADP
ejpam-2017	41	38	at	at	ADP
ejpam-2017	41	39	,	,	PUNCT
ejpam-2017	41	40	bt	bt	INTJ
ejpam-2017	41	41	,	,	PUNCT
ejpam-2017	41	42	and	and	CCONJ
ejpam-2017	41	43	(	(	PUNCT
ejpam-2017	41	44	ab)t	ab)t	PROPN
ejpam-2017	41	45	,	,	PUNCT
ejpam-2017	41	46	respectively	respectively	ADV
ejpam-2017	41	47	.	.	PUNCT
ejpam-2017	42	1	for	for	ADP
ejpam-2017	42	2	1	1	NUM
ejpam-2017	42	3	×	×	NOUN
ejpam-2017	42	4	1	1	NUM
ejpam-2017	42	5	matrices	matrix	NOUN
ejpam-2017	42	6	,	,	PUNCT
ejpam-2017	42	7	(	(	PUNCT
ejpam-2017	42	8	ab)t	ab)t	PROPN
ejpam-2017	42	9	=	=	PUNCT
ejpam-2017	42	10	bt	bt	PROPN
ejpam-2017	42	11	at	at	ADP
ejpam-2017	42	12	can	can	AUX
ejpam-2017	42	13	be	be	AUX
ejpam-2017	42	14	written	write	VERB
ejpam-2017	42	15	as	as	ADP
ejpam-2017	42	16	(	(	PUNCT
ejpam-2017	42	17	a)(b	a)(b	ADJ
ejpam-2017	42	18	)	)	PUNCT
ejpam-2017	42	19	=	=	SYM
ejpam-2017	42	20	(	(	PUNCT
ejpam-2017	42	21	b)(a	b)(a	ADV
ejpam-2017	42	22	)	)	PUNCT
ejpam-2017	42	23	,	,	PUNCT
ejpam-2017	42	24	which	which	PRON
ejpam-2017	42	25	can	can	AUX
ejpam-2017	42	26	be	be	AUX
ejpam-2017	42	27	regarded	regard	VERB
ejpam-2017	42	28	as	as	ADP
ejpam-2017	42	29	ab	ab	PROPN
ejpam-2017	42	30	=	=	PROPN
ejpam-2017	42	31	ba	ba	PROPN
ejpam-2017	42	32	.	.	PUNCT
ejpam-2017	43	1	therefore	therefore	ADV
ejpam-2017	43	2	,	,	PUNCT
ejpam-2017	43	3	we	we	PRON
ejpam-2017	43	4	can	can	AUX
ejpam-2017	43	5	consider	consider	VERB
ejpam-2017	43	6	(	(	PUNCT
ejpam-2017	43	7	ab)t	ab)t	PROPN
ejpam-2017	43	8	=	=	PUNCT
ejpam-2017	43	9	bt	bt	PROPN
ejpam-2017	43	10	at	at	ADP
ejpam-2017	43	11	as	as	ADP
ejpam-2017	43	12	an	an	DET
ejpam-2017	43	13	extension	extension	NOUN
ejpam-2017	43	14	of	of	ADP
ejpam-2017	43	15	the	the	DET
ejpam-2017	43	16	commutative	commutative	ADJ
ejpam-2017	43	17	law	law	NOUN
ejpam-2017	43	18	for	for	ADP
ejpam-2017	43	19	the	the	DET
ejpam-2017	43	20	multiplication	multiplication	NOUN
ejpam-2017	43	21	of	of	ADP
ejpam-2017	43	22	real	real	ADJ
ejpam-2017	43	23	numbers	number	NOUN
ejpam-2017	43	24	,	,	PUNCT
ejpam-2017	44	1	ab	ab	PROPN
ejpam-2017	44	2	=	=	SYM
ejpam-2017	44	3	ba	ba	PROPN
ejpam-2017	44	4	.	.	PUNCT
ejpam-2017	45	1	in	in	ADP
ejpam-2017	45	2	other	other	ADJ
ejpam-2017	45	3	words	word	NOUN
ejpam-2017	45	4	,	,	PUNCT
ejpam-2017	45	5	ab	ab	PROPN
ejpam-2017	45	6	=	=	PUNCT
ejpam-2017	45	7	ba	ba	PROPN
ejpam-2017	45	8	is	be	AUX
ejpam-2017	45	9	a	a	DET
ejpam-2017	45	10	special	special	ADJ
ejpam-2017	45	11	case	case	NOUN
ejpam-2017	45	12	of	of	ADP
ejpam-2017	45	13	(	(	PUNCT
ejpam-2017	45	14	ab)t	ab)t	PROPN
ejpam-2017	45	15	=	=	PUNCT
ejpam-2017	45	16	bt	bt	PROPN
ejpam-2017	45	17	at	at	ADP
ejpam-2017	45	18	.	.	PUNCT
ejpam-2017	46	1	taking	take	VERB
ejpam-2017	46	2	this	this	DET
ejpam-2017	46	3	view	view	NOUN
ejpam-2017	46	4	,	,	PUNCT
ejpam-2017	46	5	“	"	PUNCT
ejpam-2017	46	6	the	the	DET
ejpam-2017	46	7	principle	principle	NOUN
ejpam-2017	46	8	of	of	ADP
ejpam-2017	46	9	the	the	DET
ejpam-2017	46	10	permanence	permanence	NOUN
ejpam-2017	46	11	of	of	ADP
ejpam-2017	46	12	form	form	NOUN
ejpam-2017	46	13	and	and	CCONJ
ejpam-2017	46	14	its	its	PRON
ejpam-2017	46	15	transition	transition	NOUN
ejpam-2017	46	16	”	"	PUNCT
ejpam-2017	46	17	also	also	ADV
ejpam-2017	46	18	holds	hold	VERB
ejpam-2017	46	19	for	for	ADP
ejpam-2017	46	20	the	the	DET
ejpam-2017	46	21	commutative	commutative	ADJ
ejpam-2017	46	22	law	law	NOUN
ejpam-2017	46	23	for	for	ADP
ejpam-2017	46	24	matrix	matrix	NOUN
ejpam-2017	46	25	multiplication	multiplication	NOUN
ejpam-2017	46	26	.	.	PUNCT
ejpam-2017	47	1	3	3	X
ejpam-2017	47	2	.	.	NOUN
ejpam-2017	47	3	scalar	scalar	ADJ
ejpam-2017	47	4	multiplication	multiplication	NOUN
ejpam-2017	47	5	of	of	ADP
ejpam-2017	47	6	a	a	DET
ejpam-2017	47	7	matrix	matrix	NOUN
ejpam-2017	47	8	the	the	DET
ejpam-2017	47	9	transpose	transpose	NOUN
ejpam-2017	47	10	of	of	ADP
ejpam-2017	47	11	a	a	DET
ejpam-2017	47	12	matrix	matrix	NOUN
ejpam-2017	47	13	plays	play	VERB
ejpam-2017	47	14	an	an	DET
ejpam-2017	47	15	essential	essential	ADJ
ejpam-2017	47	16	role	role	NOUN
ejpam-2017	47	17	in	in	ADP
ejpam-2017	47	18	maintaining	maintain	VERB
ejpam-2017	47	19	“	"	PUNCT
ejpam-2017	47	20	the	the	DET
ejpam-2017	47	21	principle	principle	NOUN
ejpam-2017	47	22	of	of	ADP
ejpam-2017	47	23	the	the	DET
ejpam-2017	47	24	permanence	permanence	NOUN
ejpam-2017	47	25	of	of	ADP
ejpam-2017	47	26	form	form	NOUN
ejpam-2017	47	27	and	and	CCONJ
ejpam-2017	47	28	its	its	PRON
ejpam-2017	47	29	transition	transition	NOUN
ejpam-2017	47	30	”	"	PUNCT
ejpam-2017	47	31	for	for	ADP
ejpam-2017	47	32	matrix	matrix	NOUN
ejpam-2017	47	33	multiplication	multiplication	NOUN
ejpam-2017	47	34	.	.	PUNCT
ejpam-2017	48	1	as	as	SCONJ
ejpam-2017	48	2	shown	show	VERB
ejpam-2017	48	3	in	in	ADP
ejpam-2017	48	4	the	the	DET
ejpam-2017	48	5	previous	previous	ADJ
ejpam-2017	48	6	section	section	NOUN
ejpam-2017	48	7	,	,	PUNCT
ejpam-2017	48	8	y.	y.	PROPN
ejpam-2017	48	9	kobayashi	kobayashi	PROPN
ejpam-2017	48	10	/	/	SYM
ejpam-2017	48	11	eur	eur	PROPN
ejpam-2017	48	12	.	.	PUNCT
ejpam-2017	49	1	j.	j.	PROPN
ejpam-2017	49	2	pure	pure	PROPN
ejpam-2017	49	3	appl	appl	PROPN
ejpam-2017	49	4	.	.	PROPN
ejpam-2017	49	5	math	math	PROPN
ejpam-2017	49	6	,	,	PUNCT
ejpam-2017	49	7	7	7	NUM
ejpam-2017	49	8	(	(	PUNCT
ejpam-2017	49	9	2014	2014	NUM
ejpam-2017	49	10	)	)	PUNCT
ejpam-2017	49	11	,	,	PUNCT
ejpam-2017	49	12	405	405	NUM
ejpam-2017	49	13	-	-	SYM
ejpam-2017	49	14	411	411	NUM
ejpam-2017	49	15	407	407	NUM
ejpam-2017	49	16	ba′x	ba′x	PROPN
ejpam-2017	49	17	is	be	AUX
ejpam-2017	49	18	valid	valid	ADJ
ejpam-2017	49	19	,	,	PUNCT
ejpam-2017	49	20	whereas	whereas	SCONJ
ejpam-2017	49	21	b′a′x	b′a′x	NOUN
ejpam-2017	49	22	is	be	AUX
ejpam-2017	49	23	not	not	PART
ejpam-2017	49	24	.	.	PUNCT
ejpam-2017	50	1	the	the	DET
ejpam-2017	50	2	essence	essence	NOUN
ejpam-2017	50	3	of	of	ADP
ejpam-2017	50	4	the	the	DET
ejpam-2017	50	5	reason	reason	NOUN
ejpam-2017	50	6	is	be	AUX
ejpam-2017	50	7	that	that	PRON
ejpam-2017	50	8	scalar	scalar	ADJ
ejpam-2017	50	9	multiplication	multiplication	NOUN
ejpam-2017	50	10	can	can	AUX
ejpam-2017	50	11	be	be	AUX
ejpam-2017	50	12	treated	treat	VERB
ejpam-2017	50	13	as	as	ADP
ejpam-2017	50	14	only	only	ADV
ejpam-2017	50	15	an	an	DET
ejpam-2017	50	16	abbreviation	abbreviation	NOUN
ejpam-2017	50	17	to	to	PART
ejpam-2017	50	18	indicate	indicate	VERB
ejpam-2017	50	19	multiplication	multiplication	NOUN
ejpam-2017	50	20	by	by	ADP
ejpam-2017	50	21	a	a	DET
ejpam-2017	50	22	scalar	scalar	ADJ
ejpam-2017	50	23	matrix	matrix	NOUN
ejpam-2017	50	24	,	,	PUNCT
ejpam-2017	50	25	which	which	PRON
ejpam-2017	50	26	is	be	AUX
ejpam-2017	50	27	a	a	DET
ejpam-2017	50	28	diagonal	diagonal	ADJ
ejpam-2017	50	29	matrix	matrix	NOUN
ejpam-2017	50	30	whose	whose	DET
ejpam-2017	50	31	diagonal	diagonal	ADJ
ejpam-2017	50	32	elements	element	NOUN
ejpam-2017	50	33	all	all	PRON
ejpam-2017	50	34	contain	contain	VERB
ejpam-2017	50	35	the	the	DET
ejpam-2017	50	36	same	same	ADJ
ejpam-2017	50	37	scalar	scalar	NOUN
ejpam-2017	50	38	.	.	PUNCT
ejpam-2017	51	1	here	here	ADV
ejpam-2017	51	2	,	,	PUNCT
ejpam-2017	51	3	we	we	PRON
ejpam-2017	51	4	express	express	VERB
ejpam-2017	51	5	a′x	a′x	NOUN
ejpam-2017	51	6	as	as	ADP
ejpam-2017	51	7	a	a	DET
ejpam-2017	51	8	scalar	scalar	ADJ
ejpam-2017	51	9	λ	λ	NOUN
ejpam-2017	51	10	.	.	PROPN
ejpam-2017	51	11	for	for	ADP
ejpam-2017	51	12	simplicity	simplicity	NOUN
ejpam-2017	51	13	,	,	PUNCT
ejpam-2017	51	14	let	let	VERB
ejpam-2017	51	15	us	we	PRON
ejpam-2017	51	16	consider	consider	VERB
ejpam-2017	51	17	the	the	DET
ejpam-2017	51	18	case	case	NOUN
ejpam-2017	51	19	n	n	NOUN
ejpam-2017	51	20	=	=	SYM
ejpam-2017	51	21	3	3	X
ejpam-2017	51	22	.	.	PUNCT
ejpam-2017	52	1	then	then	ADV
ejpam-2017	52	2	,	,	PUNCT
ejpam-2017	52	3	b′λ	b′λ	NOUN
ejpam-2017	52	4	=	=	SYM
ejpam-2017	52	5	(	(	PUNCT
ejpam-2017	52	6	b1	b1	NOUN
ejpam-2017	52	7	b2	b2	NOUN
ejpam-2017	52	8	b3)λ	b3)λ	NOUN
ejpam-2017	52	9	=	=	SYM
ejpam-2017	52	10	(	(	PUNCT
ejpam-2017	52	11	b1λ	b1λ	PROPN
ejpam-2017	52	12	b2λ	b2λ	PROPN
ejpam-2017	52	13	b3λ	b3λ	NUM
ejpam-2017	52	14	)	)	PUNCT
ejpam-2017	52	15	is	be	AUX
ejpam-2017	52	16	a	a	DET
ejpam-2017	52	17	convenient	convenient	ADJ
ejpam-2017	52	18	operation	operation	NOUN
ejpam-2017	52	19	,	,	PUNCT
ejpam-2017	52	20	but	but	CCONJ
ejpam-2017	52	21	deviates	deviate	VERB
ejpam-2017	52	22	from	from	ADP
ejpam-2017	52	23	the	the	DET
ejpam-2017	52	24	rule	rule	NOUN
ejpam-2017	52	25	of	of	ADP
ejpam-2017	52	26	matrix	matrix	NOUN
ejpam-2017	52	27	multiplication	multiplication	NOUN
ejpam-2017	52	28	.	.	PUNCT
ejpam-2017	53	1	the	the	DET
ejpam-2017	53	2	proper	proper	ADJ
ejpam-2017	53	3	operation	operation	NOUN
ejpam-2017	53	4	is	be	AUX
ejpam-2017	53	5	(	(	PUNCT
ejpam-2017	53	6	b1	b1	NOUN
ejpam-2017	53	7	b2	b2	NOUN
ejpam-2017	53	8	b3	b3	PROPN
ejpam-2017	53	9	)	)	PUNCT
ejpam-2017	53	10			VERB
ejpam-2017	53	11			NOUN
ejpam-2017	53	12	λ	λ	NOUN
ejpam-2017	53	13	0	0	NUM
ejpam-2017	54	1	0	0	NUM
ejpam-2017	54	2	0	0	NUM
ejpam-2017	54	3	λ	λ	NOUN
ejpam-2017	54	4	0	0	NUM
ejpam-2017	54	5	0	0	NUM
ejpam-2017	54	6	0	0	NUM
ejpam-2017	55	1	λ	λ	INTJ
ejpam-2017	55	2			PROPN
ejpam-2017	55	3	=	=	PROPN
ejpam-2017	55	4	(	(	PUNCT
ejpam-2017	55	5	b1λ	b1λ	PROPN
ejpam-2017	55	6	b2λ	b2λ	PROPN
ejpam-2017	55	7	b3λ	b3λ	NUM
ejpam-2017	55	8	)	)	PUNCT
ejpam-2017	55	9	,	,	PUNCT
ejpam-2017	55	10	because	because	SCONJ
ejpam-2017	55	11	the	the	DET
ejpam-2017	55	12	multiplication	multiplication	NOUN
ejpam-2017	55	13	of	of	ADP
ejpam-2017	55	14	the	the	DET
ejpam-2017	55	15	1×3	1×3	NUM
ejpam-2017	55	16	matrix	matrix	NOUN
ejpam-2017	55	17	b′	b′	NUM
ejpam-2017	55	18	and	and	CCONJ
ejpam-2017	55	19	the	the	DET
ejpam-2017	55	20	1×1	1×1	ADJ
ejpam-2017	55	21	matrix	matrix	NOUN
ejpam-2017	55	22	λ	λ	NOUN
ejpam-2017	55	23	is	be	AUX
ejpam-2017	55	24	not	not	PART
ejpam-2017	55	25	defined	define	VERB
ejpam-2017	55	26	.	.	PUNCT
ejpam-2017	56	1	a	a	DET
ejpam-2017	56	2	scalar	scalar	ADJ
ejpam-2017	56	3	λ	λ	NOUN
ejpam-2017	56	4	in	in	ADP
ejpam-2017	56	5	b′λ	b′λ	NOUN
ejpam-2017	56	6	is	be	AUX
ejpam-2017	56	7	an	an	DET
ejpam-2017	56	8	abbreviation	abbreviation	NOUN
ejpam-2017	56	9	of	of	ADP
ejpam-2017	56	10	a	a	DET
ejpam-2017	56	11	scalar	scalar	ADJ
ejpam-2017	56	12	matrix	matrix	NOUN
ejpam-2017	56	13	λ	λ	NOUN
ejpam-2017	56	14	,	,	PUNCT
ejpam-2017	56	15	where	where	SCONJ
ejpam-2017	56	16	λ	λ	X
ejpam-2017	56	17	=	=	SYM
ejpam-2017	56	18			VERB
ejpam-2017	56	19			NOUN
ejpam-2017	56	20	λ	λ	NOUN
ejpam-2017	56	21	0	0	NUM
ejpam-2017	56	22	0	0	NUM
ejpam-2017	56	23	0	0	NUM
ejpam-2017	57	1	λ	λ	NOUN
ejpam-2017	57	2	0	0	NUM
ejpam-2017	57	3	0	0	NUM
ejpam-2017	57	4	0	0	NUM
ejpam-2017	58	1	λ	λ	INTJ
ejpam-2017	58	2			INTJ
ejpam-2017	58	3			PUNCT
ejpam-2017	58	4	,	,	PUNCT
ejpam-2017	58	5	and	and	CCONJ
ejpam-2017	58	6	thus	thus	ADV
ejpam-2017	58	7	scalar	scalar	ADJ
ejpam-2017	58	8	multiplication	multiplication	NOUN
ejpam-2017	58	9	implies	imply	VERB
ejpam-2017	58	10	a	a	DET
ejpam-2017	58	11	mapping	mapping	NOUN
ejpam-2017	58	12	referred	refer	VERB
ejpam-2017	58	13	to	to	ADP
ejpam-2017	58	14	as	as	ADP
ejpam-2017	58	15	homothety	homothety	NOUN
ejpam-2017	58	16	of	of	ADP
ejpam-2017	58	17	ratio	ratio	NOUN
ejpam-2017	58	18	λ	λ	PROPN
ejpam-2017	58	19	.	.	PUNCT
ejpam-2017	59	1	if	if	SCONJ
ejpam-2017	59	2	we	we	PRON
ejpam-2017	59	3	apply	apply	VERB
ejpam-2017	59	4	the	the	DET
ejpam-2017	59	5	rule	rule	NOUN
ejpam-2017	59	6	of	of	ADP
ejpam-2017	59	7	matrix	matrix	NOUN
ejpam-2017	59	8	multiplication	multiplication	NOUN
ejpam-2017	59	9	properly	properly	ADV
ejpam-2017	59	10	,	,	PUNCT
ejpam-2017	59	11	we	we	PRON
ejpam-2017	59	12	are	be	AUX
ejpam-2017	59	13	easily	easily	ADV
ejpam-2017	59	14	convinced	convinced	ADJ
ejpam-2017	59	15	that	that	SCONJ
ejpam-2017	59	16	b′a′x	b′a′x	PROPN
ejpam-2017	59	17	is	be	AUX
ejpam-2017	59	18	not	not	PART
ejpam-2017	59	19	valid	valid	ADJ
ejpam-2017	59	20	.	.	PUNCT
ejpam-2017	60	1	the	the	DET
ejpam-2017	60	2	transpose	transpose	NOUN
ejpam-2017	60	3	of	of	ADP
ejpam-2017	60	4	b′λ	b′λ	NOUN
ejpam-2017	60	5	is	be	AUX
ejpam-2017	60	6	λb	λb	ADP
ejpam-2017	60	7	,	,	PUNCT
ejpam-2017	60	8	which	which	PRON
ejpam-2017	60	9	is	be	AUX
ejpam-2017	60	10	an	an	DET
ejpam-2017	60	11	abbreviation	abbreviation	NOUN
ejpam-2017	60	12	of	of	ADP
ejpam-2017	60	13			NOUN
ejpam-2017	60	14			NOUN
ejpam-2017	60	15	λ	λ	NOUN
ejpam-2017	60	16	0	0	NUM
ejpam-2017	60	17	0	0	NUM
ejpam-2017	60	18	0	0	NUM
ejpam-2017	60	19	λ	λ	NOUN
ejpam-2017	60	20	0	0	NUM
ejpam-2017	60	21	0	0	NUM
ejpam-2017	60	22	0	0	NUM
ejpam-2017	61	1	λ	λ	INTJ
ejpam-2017	61	2			PROPN
ejpam-2017	61	3			PUNCT
ejpam-2017	61	4			PROPN
ejpam-2017	61	5			NOUN
ejpam-2017	61	6	b1	b1	NOUN
ejpam-2017	61	7	b2	b2	NOUN
ejpam-2017	61	8	b3	b3	PROPN
ejpam-2017	61	9			PROPN
ejpam-2017	61	10			PUNCT
ejpam-2017	61	11	.	.	PUNCT
ejpam-2017	62	1	the	the	DET
ejpam-2017	62	2	commutative	commutative	ADJ
ejpam-2017	62	3	law	law	NOUN
ejpam-2017	62	4	(	(	PUNCT
ejpam-2017	62	5	b1	b1	NOUN
ejpam-2017	62	6	b2	b2	NOUN
ejpam-2017	62	7	b3)λ=	b3)λ=	AUX
ejpam-2017	62	8	λ(b1	λ(b1	NOUN
ejpam-2017	62	9	b2	b2	NOUN
ejpam-2017	62	10	b3	b3	PROPN
ejpam-2017	62	11	)	)	PUNCT
ejpam-2017	62	12	indicates	indicate	VERB
ejpam-2017	62	13	that	that	SCONJ
ejpam-2017	62	14	(	(	PUNCT
ejpam-2017	62	15	b1λ	b1λ	PROPN
ejpam-2017	62	16	b2λ	b2λ	PROPN
ejpam-2017	62	17	b3λ	b3λ	NUM
ejpam-2017	62	18	)	)	PUNCT
ejpam-2017	62	19	=(	=(	PROPN
ejpam-2017	62	20	b1	b1	PROPN
ejpam-2017	62	21	b2	b2	NOUN
ejpam-2017	62	22	b3	b3	PROPN
ejpam-2017	62	23	)	)	PUNCT
ejpam-2017	62	24			VERB
ejpam-2017	62	25			NOUN
ejpam-2017	62	26	λ	λ	NOUN
ejpam-2017	62	27	0	0	NUM
ejpam-2017	62	28	0	0	NUM
ejpam-2017	62	29	0	0	NUM
ejpam-2017	62	30	λ	λ	NOUN
ejpam-2017	62	31	0	0	NUM
ejpam-2017	62	32	0	0	NUM
ejpam-2017	62	33	0	0	NUM
ejpam-2017	63	1	λ	λ	PROPN
ejpam-2017	63	2			PROPN
ejpam-2017	63	3	=	=	PROPN
ejpam-2017	63	4			PROPN
ejpam-2017	63	5			NOUN
ejpam-2017	63	6			VERB
ejpam-2017	63	7			PRON
ejpam-2017	63	8	λ	λ	NOUN
ejpam-2017	63	9	0	0	NUM
ejpam-2017	63	10	0	0	NUM
ejpam-2017	63	11	0	0	NUM
ejpam-2017	63	12	λ	λ	NOUN
ejpam-2017	63	13	0	0	NUM
ejpam-2017	63	14	0	0	NUM
ejpam-2017	63	15	0	0	NUM
ejpam-2017	64	1	λ	λ	INTJ
ejpam-2017	64	2			PROPN
ejpam-2017	64	3			PUNCT
ejpam-2017	64	4			PROPN
ejpam-2017	64	5			NOUN
ejpam-2017	64	6	b1	b1	NOUN
ejpam-2017	64	7	b2	b2	NOUN
ejpam-2017	64	8	b3	b3	PROPN
ejpam-2017	64	9			PROPN
ejpam-2017	64	10			PUNCT
ejpam-2017	65	1			PROPN
ejpam-2017	65	2			PROPN
ejpam-2017	65	3	t	t	NOUN
ejpam-2017	65	4	=(	=(	NOUN
ejpam-2017	65	5	λb1	λb1	PROPN
ejpam-2017	65	6	λb2	λb2	PROPN
ejpam-2017	65	7	λb3	λb3	PROPN
ejpam-2017	65	8	)	)	PUNCT
ejpam-2017	65	9	.	.	PUNCT
ejpam-2017	66	1	similarly	similarly	ADV
ejpam-2017	66	2	,	,	PUNCT
ejpam-2017	66	3	the	the	DET
ejpam-2017	66	4	commutative	commutative	ADJ
ejpam-2017	66	5	law	law	NOUN
ejpam-2017	66	6	λ	λ	PROPN
ejpam-2017	66	7			VERB
ejpam-2017	66	8			NOUN
ejpam-2017	66	9	b1	b1	NOUN
ejpam-2017	66	10	b2	b2	NOUN
ejpam-2017	66	11	b3	b3	PROPN
ejpam-2017	66	12			PROPN
ejpam-2017	67	1	=	=	PROPN
ejpam-2017	67	2			VERB
ejpam-2017	67	3			NOUN
ejpam-2017	67	4	b1	b1	NOUN
ejpam-2017	67	5	b2	b2	NOUN
ejpam-2017	67	6	b3	b3	PROPN
ejpam-2017	67	7			PUNCT
ejpam-2017	68	1	λ	λ	PROPN
ejpam-2017	68	2	indicates	indicate	VERB
ejpam-2017	68	3	that	that	SCONJ
ejpam-2017	68	4			VERB
ejpam-2017	68	5			PRON
ejpam-2017	68	6	λb1	λb1	NOUN
ejpam-2017	68	7	λb2	λb2	PROPN
ejpam-2017	68	8	λb3	λb3	PROPN
ejpam-2017	68	9			PROPN
ejpam-2017	69	1	=	=	PROPN
ejpam-2017	69	2			VERB
ejpam-2017	69	3			PRON
ejpam-2017	69	4	λ	λ	NOUN
ejpam-2017	69	5	0	0	NUM
ejpam-2017	69	6	0	0	NUM
ejpam-2017	69	7	0	0	NUM
ejpam-2017	70	1	λ	λ	NOUN
ejpam-2017	70	2	0	0	NUM
ejpam-2017	70	3	0	0	NUM
ejpam-2017	70	4	0	0	NUM
ejpam-2017	71	1	λ	λ	INTJ
ejpam-2017	71	2			PROPN
ejpam-2017	71	3			PUNCT
ejpam-2017	71	4			PROPN
ejpam-2017	71	5			NOUN
ejpam-2017	71	6	b1	b1	NOUN
ejpam-2017	71	7	b2	b2	NOUN
ejpam-2017	71	8	b3	b3	PROPN
ejpam-2017	71	9			PROPN
ejpam-2017	72	1	=	=	PROPN
ejpam-2017	72	2			PROPN
ejpam-2017	72	3	(b1	(b1	PROPN
ejpam-2017	72	4	b2	b2	NOUN
ejpam-2017	72	5	b3	b3	NOUN
ejpam-2017	72	6	)	)	PUNCT
ejpam-2017	72	7			VERB
ejpam-2017	72	8			NOUN
ejpam-2017	72	9	λ	λ	NOUN
ejpam-2017	72	10	0	0	NUM
ejpam-2017	72	11	0	0	NUM
ejpam-2017	72	12	0	0	NUM
ejpam-2017	73	1	λ	λ	NOUN
ejpam-2017	73	2	0	0	NUM
ejpam-2017	73	3	0	0	NUM
ejpam-2017	73	4	0	0	NUM
ejpam-2017	74	1	λ	λ	INTJ
ejpam-2017	74	2			INTJ
ejpam-2017	74	3			PUNCT
ejpam-2017	75	1			PROPN
ejpam-2017	75	2			PROPN
ejpam-2017	75	3	t	t	NOUN
ejpam-2017	75	4	=	=	SYM
ejpam-2017	75	5			NOUN
ejpam-2017	75	6			NOUN
ejpam-2017	75	7	b1λ	b1λ	NUM
ejpam-2017	75	8	b2λ	b2λ	PROPN
ejpam-2017	75	9	b3λ	b3λ	ADV
ejpam-2017	75	10			PUNCT
ejpam-2017	75	11			PUNCT
ejpam-2017	75	12	.	.	PUNCT
ejpam-2017	76	1	y.	y.	PROPN
ejpam-2017	76	2	kobayashi	kobayashi	PROPN
ejpam-2017	76	3	/	/	SYM
ejpam-2017	76	4	eur	eur	PROPN
ejpam-2017	76	5	.	.	PUNCT
ejpam-2017	77	1	j.	j.	PROPN
ejpam-2017	77	2	pure	pure	PROPN
ejpam-2017	77	3	appl	appl	PROPN
ejpam-2017	77	4	.	.	PROPN
ejpam-2017	77	5	math	math	PROPN
ejpam-2017	77	6	,	,	PUNCT
ejpam-2017	77	7	7	7	NUM
ejpam-2017	77	8	(	(	PUNCT
ejpam-2017	77	9	2014	2014	NUM
ejpam-2017	77	10	)	)	PUNCT
ejpam-2017	77	11	,	,	PUNCT
ejpam-2017	77	12	405	405	NUM
ejpam-2017	77	13	-	-	SYM
ejpam-2017	77	14	411	411	NUM
ejpam-2017	77	15	408	408	NUM
ejpam-2017	77	16	these	these	DET
ejpam-2017	77	17	forms	form	NOUN
ejpam-2017	77	18	show	show	VERB
ejpam-2017	77	19	an	an	DET
ejpam-2017	77	20	extension	extension	NOUN
ejpam-2017	77	21	of	of	ADP
ejpam-2017	77	22	the	the	DET
ejpam-2017	77	23	commutative	commutative	ADJ
ejpam-2017	77	24	law	law	NOUN
ejpam-2017	77	25	for	for	ADP
ejpam-2017	77	26	the	the	DET
ejpam-2017	77	27	multiplication	multiplication	NOUN
ejpam-2017	77	28	of	of	ADP
ejpam-2017	77	29	real	real	ADJ
ejpam-2017	77	30	numbers	number	NOUN
ejpam-2017	77	31	,	,	PUNCT
ejpam-2017	77	32	λb	λb	ADP
ejpam-2017	77	33	=	=	PUNCT
ejpam-2017	77	34	bλ	bλ	PROPN
ejpam-2017	77	35	.	.	PUNCT
ejpam-2017	78	1	if	if	SCONJ
ejpam-2017	78	2	linear	linear	ADJ
ejpam-2017	78	3	transformation	transformation	NOUN
ejpam-2017	78	4	is	be	AUX
ejpam-2017	78	5	homothety	homothety	NOUN
ejpam-2017	78	6	,	,	PUNCT
ejpam-2017	78	7	(	(	PUNCT
ejpam-2017	78	8	b1	b1	NOUN
ejpam-2017	78	9	b2	b2	NOUN
ejpam-2017	78	10	b3)λ=	b3)λ=	AUX
ejpam-2017	78	11	λ(b1	λ(b1	VERB
ejpam-2017	78	12	b2	b2	NOUN
ejpam-2017	78	13	b3	b3	NOUN
ejpam-2017	78	14	)	)	PUNCT
ejpam-2017	78	15	and	and	CCONJ
ejpam-2017	78	16	λ	λ	NOUN
ejpam-2017	78	17			VERB
ejpam-2017	78	18			NOUN
ejpam-2017	78	19	b1	b1	NOUN
ejpam-2017	78	20	b2	b2	NOUN
ejpam-2017	78	21	b3	b3	PROPN
ejpam-2017	78	22			NOUN
ejpam-2017	78	23			PUNCT
ejpam-2017	79	1	=	=	PUNCT
ejpam-2017	79	2			VERB
ejpam-2017	79	3			NOUN
ejpam-2017	79	4	b1	b1	NOUN
ejpam-2017	79	5	b2	b2	NOUN
ejpam-2017	79	6	b3	b3	PROPN
ejpam-2017	79	7			PROPN
ejpam-2017	80	1	λ	λ	PROPN
ejpam-2017	80	2	indicates	indicate	VERB
ejpam-2017	80	3	the	the	DET
ejpam-2017	80	4	left	left	ADV
ejpam-2017	80	5	-	-	PUNCT
ejpam-2017	80	6	handed	hand	VERB
ejpam-2017	80	7	vector	vector	NOUN
ejpam-2017	80	8	space	space	NOUN
ejpam-2017	80	9	can	can	AUX
ejpam-2017	80	10	be	be	AUX
ejpam-2017	80	11	equated	equate	VERB
ejpam-2017	80	12	with	with	ADP
ejpam-2017	80	13	the	the	DET
ejpam-2017	80	14	righthanded	righthande	VERB
ejpam-2017	80	15	vector	vector	NOUN
ejpam-2017	80	16	space	space	NOUN
ejpam-2017	80	17	.	.	PUNCT
ejpam-2017	81	1	the	the	DET
ejpam-2017	81	2	right	right	ADJ
ejpam-2017	81	3	multiplication	multiplication	NOUN
ejpam-2017	81	4	of	of	ADP
ejpam-2017	81	5	a	a	DET
ejpam-2017	81	6	row	row	NOUN
ejpam-2017	81	7	vector	vector	NOUN
ejpam-2017	81	8	with	with	ADP
ejpam-2017	81	9	a	a	DET
ejpam-2017	81	10	scalar	scalar	ADJ
ejpam-2017	81	11	,	,	PUNCT
ejpam-2017	81	12	b′λ	b′λ	NOUN
ejpam-2017	81	13	,	,	PUNCT
ejpam-2017	81	14	and	and	CCONJ
ejpam-2017	81	15	the	the	DET
ejpam-2017	81	16	left	left	ADJ
ejpam-2017	81	17	multiplication	multiplication	NOUN
ejpam-2017	81	18	of	of	ADP
ejpam-2017	81	19	a	a	DET
ejpam-2017	81	20	column	column	NOUN
ejpam-2017	81	21	vector	vector	NOUN
ejpam-2017	81	22	with	with	ADP
ejpam-2017	81	23	a	a	DET
ejpam-2017	81	24	scalar	scalar	ADJ
ejpam-2017	81	25	,	,	PUNCT
ejpam-2017	81	26	λb	λb	ADV
ejpam-2017	81	27	,	,	PUNCT
ejpam-2017	81	28	are	be	AUX
ejpam-2017	81	29	not	not	PART
ejpam-2017	81	30	a	a	DET
ejpam-2017	81	31	rule	rule	NOUN
ejpam-2017	81	32	of	of	ADP
ejpam-2017	81	33	matrix	matrix	NOUN
ejpam-2017	81	34	arithmetic	arithmetic	NOUN
ejpam-2017	81	35	but	but	CCONJ
ejpam-2017	81	36	the	the	DET
ejpam-2017	81	37	abbreviations	abbreviation	NOUN
ejpam-2017	81	38	of	of	ADP
ejpam-2017	81	39	b′λ	b′λ	NOUN
ejpam-2017	81	40	and	and	CCONJ
ejpam-2017	81	41	λb	λb	NOUN
ejpam-2017	81	42	,	,	PUNCT
ejpam-2017	81	43	respectively	respectively	ADV
ejpam-2017	81	44	,	,	PUNCT
ejpam-2017	81	45	and	and	CCONJ
ejpam-2017	81	46	thus	thus	ADV
ejpam-2017	81	47	the	the	DET
ejpam-2017	81	48	vectors	vector	NOUN
ejpam-2017	81	49	obtained	obtain	VERB
ejpam-2017	81	50	by	by	ADP
ejpam-2017	81	51	multiplying	multiply	VERB
ejpam-2017	81	52	each	each	DET
ejpam-2017	81	53	entry	entry	NOUN
ejpam-2017	81	54	of	of	ADP
ejpam-2017	81	55	b′	b′	NUM
ejpam-2017	81	56	and	and	CCONJ
ejpam-2017	81	57	b	b	X
ejpam-2017	81	58	by	by	ADP
ejpam-2017	81	59	λ	λ	NOUN
ejpam-2017	81	60	are	be	AUX
ejpam-2017	81	61	the	the	DET
ejpam-2017	81	62	definition	definition	NOUN
ejpam-2017	81	63	of	of	ADP
ejpam-2017	81	64	scalar	scalar	ADJ
ejpam-2017	81	65	multiples	multiple	NOUN
ejpam-2017	81	66	.	.	PUNCT
ejpam-2017	82	1	4	4	X
ejpam-2017	82	2	.	.	NUM
ejpam-2017	82	3	related	relate	VERB
ejpam-2017	82	4	remarks	remark	NOUN
ejpam-2017	82	5	at	at	ADP
ejpam-2017	82	6	the	the	DET
ejpam-2017	82	7	high	high	ADJ
ejpam-2017	82	8	school	school	NOUN
ejpam-2017	82	9	and	and	CCONJ
ejpam-2017	82	10	undergraduate	undergraduate	NOUN
ejpam-2017	82	11	level	level	NOUN
ejpam-2017	82	12	,	,	PUNCT
ejpam-2017	82	13	the	the	DET
ejpam-2017	82	14	scalar	scalar	ADJ
ejpam-2017	82	15	multiplication	multiplication	NOUN
ejpam-2017	82	16	of	of	ADP
ejpam-2017	82	17	a	a	DET
ejpam-2017	82	18	column	column	NOUN
ejpam-2017	82	19	vector	vector	NOUN
ejpam-2017	82	20	is	be	AUX
ejpam-2017	82	21	expressed	express	VERB
ejpam-2017	82	22	as	as	ADP
ejpam-2017	82	23	λ	λ	NOUN
ejpam-2017	82	24			VERB
ejpam-2017	82	25			NOUN
ejpam-2017	82	26	b1	b1	NOUN
ejpam-2017	82	27	b2	b2	NOUN
ejpam-2017	82	28	b3	b3	PROPN
ejpam-2017	82	29			PROPN
ejpam-2017	83	1			INTJ
ejpam-2017	83	2	,	,	PUNCT
ejpam-2017	83	3	where	where	SCONJ
ejpam-2017	83	4	λ	λ	PROPN
ejpam-2017	83	5	is	be	AUX
ejpam-2017	83	6	a	a	DET
ejpam-2017	83	7	scalar	scalar	NOUN
ejpam-2017	83	8	.	.	PUNCT
ejpam-2017	84	1	as	as	SCONJ
ejpam-2017	84	2	shown	show	VERB
ejpam-2017	84	3	in	in	ADP
ejpam-2017	84	4	the	the	DET
ejpam-2017	84	5	previous	previous	ADJ
ejpam-2017	84	6	section	section	NOUN
ejpam-2017	84	7	,	,	PUNCT
ejpam-2017	84	8	this	this	DET
ejpam-2017	84	9	form	form	NOUN
ejpam-2017	84	10	is	be	AUX
ejpam-2017	84	11	not	not	PART
ejpam-2017	84	12	proper	proper	ADJ
ejpam-2017	84	13	from	from	ADP
ejpam-2017	84	14	the	the	DET
ejpam-2017	84	15	viewpoint	viewpoint	NOUN
ejpam-2017	84	16	of	of	ADP
ejpam-2017	84	17	matrix	matrix	NOUN
ejpam-2017	84	18	multiplication	multiplication	NOUN
ejpam-2017	84	19	.	.	PUNCT
ejpam-2017	85	1	in	in	ADP
ejpam-2017	85	2	standard	standard	ADJ
ejpam-2017	85	3	textbooks	textbook	NOUN
ejpam-2017	85	4	on	on	ADP
ejpam-2017	85	5	linear	linear	ADJ
ejpam-2017	85	6	algebra	algebra	PROPN
ejpam-2017	85	7	(	(	PUNCT
ejpam-2017	85	8	for	for	ADP
ejpam-2017	85	9	example	example	NOUN
ejpam-2017	85	10	,	,	PUNCT
ejpam-2017	85	11	[	[	X
ejpam-2017	85	12	1	1	NUM
ejpam-2017	85	13	]	]	NUM
ejpam-2017	85	14	)	)	PUNCT
ejpam-2017	85	15	,	,	PUNCT
ejpam-2017	85	16	however	however	ADV
ejpam-2017	85	17	,	,	PUNCT
ejpam-2017	85	18	this	this	DET
ejpam-2017	85	19	form	form	NOUN
ejpam-2017	85	20	is	be	AUX
ejpam-2017	85	21	used	use	VERB
ejpam-2017	85	22	as	as	ADP
ejpam-2017	85	23	the	the	DET
ejpam-2017	85	24	first	first	ADJ
ejpam-2017	85	25	step	step	NOUN
ejpam-2017	85	26	of	of	ADP
ejpam-2017	85	27	the	the	DET
ejpam-2017	85	28	procedures	procedure	NOUN
ejpam-2017	85	29	for	for	ADP
ejpam-2017	85	30	diagonalizing	diagonalize	VERB
ejpam-2017	85	31	a	a	DET
ejpam-2017	85	32	matrix	matrix	NOUN
ejpam-2017	85	33	and	and	CCONJ
ejpam-2017	85	34	that	that	SCONJ
ejpam-2017	85	35	for	for	ADP
ejpam-2017	85	36	deriving	derive	VERB
ejpam-2017	85	37	the	the	DET
ejpam-2017	85	38	standard	standard	ADJ
ejpam-2017	85	39	matrix	matrix	NOUN
ejpam-2017	85	40	for	for	ADP
ejpam-2017	85	41	a	a	DET
ejpam-2017	85	42	rotation	rotation	NOUN
ejpam-2017	85	43	operator	operator	NOUN
ejpam-2017	85	44	.	.	PUNCT
ejpam-2017	86	1	these	these	DET
ejpam-2017	86	2	procedures	procedure	NOUN
ejpam-2017	86	3	are	be	AUX
ejpam-2017	86	4	not	not	PART
ejpam-2017	86	5	necessarily	necessarily	ADV
ejpam-2017	86	6	easy	easy	ADJ
ejpam-2017	86	7	for	for	ADP
ejpam-2017	86	8	some	some	DET
ejpam-2017	86	9	students	student	NOUN
ejpam-2017	86	10	for	for	ADP
ejpam-2017	86	11	the	the	DET
ejpam-2017	86	12	following	follow	VERB
ejpam-2017	86	13	reason	reason	NOUN
ejpam-2017	86	14	.	.	PUNCT
ejpam-2017	87	1	diagonalization	diagonalization	NOUN
ejpam-2017	87	2	of	of	ADP
ejpam-2017	87	3	a	a	DET
ejpam-2017	87	4	matrix	matrix	NOUN
ejpam-2017	87	5	for	for	ADP
ejpam-2017	87	6	an	an	DET
ejpam-2017	87	7	n×	n×	ADV
ejpam-2017	87	8	n	n	CCONJ
ejpam-2017	87	9	diagonalizable	diagonalizable	ADJ
ejpam-2017	87	10	matrix	matrix	NOUN
ejpam-2017	87	11	a	a	PRON
ejpam-2017	87	12	,	,	PUNCT
ejpam-2017	87	13	there	there	PRON
ejpam-2017	87	14	is	be	VERB
ejpam-2017	87	15	an	an	DET
ejpam-2017	87	16	invertible	invertible	ADJ
ejpam-2017	87	17	matrix	matrix	NOUN
ejpam-2017	87	18	u	u	NOUN
ejpam-2017	87	19	=	=	SYM
ejpam-2017	87	20			PROPN
ejpam-2017	87	21			NOUN
ejpam-2017	87	22			NOUN
ejpam-2017	87	23			NOUN
ejpam-2017	87	24			NOUN
ejpam-2017	87	25	u11	u11	VERB
ejpam-2017	87	26	u12	u12	X
ejpam-2017	87	27	·	·	PUNCT
ejpam-2017	87	28	·	·	PUNCT
ejpam-2017	87	29	·	·	PUNCT
ejpam-2017	87	30	u1n	u1n	NOUN
ejpam-2017	87	31	u21	u21	PROPN
ejpam-2017	87	32	u22	u22	PROPN
ejpam-2017	87	33	·	·	PUNCT
ejpam-2017	87	34	·	·	PUNCT
ejpam-2017	87	35	·	·	PUNCT
ejpam-2017	88	1	u2n	u2n	PROPN
ejpam-2017	88	2	...	...	PUNCT
ejpam-2017	88	3	...	...	PUNCT
ejpam-2017	88	4	·	·	PUNCT
ejpam-2017	88	5	·	·	PUNCT
ejpam-2017	88	6	·	·	PUNCT
ejpam-2017	88	7	...	...	PUNCT
ejpam-2017	89	1	un1	un1	PRON
ejpam-2017	89	2	un2	un2	ADJ
ejpam-2017	89	3	·	·	PUNCT
ejpam-2017	89	4	·	·	PUNCT
ejpam-2017	89	5	·	·	PUNCT
ejpam-2017	89	6	unn	unn	INTJ
ejpam-2017	89	7			PROPN
ejpam-2017	89	8			NOUN
ejpam-2017	89	9			VERB
ejpam-2017	89	10			NOUN
ejpam-2017	89	11			PUNCT
ejpam-2017	89	12	,	,	PUNCT
ejpam-2017	89	13	where	where	SCONJ
ejpam-2017	89	14			VERB
ejpam-2017	89	15			NOUN
ejpam-2017	89	16			NOUN
ejpam-2017	89	17			NOUN
ejpam-2017	89	18			NOUN
ejpam-2017	89	19	u11	u11	ADJ
ejpam-2017	89	20	u21	u21	NOUN
ejpam-2017	89	21	...	...	PUNCT
ejpam-2017	90	1	un1	un1	INTJ
ejpam-2017	90	2			NOUN
ejpam-2017	90	3			NOUN
ejpam-2017	90	4			VERB
ejpam-2017	90	5			NOUN
ejpam-2017	90	6			X
ejpam-2017	90	7	,	,	PUNCT
ejpam-2017	90	8			PROPN
ejpam-2017	90	9			NOUN
ejpam-2017	90	10			NOUN
ejpam-2017	90	11			NOUN
ejpam-2017	90	12			NOUN
ejpam-2017	90	13	u12	u12	VERB
ejpam-2017	90	14	u22	u22	NOUN
ejpam-2017	90	15	...	...	PUNCT
ejpam-2017	91	1	un2	un2	ADJ
ejpam-2017	91	2			PROPN
ejpam-2017	91	3			NOUN
ejpam-2017	91	4			VERB
ejpam-2017	91	5			NOUN
ejpam-2017	91	6			PUNCT
ejpam-2017	91	7	,	,	PUNCT
ejpam-2017	91	8	.	.	PUNCT
ejpam-2017	91	9	.	.	PUNCT
ejpam-2017	92	1	.	.	PUNCT
ejpam-2017	93	1	,	,	PUNCT
ejpam-2017	93	2			PROPN
ejpam-2017	93	3			NOUN
ejpam-2017	93	4			NOUN
ejpam-2017	93	5			NOUN
ejpam-2017	93	6			PROPN
ejpam-2017	93	7	u1n	u1n	PROPN
ejpam-2017	93	8	u2n	u2n	PROPN
ejpam-2017	93	9	...	...	PUNCT
ejpam-2017	93	10	unn	unn	PROPN
ejpam-2017	93	11			PROPN
ejpam-2017	93	12			NOUN
ejpam-2017	93	13			VERB
ejpam-2017	93	14			NOUN
ejpam-2017	93	15			X
ejpam-2017	93	16	are	be	AUX
ejpam-2017	93	17	the	the	DET
ejpam-2017	93	18	eigenvectors	eigenvector	NOUN
ejpam-2017	93	19	of	of	ADP
ejpam-2017	93	20	a	a	PRON
ejpam-2017	93	21	,	,	PUNCT
ejpam-2017	93	22	such	such	ADJ
ejpam-2017	93	23	that	that	DET
ejpam-2017	93	24	matrix	matrix	NOUN
ejpam-2017	93	25	u	u	NOUN
ejpam-2017	93	26	diagonalizes	diagonalize	VERB
ejpam-2017	93	27	a	a	PRON
ejpam-2017	93	28	,	,	PUNCT
ejpam-2017	93	29	that	that	ADV
ejpam-2017	93	30	is	is	ADV
ejpam-2017	93	31	,	,	PUNCT
ejpam-2017	93	32	u−1au	u−1au	ADJ
ejpam-2017	93	33	=	=	SYM
ejpam-2017	93	34	λ	λ	PROPN
ejpam-2017	93	35	,	,	PUNCT
ejpam-2017	93	36	where	where	SCONJ
ejpam-2017	93	37	λ	λ	NOUN
ejpam-2017	93	38	=	=	SYM
ejpam-2017	93	39			VERB
ejpam-2017	93	40			PRON
ejpam-2017	93	41	λ1	λ1	ADJ
ejpam-2017	93	42	0	0	NUM
ejpam-2017	93	43	·	·	PUNCT
ejpam-2017	93	44	·	·	PUNCT
ejpam-2017	93	45	·	·	PUNCT
ejpam-2017	93	46	0	0	NUM
ejpam-2017	93	47	0	0	NUM
ejpam-2017	93	48	λ2	λ2	NOUN
ejpam-2017	93	49	·	·	PUNCT
ejpam-2017	93	50	·	·	PUNCT
ejpam-2017	93	51	·	·	PUNCT
ejpam-2017	93	52	0	0	NUM
ejpam-2017	93	53	0	0	NUM
ejpam-2017	93	54	0	0	NUM
ejpam-2017	93	55	·	·	PUNCT
ejpam-2017	93	56	·	·	PUNCT
ejpam-2017	93	57	·	·	PUNCT
ejpam-2017	94	1	λn	λn	INTJ
ejpam-2017	94	2			INTJ
ejpam-2017	94	3			PUNCT
ejpam-2017	95	1	y.	y.	PROPN
ejpam-2017	95	2	kobayashi	kobayashi	PROPN
ejpam-2017	95	3	/	/	SYM
ejpam-2017	95	4	eur	eur	PROPN
ejpam-2017	95	5	.	.	PUNCT
ejpam-2017	96	1	j.	j.	PROPN
ejpam-2017	96	2	pure	pure	PROPN
ejpam-2017	96	3	appl	appl	PROPN
ejpam-2017	96	4	.	.	PROPN
ejpam-2017	96	5	math	math	PROPN
ejpam-2017	96	6	,	,	PUNCT
ejpam-2017	96	7	7	7	NUM
ejpam-2017	96	8	(	(	PUNCT
ejpam-2017	96	9	2014	2014	NUM
ejpam-2017	96	10	)	)	PUNCT
ejpam-2017	96	11	,	,	PUNCT
ejpam-2017	96	12	405	405	NUM
ejpam-2017	96	13	-	-	SYM
ejpam-2017	96	14	411	411	NUM
ejpam-2017	96	15	409	409	NUM
ejpam-2017	96	16	and	and	CCONJ
ejpam-2017	96	17	λ1,λ2	λ1,λ2	PROPN
ejpam-2017	96	18	,	,	PUNCT
ejpam-2017	96	19	.	.	PUNCT
ejpam-2017	96	20	.	.	PUNCT
ejpam-2017	97	1	.	.	PUNCT
ejpam-2017	98	1	,	,	PUNCT
ejpam-2017	98	2	λn	λn	PROPN
ejpam-2017	98	3	are	be	AUX
ejpam-2017	98	4	the	the	DET
ejpam-2017	98	5	eigenvalues	eigenvalue	NOUN
ejpam-2017	98	6	of	of	ADP
ejpam-2017	98	7	a.	a.	NOUN
ejpam-2017	98	8	this	this	PRON
ejpam-2017	98	9	raises	raise	VERB
ejpam-2017	98	10	a	a	DET
ejpam-2017	98	11	question	question	NOUN
ejpam-2017	98	12	:	:	PUNCT
ejpam-2017	98	13	it	it	PRON
ejpam-2017	98	14	follows	follow	VERB
ejpam-2017	98	15	from	from	ADP
ejpam-2017	98	16	the	the	DET
ejpam-2017	98	17	formula	formula	NOUN
ejpam-2017	98	18	u−1au	u−1au	NOUN
ejpam-2017	99	1	=	=	PUNCT
ejpam-2017	99	2	λ	λ	PROPN
ejpam-2017	99	3	that	that	ADV
ejpam-2017	99	4	au	au	ADV
ejpam-2017	99	5	=	=	SYM
ejpam-2017	99	6	uλ	uλ	NOUN
ejpam-2017	99	7	.	.	PUNCT
ejpam-2017	100	1	we	we	PRON
ejpam-2017	100	2	have	have	VERB
ejpam-2017	100	3	au1	au1	NOUN
ejpam-2017	100	4	=	=	SYM
ejpam-2017	100	5	λ1u1	λ1u1	NOUN
ejpam-2017	100	6	,	,	PUNCT
ejpam-2017	100	7	au2	au2	NOUN
ejpam-2017	100	8	=	=	SYM
ejpam-2017	100	9	λ2u2	λ2u2	PROPN
ejpam-2017	100	10	,	,	PUNCT
ejpam-2017	100	11	.	.	PUNCT
ejpam-2017	100	12	.	.	PUNCT
ejpam-2017	101	1	.	.	PUNCT
ejpam-2017	101	2	,	,	PUNCT
ejpam-2017	101	3	aun	aun	NOUN
ejpam-2017	101	4	=	=	SYM
ejpam-2017	101	5	λnun	λnun	PROPN
ejpam-2017	101	6	,	,	PUNCT
ejpam-2017	101	7	where	where	SCONJ
ejpam-2017	101	8	u1,u2	u1,u2	PROPN
ejpam-2017	101	9	,	,	PUNCT
ejpam-2017	101	10	.	.	PUNCT
ejpam-2017	101	11	.	.	PUNCT
ejpam-2017	101	12	.	.	PUNCT
ejpam-2017	102	1	,	,	PUNCT
ejpam-2017	102	2	un	un	PROPN
ejpam-2017	102	3	are	be	AUX
ejpam-2017	102	4	the	the	DET
ejpam-2017	102	5	eigenvectors	eigenvector	NOUN
ejpam-2017	102	6	of	of	ADP
ejpam-2017	102	7	a	a	DET
ejpam-2017	102	8	corresponding	corresponding	NOUN
ejpam-2017	102	9	to	to	ADP
ejpam-2017	102	10	the	the	DET
ejpam-2017	102	11	eigenvalues	eigenvalue	NOUN
ejpam-2017	102	12	of	of	ADP
ejpam-2017	102	13	a	a	DET
ejpam-2017	102	14	,	,	PUNCT
ejpam-2017	102	15	λ1,λ2	λ1,λ2	PROPN
ejpam-2017	102	16	,	,	PUNCT
ejpam-2017	102	17	.	.	PUNCT
ejpam-2017	102	18	.	.	PUNCT
ejpam-2017	103	1	.	.	PUNCT
ejpam-2017	104	1	,	,	PUNCT
ejpam-2017	104	2	λn	λn	NOUN
ejpam-2017	104	3	,	,	PUNCT
ejpam-2017	104	4	respectively	respectively	ADV
ejpam-2017	104	5	.	.	PUNCT
ejpam-2017	105	1	the	the	DET
ejpam-2017	105	2	question	question	NOUN
ejpam-2017	105	3	is	be	AUX
ejpam-2017	105	4	,	,	PUNCT
ejpam-2017	105	5	why	why	SCONJ
ejpam-2017	105	6	do	do	AUX
ejpam-2017	105	7	we	we	PRON
ejpam-2017	105	8	consider	consider	VERB
ejpam-2017	105	9	uλ	uλ	PRON
ejpam-2017	105	10	instead	instead	ADV
ejpam-2017	105	11	of	of	ADP
ejpam-2017	105	12	λu	λu	PROPN
ejpam-2017	105	13	as	as	ADP
ejpam-2017	105	14	equivalent	equivalent	ADJ
ejpam-2017	105	15	to	to	ADP
ejpam-2017	105	16	the	the	DET
ejpam-2017	105	17	forms	form	NOUN
ejpam-2017	105	18	of	of	ADP
ejpam-2017	105	19	λ1u1,λ2u2	λ1u1,λ2u2	NUM
ejpam-2017	105	20	,	,	PUNCT
ejpam-2017	105	21	.	.	PUNCT
ejpam-2017	105	22	.	.	PUNCT
ejpam-2017	105	23	.	.	PUNCT
ejpam-2017	106	1	,	,	PUNCT
ejpam-2017	106	2	λnun	λnun	PROPN
ejpam-2017	106	3	?	?	PUNCT
ejpam-2017	107	1	we	we	PRON
ejpam-2017	107	2	can	can	AUX
ejpam-2017	107	3	avoid	avoid	VERB
ejpam-2017	107	4	this	this	DET
ejpam-2017	107	5	question	question	NOUN
ejpam-2017	107	6	by	by	ADP
ejpam-2017	107	7	following	follow	VERB
ejpam-2017	107	8	the	the	DET
ejpam-2017	107	9	rule	rule	NOUN
ejpam-2017	107	10	of	of	ADP
ejpam-2017	107	11	matrix	matrix	NOUN
ejpam-2017	107	12	multiplication	multiplication	NOUN
ejpam-2017	107	13	.	.	PUNCT
ejpam-2017	108	1	the	the	DET
ejpam-2017	108	2	forms	form	NOUN
ejpam-2017	108	3	λ1u1,λ2u2	λ1u1,λ2u2	NOUN
ejpam-2017	108	4	,	,	PUNCT
ejpam-2017	108	5	.	.	PUNCT
ejpam-2017	108	6	.	.	PUNCT
ejpam-2017	108	7	.	.	PUNCT
ejpam-2017	109	1	,	,	PUNCT
ejpam-2017	109	2	λnun	λnun	INTJ
ejpam-2017	109	3	deviate	deviate	VERB
ejpam-2017	109	4	from	from	ADP
ejpam-2017	109	5	this	this	DET
ejpam-2017	109	6	rule	rule	NOUN
ejpam-2017	109	7	because	because	SCONJ
ejpam-2017	109	8	the	the	DET
ejpam-2017	109	9	multiplication	multiplication	NOUN
ejpam-2017	109	10	of	of	ADP
ejpam-2017	109	11	a	a	DET
ejpam-2017	109	12	1×1	1×1	NUM
ejpam-2017	109	13	matrix	matrix	NOUN
ejpam-2017	109	14	and	and	CCONJ
ejpam-2017	109	15	an	an	DET
ejpam-2017	109	16	n×1	n×1	NOUN
ejpam-2017	109	17	matrix	matrix	NOUN
ejpam-2017	109	18	is	be	AUX
ejpam-2017	109	19	not	not	PART
ejpam-2017	109	20	defined	define	VERB
ejpam-2017	109	21	.	.	PUNCT
ejpam-2017	110	1	therefore	therefore	ADV
ejpam-2017	110	2	,	,	PUNCT
ejpam-2017	110	3	if	if	SCONJ
ejpam-2017	110	4	we	we	PRON
ejpam-2017	110	5	consider	consider	VERB
ejpam-2017	110	6	u1λ1,u2λ2	u1λ1,u2λ2	NOUN
ejpam-2017	110	7	,	,	PUNCT
ejpam-2017	110	8	.	.	PUNCT
ejpam-2017	110	9	.	.	PUNCT
ejpam-2017	110	10	.	.	PUNCT
ejpam-2017	111	1	,	,	PUNCT
ejpam-2017	111	2	unλn	unλn	VERB
ejpam-2017	111	3	instead	instead	ADV
ejpam-2017	111	4	of	of	ADP
ejpam-2017	111	5	the	the	DET
ejpam-2017	111	6	above	above	ADJ
ejpam-2017	111	7	forms	form	NOUN
ejpam-2017	111	8	,	,	PUNCT
ejpam-2017	111	9	a	a	DET
ejpam-2017	111	10	combined	combine	VERB
ejpam-2017	111	11	form	form	NOUN
ejpam-2017	111	12	uλ	uλ	NOUN
ejpam-2017	111	13	,	,	PUNCT
ejpam-2017	111	14	or	or	CCONJ
ejpam-2017	111	15			VERB
ejpam-2017	111	16			NOUN
ejpam-2017	111	17			NOUN
ejpam-2017	111	18			NOUN
ejpam-2017	111	19			NOUN
ejpam-2017	111	20	u11	u11	VERB
ejpam-2017	111	21	u12	u12	X
ejpam-2017	111	22	·	·	PUNCT
ejpam-2017	111	23	·	·	PUNCT
ejpam-2017	111	24	·	·	PUNCT
ejpam-2017	111	25	u1n	u1n	NOUN
ejpam-2017	111	26	u21	u21	PROPN
ejpam-2017	111	27	u22	u22	PROPN
ejpam-2017	111	28	·	·	PUNCT
ejpam-2017	111	29	·	·	PUNCT
ejpam-2017	111	30	·	·	PUNCT
ejpam-2017	112	1	u2n	u2n	PROPN
ejpam-2017	112	2	...	...	PUNCT
ejpam-2017	112	3	...	...	PUNCT
ejpam-2017	112	4	·	·	PUNCT
ejpam-2017	112	5	·	·	PUNCT
ejpam-2017	112	6	·	·	PUNCT
ejpam-2017	112	7	...	...	PUNCT
ejpam-2017	113	1	un1	un1	PRON
ejpam-2017	113	2	un2	un2	ADJ
ejpam-2017	113	3	·	·	PUNCT
ejpam-2017	113	4	·	·	PUNCT
ejpam-2017	113	5	·	·	PUNCT
ejpam-2017	113	6	unn	unn	INTJ
ejpam-2017	113	7			PROPN
ejpam-2017	113	8			NOUN
ejpam-2017	113	9			VERB
ejpam-2017	113	10			NOUN
ejpam-2017	113	11			PUNCT
ejpam-2017	114	1			PROPN
ejpam-2017	114	2			NOUN
ejpam-2017	114	3			NOUN
ejpam-2017	114	4			NOUN
ejpam-2017	114	5			NOUN
ejpam-2017	114	6	λ1	λ1	ADJ
ejpam-2017	114	7	0	0	NUM
ejpam-2017	114	8	·	·	PUNCT
ejpam-2017	114	9	·	·	PUNCT
ejpam-2017	114	10	·	·	PUNCT
ejpam-2017	114	11	0	0	NUM
ejpam-2017	114	12	0	0	NUM
ejpam-2017	114	13	λ2	λ2	NOUN
ejpam-2017	114	14	·	·	PUNCT
ejpam-2017	114	15	·	·	PUNCT
ejpam-2017	114	16	·	·	PUNCT
ejpam-2017	114	17	0	0	NUM
ejpam-2017	114	18	...	...	PUNCT
ejpam-2017	114	19	...	...	PUNCT
ejpam-2017	114	20	·	·	PUNCT
ejpam-2017	114	21	·	·	PUNCT
ejpam-2017	114	22	·	·	PUNCT
ejpam-2017	114	23	...	...	PUNCT
ejpam-2017	115	1	0	0	NUM
ejpam-2017	115	2	0	0	NUM
ejpam-2017	115	3	·	·	PUNCT
ejpam-2017	115	4	·	·	PUNCT
ejpam-2017	115	5	·	·	PUNCT
ejpam-2017	115	6	λn	λn	NOUN
ejpam-2017	115	7			NOUN
ejpam-2017	115	8			NOUN
ejpam-2017	115	9			VERB
ejpam-2017	115	10			NOUN
ejpam-2017	115	11			X
ejpam-2017	115	12	,	,	PUNCT
ejpam-2017	115	13	can	can	AUX
ejpam-2017	115	14	easily	easily	ADV
ejpam-2017	115	15	be	be	AUX
ejpam-2017	115	16	obtained	obtain	VERB
ejpam-2017	115	17	.	.	PUNCT
ejpam-2017	116	1	some	some	DET
ejpam-2017	116	2	instructors	instructor	NOUN
ejpam-2017	116	3	do	do	AUX
ejpam-2017	116	4	not	not	PART
ejpam-2017	116	5	regard	regard	VERB
ejpam-2017	116	6	eigenvalues	eigenvalue	NOUN
ejpam-2017	116	7	as	as	ADP
ejpam-2017	116	8	matrices	matrix	NOUN
ejpam-2017	116	9	and	and	CCONJ
ejpam-2017	116	10	explain	explain	VERB
ejpam-2017	116	11	that	that	SCONJ
ejpam-2017	116	12	λk	λk	NOUN
ejpam-2017	116	13	is	be	AUX
ejpam-2017	116	14	just	just	ADV
ejpam-2017	116	15	taken	take	VERB
ejpam-2017	116	16	from	from	ADP
ejpam-2017	116	17	left	left	NOUN
ejpam-2017	116	18	to	to	ADP
ejpam-2017	116	19	right	right	ADV
ejpam-2017	116	20	in	in	ADP
ejpam-2017	116	21	actually	actually	ADV
ejpam-2017	116	22	operating	operate	VERB
ejpam-2017	116	23	with	with	ADP
ejpam-2017	116	24	the	the	DET
ejpam-2017	116	25	commutativity	commutativity	NOUN
ejpam-2017	116	26	as	as	SCONJ
ejpam-2017	116	27	it	it	PRON
ejpam-2017	116	28	is	be	AUX
ejpam-2017	116	29	a	a	DET
ejpam-2017	116	30	scalar	scalar	NOUN
ejpam-2017	116	31	.	.	PUNCT
ejpam-2017	117	1	this	this	DET
ejpam-2017	117	2	interpretation	interpretation	NOUN
ejpam-2017	117	3	is	be	AUX
ejpam-2017	117	4	ambiguous	ambiguous	ADJ
ejpam-2017	117	5	in	in	ADP
ejpam-2017	117	6	meaning	meaning	NOUN
ejpam-2017	117	7	,	,	PUNCT
ejpam-2017	117	8	although	although	SCONJ
ejpam-2017	117	9	we	we	PRON
ejpam-2017	117	10	can	can	AUX
ejpam-2017	117	11	consider	consider	VERB
ejpam-2017	117	12	that	that	SCONJ
ejpam-2017	117	13	the	the	DET
ejpam-2017	117	14	column	column	NOUN
ejpam-2017	117	15	vectors	vector	NOUN
ejpam-2017	117	16	of	of	ADP
ejpam-2017	117	17	the	the	DET
ejpam-2017	117	18	product	product	NOUN
ejpam-2017	117	19	uλ	uλ	ADP
ejpam-2017	117	20	are	be	AUX
ejpam-2017	117	21	λ1u1,λ2u2	λ1u1,λ2u2	NUM
ejpam-2017	117	22	,	,	PUNCT
ejpam-2017	117	23	.	.	PUNCT
ejpam-2017	117	24	.	.	PUNCT
ejpam-2017	118	1	.	.	PUNCT
ejpam-2017	119	1	,	,	PUNCT
ejpam-2017	119	2	λnun	λnun	PROPN
ejpam-2017	119	3	.	.	PUNCT
ejpam-2017	120	1	from	from	ADP
ejpam-2017	120	2	a	a	DET
ejpam-2017	120	3	pedagogical	pedagogical	ADJ
ejpam-2017	120	4	standpoint	standpoint	NOUN
ejpam-2017	120	5	,	,	PUNCT
ejpam-2017	120	6	it	it	PRON
ejpam-2017	120	7	is	be	AUX
ejpam-2017	120	8	not	not	PART
ejpam-2017	120	9	necessarily	necessarily	ADV
ejpam-2017	120	10	easy	easy	ADJ
ejpam-2017	120	11	for	for	SCONJ
ejpam-2017	120	12	some	some	DET
ejpam-2017	120	13	students	student	NOUN
ejpam-2017	120	14	to	to	PART
ejpam-2017	120	15	understand	understand	VERB
ejpam-2017	120	16	the	the	DET
ejpam-2017	120	17	process	process	NOUN
ejpam-2017	120	18	of	of	ADP
ejpam-2017	120	19	the	the	DET
ejpam-2017	120	20	construction	construction	NOUN
ejpam-2017	120	21	of	of	ADP
ejpam-2017	120	22	the	the	DET
ejpam-2017	120	23	combined	combine	VERB
ejpam-2017	120	24	form	form	NOUN
ejpam-2017	120	25	uλ	uλ	ADV
ejpam-2017	120	26	from	from	ADP
ejpam-2017	120	27	λ1u1,λ2u2	λ1u1,λ2u2	NUM
ejpam-2017	120	28	,	,	PUNCT
ejpam-2017	120	29	.	.	PUNCT
ejpam-2017	120	30	.	.	PUNCT
ejpam-2017	120	31	.	.	PUNCT
ejpam-2017	121	1	,	,	PUNCT
ejpam-2017	121	2	λnun	λnun	PROPN
ejpam-2017	121	3	.	.	PUNCT
ejpam-2017	122	1	properly	properly	ADV
ejpam-2017	122	2	,	,	PUNCT
ejpam-2017	122	3	the	the	DET
ejpam-2017	122	4	right	right	ADJ
ejpam-2017	122	5	multiplication	multiplication	NOUN
ejpam-2017	122	6	of	of	ADP
ejpam-2017	122	7	a	a	DET
ejpam-2017	122	8	column	column	NOUN
ejpam-2017	122	9	vector	vector	NOUN
ejpam-2017	122	10	uk	uk	PROPN
ejpam-2017	122	11	with	with	ADP
ejpam-2017	122	12	a	a	DET
ejpam-2017	122	13	scalar	scalar	ADJ
ejpam-2017	122	14	λk	λk	ADP
ejpam-2017	122	15	,	,	PUNCT
ejpam-2017	122	16	ukλk	ukλk	ADJ
ejpam-2017	122	17	,	,	PUNCT
ejpam-2017	122	18	implies	imply	VERB
ejpam-2017	122	19	a	a	DET
ejpam-2017	122	20	mapping	mapping	NOUN
ejpam-2017	122	21	referred	refer	VERB
ejpam-2017	122	22	to	to	ADP
ejpam-2017	122	23	as	as	ADP
ejpam-2017	122	24	homothety	homothety	NOUN
ejpam-2017	122	25	of	of	ADP
ejpam-2017	122	26	ratio	ratio	NOUN
ejpam-2017	122	27	λk	λk	ADP
ejpam-2017	122	28	,	,	PUNCT
ejpam-2017	122	29	and	and	CCONJ
ejpam-2017	122	30	thus	thus	ADV
ejpam-2017	122	31	eigenvalues	eigenvalue	VERB
ejpam-2017	122	32	can	can	AUX
ejpam-2017	122	33	be	be	AUX
ejpam-2017	122	34	regarded	regard	VERB
ejpam-2017	122	35	as	as	ADP
ejpam-2017	122	36	1	1	NUM
ejpam-2017	122	37	×	×	NOUN
ejpam-2017	122	38	1	1	NUM
ejpam-2017	122	39	matrices	matrix	NOUN
ejpam-2017	122	40	for	for	ADP
ejpam-2017	122	41	representing	represent	VERB
ejpam-2017	122	42	linear	linear	ADJ
ejpam-2017	122	43	maps	map	NOUN
ejpam-2017	122	44	.	.	PUNCT
ejpam-2017	123	1	the	the	DET
ejpam-2017	123	2	right	right	ADJ
ejpam-2017	123	3	multiplication	multiplication	NOUN
ejpam-2017	123	4	of	of	ADP
ejpam-2017	123	5	a	a	DET
ejpam-2017	123	6	column	column	NOUN
ejpam-2017	123	7	vector	vector	NOUN
ejpam-2017	123	8	with	with	ADP
ejpam-2017	123	9	a	a	DET
ejpam-2017	123	10	scalar	scalar	NOUN
ejpam-2017	123	11	is	be	AUX
ejpam-2017	123	12	compatible	compatible	ADJ
ejpam-2017	123	13	with	with	ADP
ejpam-2017	123	14	the	the	DET
ejpam-2017	123	15	definition	definition	NOUN
ejpam-2017	123	16	of	of	ADP
ejpam-2017	123	17	matrix	matrix	NOUN
ejpam-2017	123	18	multiplication	multiplication	NOUN
ejpam-2017	123	19	,	,	PUNCT
ejpam-2017	123	20	because	because	SCONJ
ejpam-2017	123	21	the	the	DET
ejpam-2017	123	22	number	number	NOUN
ejpam-2017	123	23	of	of	ADP
ejpam-2017	123	24	columns	column	NOUN
ejpam-2017	123	25	of	of	ADP
ejpam-2017	123	26	the	the	DET
ejpam-2017	123	27	column	column	NOUN
ejpam-2017	123	28	matrix	matrix	NOUN
ejpam-2017	123	29	(	(	PUNCT
ejpam-2017	123	30	or	or	CCONJ
ejpam-2017	123	31	the	the	DET
ejpam-2017	123	32	column	column	NOUN
ejpam-2017	123	33	vector	vector	NOUN
ejpam-2017	123	34	)	)	PUNCT
ejpam-2017	123	35	is	be	AUX
ejpam-2017	123	36	the	the	DET
ejpam-2017	123	37	same	same	ADJ
ejpam-2017	123	38	as	as	ADP
ejpam-2017	123	39	the	the	DET
ejpam-2017	123	40	number	number	NOUN
ejpam-2017	123	41	of	of	ADP
ejpam-2017	123	42	row	row	NOUN
ejpam-2017	123	43	of	of	ADP
ejpam-2017	123	44	the	the	DET
ejpam-2017	123	45	1×	1×	NUM
ejpam-2017	123	46	1	1	NUM
ejpam-2017	123	47	matrix	matrix	NOUN
ejpam-2017	123	48	(	(	PUNCT
ejpam-2017	123	49	or	or	CCONJ
ejpam-2017	123	50	the	the	DET
ejpam-2017	123	51	scalar	scalar	ADJ
ejpam-2017	123	52	)	)	PUNCT
ejpam-2017	123	53	.	.	PUNCT
ejpam-2017	124	1	the	the	DET
ejpam-2017	124	2	column	column	NOUN
ejpam-2017	124	3	vectors	vector	NOUN
ejpam-2017	124	4	of	of	ADP
ejpam-2017	124	5	the	the	DET
ejpam-2017	124	6	product	product	NOUN
ejpam-2017	124	7	uλ	uλ	ADP
ejpam-2017	124	8	are	be	AUX
ejpam-2017	124	9	u1λ1,u2λ2	u1λ1,u2λ2	ADJ
ejpam-2017	124	10	,	,	PUNCT
ejpam-2017	124	11	.	.	PUNCT
ejpam-2017	124	12	.	.	PUNCT
ejpam-2017	124	13	.	.	PUNCT
ejpam-2017	125	1	,	,	PUNCT
ejpam-2017	125	2	unλn	unλn	PROPN
ejpam-2017	125	3	.	.	PUNCT
ejpam-2017	126	1	we	we	PRON
ejpam-2017	126	2	can	can	AUX
ejpam-2017	126	3	also	also	ADV
ejpam-2017	126	4	rewrite	rewrite	VERB
ejpam-2017	126	5	auk	auk	NOUN
ejpam-2017	126	6	=	=	PUNCT
ejpam-2017	126	7	ukλk	ukλk	ADJ
ejpam-2017	126	8	as	as	ADP
ejpam-2017	126	9	auk	auk	NOUN
ejpam-2017	126	10	=	=	SYM
ejpam-2017	126	11	λkuk	λkuk	PROPN
ejpam-2017	126	12	,	,	PUNCT
ejpam-2017	126	13	where	where	SCONJ
ejpam-2017	126	14	λk	λk	PROPN
ejpam-2017	126	15	is	be	AUX
ejpam-2017	126	16	a	a	DET
ejpam-2017	126	17	scalar	scalar	ADJ
ejpam-2017	126	18	matrix	matrix	NOUN
ejpam-2017	126	19	whose	whose	DET
ejpam-2017	126	20	diagonal	diagonal	ADJ
ejpam-2017	126	21	entries	entry	NOUN
ejpam-2017	126	22	are	be	AUX
ejpam-2017	126	23	equal	equal	ADJ
ejpam-2017	126	24	to	to	ADP
ejpam-2017	126	25	λk	λk	PROPN
ejpam-2017	126	26	,	,	PUNCT
ejpam-2017	126	27	because	because	SCONJ
ejpam-2017	126	28			NOUN
ejpam-2017	126	29			NOUN
ejpam-2017	126	30			NOUN
ejpam-2017	126	31			NOUN
ejpam-2017	126	32			NOUN
ejpam-2017	126	33	u1k	u1k	PRON
ejpam-2017	126	34	u2k	u2k	NUM
ejpam-2017	126	35	...	...	PUNCT
ejpam-2017	126	36	unk	unk	INTJ
ejpam-2017	126	37			NOUN
ejpam-2017	126	38			NOUN
ejpam-2017	126	39			VERB
ejpam-2017	126	40			NOUN
ejpam-2017	126	41			PUNCT
ejpam-2017	127	1	λk	λk	X
ejpam-2017	127	2	=	=	PUNCT
ejpam-2017	127	3			PROPN
ejpam-2017	127	4			NOUN
ejpam-2017	127	5			NOUN
ejpam-2017	127	6			NOUN
ejpam-2017	127	7			NOUN
ejpam-2017	127	8	λk	λk	ADP
ejpam-2017	127	9	0	0	NUM
ejpam-2017	127	10	·	·	PUNCT
ejpam-2017	127	11	·	·	PUNCT
ejpam-2017	127	12	·	·	PUNCT
ejpam-2017	128	1	0	0	NUM
ejpam-2017	128	2	0	0	NUM
ejpam-2017	128	3	λk	λk	PRON
ejpam-2017	128	4	·	·	PUNCT
ejpam-2017	128	5	·	·	PUNCT
ejpam-2017	128	6	·	·	PUNCT
ejpam-2017	128	7	0	0	NUM
ejpam-2017	128	8	...	...	PUNCT
ejpam-2017	128	9	...	...	PUNCT
ejpam-2017	128	10	·	·	PUNCT
ejpam-2017	128	11	·	·	PUNCT
ejpam-2017	128	12	·	·	PUNCT
ejpam-2017	128	13	...	...	PUNCT
ejpam-2017	129	1	0	0	NUM
ejpam-2017	129	2	0	0	NUM
ejpam-2017	129	3	·	·	PUNCT
ejpam-2017	129	4	·	·	PUNCT
ejpam-2017	129	5	·	·	PUNCT
ejpam-2017	130	1	λk	λk	X
ejpam-2017	130	2			NOUN
ejpam-2017	130	3			NOUN
ejpam-2017	130	4			VERB
ejpam-2017	130	5			NOUN
ejpam-2017	130	6			PUNCT
ejpam-2017	131	1			PROPN
ejpam-2017	131	2			NOUN
ejpam-2017	131	3			NOUN
ejpam-2017	131	4			NOUN
ejpam-2017	131	5			NOUN
ejpam-2017	131	6	u1k	u1k	PRON
ejpam-2017	131	7	u2k	u2k	NUM
ejpam-2017	131	8	...	...	PUNCT
ejpam-2017	131	9	unk	unk	INTJ
ejpam-2017	131	10			NOUN
ejpam-2017	131	11			NOUN
ejpam-2017	131	12			VERB
ejpam-2017	131	13			NOUN
ejpam-2017	131	14			PUNCT
ejpam-2017	131	15	.	.	PUNCT
ejpam-2017	132	1	see	see	VERB
ejpam-2017	132	2	section	section	NOUN
ejpam-2017	132	3	3	3	NUM
ejpam-2017	132	4	for	for	ADP
ejpam-2017	132	5	this	this	PRON
ejpam-2017	132	6	.	.	PUNCT
ejpam-2017	133	1	this	this	DET
ejpam-2017	133	2	relationship	relationship	NOUN
ejpam-2017	133	3	indicates	indicate	VERB
ejpam-2017	133	4	that	that	SCONJ
ejpam-2017	133	5	homothety	homothety	NOUN
ejpam-2017	133	6	can	can	AUX
ejpam-2017	133	7	be	be	AUX
ejpam-2017	133	8	represented	represent	VERB
ejpam-2017	133	9	by	by	ADP
ejpam-2017	133	10	a	a	DET
ejpam-2017	133	11	scalar	scalar	ADJ
ejpam-2017	133	12	matrix	matrix	NOUN
ejpam-2017	133	13	.	.	PUNCT
ejpam-2017	134	1	to	to	PART
ejpam-2017	134	2	find	find	VERB
ejpam-2017	134	3	the	the	DET
ejpam-2017	134	4	eigenvalues	eigenvalue	NOUN
ejpam-2017	134	5	and	and	CCONJ
ejpam-2017	134	6	eigenvectors	eigenvector	NOUN
ejpam-2017	134	7	of	of	ADP
ejpam-2017	134	8	a	a	PRON
ejpam-2017	134	9	,	,	PUNCT
ejpam-2017	134	10	we	we	PRON
ejpam-2017	134	11	rewrite	rewrite	VERB
ejpam-2017	134	12	auk	auk	NOUN
ejpam-2017	134	13	=	=	PUNCT
ejpam-2017	134	14	ukλk	ukλk	ADJ
ejpam-2017	134	15	as	as	ADP
ejpam-2017	134	16	(	(	PUNCT
ejpam-2017	134	17	a−λk)uk	a−λk)uk	NOUN
ejpam-2017	134	18	=	=	SYM
ejpam-2017	134	19	0	0	PUNCT
ejpam-2017	134	20	and	and	CCONJ
ejpam-2017	134	21	obtain	obtain	VERB
ejpam-2017	134	22	the	the	DET
ejpam-2017	134	23	characteristic	characteristic	ADJ
ejpam-2017	134	24	equation	equation	NOUN
ejpam-2017	134	25	of	of	ADP
ejpam-2017	134	26	a.	a.	NOUN
ejpam-2017	134	27	by	by	ADP
ejpam-2017	134	28	transforming	transform	VERB
ejpam-2017	134	29	auk	auk	NOUN
ejpam-2017	134	30	=	=	PUNCT
ejpam-2017	134	31	ukλk	ukλk	ADV
ejpam-2017	134	32	into	into	ADP
ejpam-2017	134	33	(	(	PUNCT
ejpam-2017	134	34	a−λk)uk	a−λk)uk	NOUN
ejpam-2017	134	35	=	=	SYM
ejpam-2017	134	36	0	0	NUM
ejpam-2017	134	37	,	,	PUNCT
ejpam-2017	134	38	we	we	PRON
ejpam-2017	134	39	solve	solve	VERB
ejpam-2017	134	40	the	the	DET
ejpam-2017	134	41	problem	problem	NOUN
ejpam-2017	134	42	to	to	PART
ejpam-2017	134	43	obtain	obtain	VERB
ejpam-2017	134	44	the	the	DET
ejpam-2017	134	45	kernel	kernel	NOUN
ejpam-2017	134	46	of	of	ADP
ejpam-2017	134	47	a	a	DET
ejpam-2017	134	48	linear	linear	ADJ
ejpam-2017	134	49	transformation	transformation	NOUN
ejpam-2017	134	50	expressed	express	VERB
ejpam-2017	134	51	by	by	ADP
ejpam-2017	134	52	the	the	DET
ejpam-2017	134	53	n	n	NUM
ejpam-2017	134	54	×	×	NOUN
ejpam-2017	134	55	n	n	PRON
ejpam-2017	134	56	matrix	matrix	NOUN
ejpam-2017	134	57	a−λk	a−λk	VERB
ejpam-2017	134	58	.	.	PUNCT
ejpam-2017	135	1	we	we	PRON
ejpam-2017	135	2	take	take	VERB
ejpam-2017	135	3	note	note	NOUN
ejpam-2017	135	4	of	of	ADP
ejpam-2017	135	5	the	the	DET
ejpam-2017	135	6	relationship	relationship	NOUN
ejpam-2017	135	7	ukλk	ukλk	ADV
ejpam-2017	135	8	=	=	SYM
ejpam-2017	135	9	λkuk	λkuk	PROPN
ejpam-2017	135	10	only	only	ADV
ejpam-2017	135	11	in	in	ADP
ejpam-2017	135	12	the	the	DET
ejpam-2017	135	13	process	process	NOUN
ejpam-2017	135	14	of	of	ADP
ejpam-2017	135	15	obtaining	obtain	VERB
ejpam-2017	135	16	the	the	DET
ejpam-2017	135	17	characteristic	characteristic	ADJ
ejpam-2017	135	18	equation	equation	NOUN
ejpam-2017	135	19	of	of	ADP
ejpam-2017	135	20	a.	a.	PROPN
ejpam-2017	135	21	y.	y.	PROPN
ejpam-2017	135	22	kobayashi	kobayashi	PROPN
ejpam-2017	135	23	/	/	SYM
ejpam-2017	135	24	eur	eur	PROPN
ejpam-2017	135	25	.	.	PUNCT
ejpam-2017	136	1	j.	j.	PROPN
ejpam-2017	136	2	pure	pure	PROPN
ejpam-2017	136	3	appl	appl	PROPN
ejpam-2017	136	4	.	.	PROPN
ejpam-2017	136	5	math	math	PROPN
ejpam-2017	136	6	,	,	PUNCT
ejpam-2017	136	7	7	7	NUM
ejpam-2017	136	8	(	(	PUNCT
ejpam-2017	136	9	2014	2014	NUM
ejpam-2017	136	10	)	)	PUNCT
ejpam-2017	136	11	,	,	PUNCT
ejpam-2017	136	12	405	405	NUM
ejpam-2017	136	13	-	-	SYM
ejpam-2017	136	14	411	411	NUM
ejpam-2017	136	15	410	410	NUM
ejpam-2017	136	16	standard	standard	ADJ
ejpam-2017	136	17	matrix	matrix	NOUN
ejpam-2017	136	18	for	for	ADP
ejpam-2017	136	19	rotation	rotation	NOUN
ejpam-2017	136	20	operator	operator	NOUN
ejpam-2017	136	21	for	for	ADP
ejpam-2017	136	22	simplicity	simplicity	NOUN
ejpam-2017	136	23	,	,	PUNCT
ejpam-2017	136	24	we	we	PRON
ejpam-2017	136	25	consider	consider	VERB
ejpam-2017	136	26	the	the	DET
ejpam-2017	136	27	rotation	rotation	NOUN
ejpam-2017	136	28	operator	operator	NOUN
ejpam-2017	136	29	on	on	ADP
ejpam-2017	136	30	r2	r2	PROPN
ejpam-2017	136	31	.	.	PUNCT
ejpam-2017	137	1	a	a	DET
ejpam-2017	137	2	vector	vector	NOUN
ejpam-2017	137	3	r	r	NOUN
ejpam-2017	137	4	can	can	AUX
ejpam-2017	137	5	be	be	AUX
ejpam-2017	137	6	expressed	express	VERB
ejpam-2017	137	7	as	as	ADP
ejpam-2017	137	8	r=	r=	ADJ
ejpam-2017	137	9	�	�	PROPN
ejpam-2017	137	10	x	x	PUNCT
ejpam-2017	137	11	y	y	PROPN
ejpam-2017	137	12	�	�	PROPN
ejpam-2017	137	13	=	=	SYM
ejpam-2017	137	14	�	�	PROPN
ejpam-2017	138	1	1	1	NUM
ejpam-2017	138	2	0	0	NUM
ejpam-2017	138	3	�	�	PROPN
ejpam-2017	138	4	x	x	SYM
ejpam-2017	138	5	+	+	NUM
ejpam-2017	138	6	�	�	PROPN
ejpam-2017	138	7	0	0	NUM
ejpam-2017	138	8	1	1	NUM
ejpam-2017	138	9	�	�	PROPN
ejpam-2017	138	10	y.	y.	NOUN
ejpam-2017	138	11	each	each	DET
ejpam-2017	138	12	term	term	NOUN
ejpam-2017	138	13	on	on	ADP
ejpam-2017	138	14	the	the	DET
ejpam-2017	138	15	right	right	ADJ
ejpam-2017	138	16	-	-	PUNCT
ejpam-2017	138	17	hand	hand	NOUN
ejpam-2017	138	18	side	side	NOUN
ejpam-2017	138	19	is	be	AUX
ejpam-2017	138	20	in	in	ADP
ejpam-2017	138	21	the	the	DET
ejpam-2017	138	22	form	form	NOUN
ejpam-2017	138	23	of	of	ADP
ejpam-2017	138	24	a	a	DET
ejpam-2017	138	25	multiplication	multiplication	NOUN
ejpam-2017	138	26	of	of	ADP
ejpam-2017	138	27	a	a	DET
ejpam-2017	138	28	2×1	2×1	NUM
ejpam-2017	138	29	matrix	matrix	NOUN
ejpam-2017	138	30	and	and	CCONJ
ejpam-2017	138	31	a	a	DET
ejpam-2017	138	32	1×1	1×1	NUM
ejpam-2017	138	33	matrix	matrix	NOUN
ejpam-2017	138	34	.	.	PUNCT
ejpam-2017	139	1	application	application	NOUN
ejpam-2017	139	2	of	of	ADP
ejpam-2017	139	3	the	the	DET
ejpam-2017	139	4	rotation	rotation	NOUN
ejpam-2017	139	5	operator	operator	NOUN
ejpam-2017	139	6	that	that	PRON
ejpam-2017	139	7	rotates	rotate	VERB
ejpam-2017	139	8	each	each	DET
ejpam-2017	139	9	vector	vector	NOUN
ejpam-2017	139	10	counterclockwise	counterclockwise	NOUN
ejpam-2017	139	11	through	through	ADP
ejpam-2017	139	12	a	a	DET
ejpam-2017	139	13	fixed	fix	VERB
ejpam-2017	139	14	positive	positive	ADJ
ejpam-2017	139	15	angle	angle	NOUN
ejpam-2017	139	16	θ	θ	PROPN
ejpam-2017	139	17	yields	yield	VERB
ejpam-2017	139	18	r′	r′	PROPN
ejpam-2017	139	19	=	=	SYM
ejpam-2017	139	20	�	�	PROPN
ejpam-2017	139	21	x	x	PUNCT
ejpam-2017	139	22	′	′	NUM
ejpam-2017	139	23	y	y	NUM
ejpam-2017	139	24	′	′	NUM
ejpam-2017	139	25	�	�	PROPN
ejpam-2017	139	26	=	=	SYM
ejpam-2017	139	27	�	�	PROPN
ejpam-2017	139	28	cosθ	cosθ	PROPN
ejpam-2017	139	29	sinθ	sinθ	PROPN
ejpam-2017	139	30	�	�	PROPN
ejpam-2017	139	31	x	x	SYM
ejpam-2017	139	32	+	+	NUM
ejpam-2017	139	33	�	�	PROPN
ejpam-2017	139	34	−	−	PROPN
ejpam-2017	139	35	sinθ	sinθ	PROPN
ejpam-2017	139	36	cosθ	cosθ	PROPN
ejpam-2017	139	37	�	�	PROPN
ejpam-2017	139	38	y	y	PROPN
ejpam-2017	139	39	,	,	PUNCT
ejpam-2017	139	40	which	which	PRON
ejpam-2017	139	41	can	can	AUX
ejpam-2017	139	42	be	be	AUX
ejpam-2017	139	43	easily	easily	ADV
ejpam-2017	139	44	rewritten	rewrite	VERB
ejpam-2017	139	45	in	in	ADP
ejpam-2017	139	46	matrix	matrix	NOUN
ejpam-2017	139	47	form	form	NOUN
ejpam-2017	139	48	as	as	ADP
ejpam-2017	139	49	�	�	NOUN
ejpam-2017	139	50	x	x	NOUN
ejpam-2017	139	51	′	′	NUM
ejpam-2017	139	52	y	y	NUM
ejpam-2017	139	53	′	′	NUM
ejpam-2017	139	54	�	�	PROPN
ejpam-2017	139	55	=	=	SYM
ejpam-2017	139	56	�	�	PROPN
ejpam-2017	139	57	cosθ	cosθ	PROPN
ejpam-2017	139	58	−	−	PROPN
ejpam-2017	139	59	sinθ	sinθ	PROPN
ejpam-2017	139	60	sinθ	sinθ	PROPN
ejpam-2017	139	61	cosθ	cosθ	PROPN
ejpam-2017	139	62	�	�	PROPN
ejpam-2017	139	63	�	�	PROPN
ejpam-2017	139	64	x	x	SYM
ejpam-2017	139	65	y	y	PROPN
ejpam-2017	139	66	�	�	PROPN
ejpam-2017	139	67	.	.	PUNCT
ejpam-2017	140	1	if	if	SCONJ
ejpam-2017	140	2	we	we	PRON
ejpam-2017	140	3	express	express	VERB
ejpam-2017	140	4	r	r	NOUN
ejpam-2017	140	5	as	as	ADP
ejpam-2017	140	6	r=	r=	ADJ
ejpam-2017	140	7	�	�	PROPN
ejpam-2017	140	8	x	x	PUNCT
ejpam-2017	140	9	y	y	PROPN
ejpam-2017	140	10	�	�	PROPN
ejpam-2017	140	11	=	=	SYM
ejpam-2017	140	12	x	x	SYM
ejpam-2017	140	13	�	�	PROPN
ejpam-2017	140	14	1	1	NUM
ejpam-2017	140	15	0	0	NUM
ejpam-2017	140	16	�	�	PROPN
ejpam-2017	140	17	+	+	CCONJ
ejpam-2017	140	18	y	y	PROPN
ejpam-2017	140	19	�	�	PROPN
ejpam-2017	140	20	0	0	NUM
ejpam-2017	140	21	1	1	NUM
ejpam-2017	140	22	�	�	PROPN
ejpam-2017	140	23	,	,	PUNCT
ejpam-2017	140	24	we	we	PRON
ejpam-2017	140	25	obtain	obtain	VERB
ejpam-2017	140	26	r′	r′	NOUN
ejpam-2017	140	27	=	=	SYM
ejpam-2017	140	28	�	�	PROPN
ejpam-2017	140	29	x	x	PUNCT
ejpam-2017	140	30	′	′	NUM
ejpam-2017	140	31	y	y	NUM
ejpam-2017	140	32	′	′	NUM
ejpam-2017	140	33	�	�	PROPN
ejpam-2017	141	1	=	=	SYM
ejpam-2017	141	2	x	x	PROPN
ejpam-2017	141	3	�	�	PROPN
ejpam-2017	141	4	cosθ	cosθ	PROPN
ejpam-2017	141	5	sinθ	sinθ	PROPN
ejpam-2017	141	6	�	�	PROPN
ejpam-2017	141	7	+	+	CCONJ
ejpam-2017	141	8	y	y	PROPN
ejpam-2017	141	9	�	�	PROPN
ejpam-2017	141	10	−	−	PROPN
ejpam-2017	141	11	sinθ	sinθ	PROPN
ejpam-2017	141	12	cosθ	cosθ	PROPN
ejpam-2017	141	13	�	�	PROPN
ejpam-2017	141	14	.	.	PUNCT
ejpam-2017	142	1	in	in	ADP
ejpam-2017	142	2	expressing	express	VERB
ejpam-2017	142	3	this	this	DET
ejpam-2017	142	4	equation	equation	NOUN
ejpam-2017	142	5	in	in	ADP
ejpam-2017	142	6	matrix	matrix	NOUN
ejpam-2017	142	7	form	form	NOUN
ejpam-2017	142	8	,	,	PUNCT
ejpam-2017	142	9	we	we	PRON
ejpam-2017	142	10	must	must	AUX
ejpam-2017	142	11	rearrange	rearrange	VERB
ejpam-2017	142	12	the	the	DET
ejpam-2017	142	13	order	order	NOUN
ejpam-2017	142	14	of	of	ADP
ejpam-2017	142	15	x	x	SYM
ejpam-2017	142	16	,	,	PUNCT
ejpam-2017	142	17	y	y	PROPN
ejpam-2017	142	18	,	,	PUNCT
ejpam-2017	142	19	and	and	CCONJ
ejpam-2017	142	20	the	the	DET
ejpam-2017	142	21	trigonometric	trigonometric	ADJ
ejpam-2017	142	22	functions	function	NOUN
ejpam-2017	142	23	.	.	PUNCT
ejpam-2017	143	1	thus	thus	ADV
ejpam-2017	143	2	,	,	PUNCT
ejpam-2017	143	3	orders	order	NOUN
ejpam-2017	143	4	violating	violate	VERB
ejpam-2017	143	5	the	the	DET
ejpam-2017	143	6	rule	rule	NOUN
ejpam-2017	143	7	of	of	ADP
ejpam-2017	143	8	matrix	matrix	NOUN
ejpam-2017	143	9	multiplication	multiplication	NOUN
ejpam-2017	143	10	are	be	AUX
ejpam-2017	143	11	inconvenient	inconvenient	ADJ
ejpam-2017	143	12	.	.	PUNCT
ejpam-2017	144	1	similarly	similarly	ADV
ejpam-2017	144	2	,	,	PUNCT
ejpam-2017	144	3	the	the	DET
ejpam-2017	144	4	simultaneous	simultaneous	ADJ
ejpam-2017	144	5	equations	equation	NOUN
ejpam-2017	144	6	for	for	ADP
ejpam-2017	144	7	obtaining	obtain	VERB
ejpam-2017	144	8	the	the	DET
ejpam-2017	144	9	coefficients	coefficient	NOUN
ejpam-2017	144	10	of	of	ADP
ejpam-2017	144	11	a	a	DET
ejpam-2017	144	12	linear	linear	ADJ
ejpam-2017	144	13	combination	combination	NOUN
ejpam-2017	144	14	of	of	ADP
ejpam-2017	144	15	column	column	NOUN
ejpam-2017	144	16	vectors	vector	NOUN
ejpam-2017	144	17	,	,	PUNCT
ejpam-2017	144	18	c1	c1	PROPN
ejpam-2017	144	19	�	�	PROPN
ejpam-2017	144	20	5	5	NUM
ejpam-2017	144	21	2	2	NUM
ejpam-2017	144	22	�	�	PROPN
ejpam-2017	144	23	+	+	CCONJ
ejpam-2017	144	24	c2	c2	PROPN
ejpam-2017	144	25	�	�	PROPN
ejpam-2017	144	26	7	7	NUM
ejpam-2017	144	27	3	3	NUM
ejpam-2017	144	28	�	�	PROPN
ejpam-2017	144	29	=	=	SYM
ejpam-2017	144	30	�	�	PROPN
ejpam-2017	144	31	4	4	NUM
ejpam-2017	144	32	6	6	NUM
ejpam-2017	144	33	�	�	PROPN
ejpam-2017	144	34	,	,	PUNCT
ejpam-2017	144	35	are	be	AUX
ejpam-2017	144	36	�	�	PROPN
ejpam-2017	144	37	5c1	5c1	NUM
ejpam-2017	144	38	+	+	CCONJ
ejpam-2017	144	39	7c2	7c2	NUM
ejpam-2017	145	1	=	=	SYM
ejpam-2017	145	2	4	4	NUM
ejpam-2017	145	3	2c1	2c1	NUM
ejpam-2017	146	1	+	+	CCONJ
ejpam-2017	146	2	3c2	3c2	NUM
ejpam-2017	146	3	=	=	SYM
ejpam-2017	146	4	6	6	NUM
ejpam-2017	146	5	,	,	PUNCT
ejpam-2017	146	6	in	in	ADP
ejpam-2017	146	7	which	which	PRON
ejpam-2017	146	8	c15	c15	NOUN
ejpam-2017	146	9	,	,	PUNCT
ejpam-2017	146	10	c27	c27	NOUN
ejpam-2017	146	11	,	,	PUNCT
ejpam-2017	146	12	and	and	CCONJ
ejpam-2017	146	13	so	so	ADV
ejpam-2017	146	14	on	on	ADV
ejpam-2017	146	15	are	be	AUX
ejpam-2017	146	16	commuted	commute	VERB
ejpam-2017	146	17	into	into	ADP
ejpam-2017	146	18	5c1	5c1	NOUN
ejpam-2017	146	19	,	,	PUNCT
ejpam-2017	146	20	7c2	7c2	NUM
ejpam-2017	146	21	,	,	PUNCT
ejpam-2017	146	22	and	and	CCONJ
ejpam-2017	146	23	so	so	ADV
ejpam-2017	146	24	on	on	ADV
ejpam-2017	146	25	.	.	PUNCT
ejpam-2017	147	1	these	these	DET
ejpam-2017	147	2	simultaneous	simultaneous	ADJ
ejpam-2017	147	3	equations	equation	NOUN
ejpam-2017	147	4	are	be	AUX
ejpam-2017	147	5	equivalent	equivalent	ADJ
ejpam-2017	147	6	to	to	ADP
ejpam-2017	147	7	that	that	PRON
ejpam-2017	147	8	using	use	VERB
ejpam-2017	147	9	the	the	DET
ejpam-2017	147	10	transpose	transpose	NOUN
ejpam-2017	147	11	of	of	ADP
ejpam-2017	147	12	the	the	DET
ejpam-2017	147	13	original	original	ADJ
ejpam-2017	147	14	column	column	NOUN
ejpam-2017	147	15	vectors	vector	NOUN
ejpam-2017	147	16	,	,	PUNCT
ejpam-2017	147	17	(	(	PUNCT
ejpam-2017	147	18	5	5	NUM
ejpam-2017	147	19	2)c1	2)c1	NUM
ejpam-2017	147	20	+	+	CCONJ
ejpam-2017	147	21	(	(	PUNCT
ejpam-2017	147	22	7	7	NUM
ejpam-2017	147	23	3)c2	3)c2	NUM
ejpam-2017	147	24	=	=	SYM
ejpam-2017	147	25	(	(	PUNCT
ejpam-2017	147	26	4	4	NUM
ejpam-2017	147	27	6	6	NUM
ejpam-2017	147	28	)	)	PUNCT
ejpam-2017	147	29	.	.	PUNCT
ejpam-2017	148	1	if	if	SCONJ
ejpam-2017	148	2	we	we	PRON
ejpam-2017	148	3	express	express	VERB
ejpam-2017	148	4	the	the	DET
ejpam-2017	148	5	vector	vector	NOUN
ejpam-2017	148	6	equation	equation	NOUN
ejpam-2017	148	7	as	as	ADP
ejpam-2017	148	8	�	�	PROPN
ejpam-2017	148	9	5	5	NUM
ejpam-2017	148	10	2	2	NUM
ejpam-2017	148	11	�	�	PROPN
ejpam-2017	148	12	c1	c1	NOUN
ejpam-2017	148	13	+	+	CCONJ
ejpam-2017	148	14	�	�	PROPN
ejpam-2017	148	15	7	7	NUM
ejpam-2017	148	16	3	3	NUM
ejpam-2017	148	17	�	�	PROPN
ejpam-2017	148	18	c2	c2	PROPN
ejpam-2017	148	19	=	=	SYM
ejpam-2017	148	20	�	�	PROPN
ejpam-2017	148	21	4	4	NUM
ejpam-2017	148	22	6	6	NUM
ejpam-2017	148	23	�	�	PROPN
ejpam-2017	148	24	following	follow	VERB
ejpam-2017	148	25	the	the	DET
ejpam-2017	148	26	rule	rule	NOUN
ejpam-2017	148	27	of	of	ADP
ejpam-2017	148	28	matrix	matrix	NOUN
ejpam-2017	148	29	multiplication	multiplication	NOUN
ejpam-2017	148	30	,	,	PUNCT
ejpam-2017	148	31	we	we	PRON
ejpam-2017	148	32	need	need	AUX
ejpam-2017	148	33	not	not	PART
ejpam-2017	148	34	commute	commute	VERB
ejpam-2017	148	35	the	the	DET
ejpam-2017	148	36	order	order	NOUN
ejpam-2017	148	37	of	of	ADP
ejpam-2017	148	38	multiplication	multiplication	NOUN
ejpam-2017	148	39	in	in	ADP
ejpam-2017	148	40	the	the	DET
ejpam-2017	148	41	simultaneous	simultaneous	ADJ
ejpam-2017	148	42	equations	equation	NOUN
ejpam-2017	148	43	.	.	PUNCT
ejpam-2017	149	1	references	reference	NOUN
ejpam-2017	149	2	411	411	NUM
ejpam-2017	149	3	5	5	NUM
ejpam-2017	149	4	.	.	PUNCT
ejpam-2017	149	5	conclusion	conclusion	NOUN
ejpam-2017	149	6	according	accord	VERB
ejpam-2017	149	7	to	to	ADP
ejpam-2017	149	8	the	the	DET
ejpam-2017	149	9	standard	standard	ADJ
ejpam-2017	149	10	interpretation	interpretation	NOUN
ejpam-2017	149	11	,	,	PUNCT
ejpam-2017	149	12	the	the	DET
ejpam-2017	149	13	commutative	commutative	ADJ
ejpam-2017	149	14	law	law	NOUN
ejpam-2017	149	15	for	for	ADP
ejpam-2017	149	16	multiplication	multiplication	NOUN
ejpam-2017	149	17	,	,	PUNCT
ejpam-2017	149	18	ab	ab	PROPN
ejpam-2017	149	19	=	=	SYM
ejpam-2017	149	20	ba	ba	PROPN
ejpam-2017	149	21	,	,	PUNCT
ejpam-2017	149	22	is	be	AUX
ejpam-2017	149	23	not	not	PART
ejpam-2017	149	24	valid	valid	ADJ
ejpam-2017	149	25	in	in	ADP
ejpam-2017	149	26	matrix	matrix	NOUN
ejpam-2017	149	27	arithmetic	arithmetic	NOUN
ejpam-2017	149	28	.	.	PUNCT
ejpam-2017	150	1	instead	instead	ADV
ejpam-2017	150	2	,	,	PUNCT
ejpam-2017	150	3	we	we	PRON
ejpam-2017	150	4	can	can	AUX
ejpam-2017	150	5	interpret	interpret	VERB
ejpam-2017	150	6	that	that	PRON
ejpam-2017	150	7	(	(	PUNCT
ejpam-2017	150	8	ab)t	ab)t	PROPN
ejpam-2017	150	9	=	=	PUNCT
ejpam-2017	150	10	bt	bt	PROPN
ejpam-2017	150	11	at	at	ADP
ejpam-2017	150	12	is	be	AUX
ejpam-2017	150	13	a	a	DET
ejpam-2017	150	14	rule	rule	NOUN
ejpam-2017	150	15	of	of	ADP
ejpam-2017	150	16	matrix	matrix	NOUN
ejpam-2017	150	17	arithmetic	arithmetic	ADJ
ejpam-2017	150	18	.	.	PUNCT
ejpam-2017	151	1	the	the	DET
ejpam-2017	151	2	commutative	commutative	ADJ
ejpam-2017	151	3	law	law	NOUN
ejpam-2017	151	4	for	for	ADP
ejpam-2017	151	5	multiplication	multiplication	NOUN
ejpam-2017	151	6	,	,	PUNCT
ejpam-2017	151	7	ab	ab	PROPN
ejpam-2017	151	8	=	=	SYM
ejpam-2017	151	9	ba	ba	PROPN
ejpam-2017	151	10	,	,	PUNCT
ejpam-2017	151	11	for	for	ADP
ejpam-2017	151	12	any	any	DET
ejpam-2017	151	13	real	real	ADJ
ejpam-2017	151	14	numbers	number	NOUN
ejpam-2017	151	15	a	a	PRON
ejpam-2017	151	16	and	and	CCONJ
ejpam-2017	151	17	b	b	NOUN
ejpam-2017	151	18	can	can	AUX
ejpam-2017	151	19	be	be	AUX
ejpam-2017	151	20	regarded	regard	VERB
ejpam-2017	151	21	as	as	ADP
ejpam-2017	151	22	a	a	DET
ejpam-2017	151	23	spacial	spacial	ADJ
ejpam-2017	151	24	case	case	NOUN
ejpam-2017	151	25	of	of	ADP
ejpam-2017	151	26	(	(	PUNCT
ejpam-2017	151	27	ab)t	ab)t	PROPN
ejpam-2017	151	28	=	=	PUNCT
ejpam-2017	151	29	bt	bt	PROPN
ejpam-2017	151	30	at	at	ADP
ejpam-2017	151	31	.	.	PUNCT
ejpam-2017	152	1	the	the	DET
ejpam-2017	152	2	transpose	transpose	NOUN
ejpam-2017	152	3	of	of	ADP
ejpam-2017	152	4	a	a	DET
ejpam-2017	152	5	matrix	matrix	NOUN
ejpam-2017	152	6	conserves	conserve	VERB
ejpam-2017	152	7	“	"	PUNCT
ejpam-2017	152	8	the	the	DET
ejpam-2017	152	9	principle	principle	NOUN
ejpam-2017	152	10	of	of	ADP
ejpam-2017	152	11	the	the	DET
ejpam-2017	152	12	permanence	permanence	NOUN
ejpam-2017	152	13	of	of	ADP
ejpam-2017	152	14	form	form	NOUN
ejpam-2017	152	15	and	and	CCONJ
ejpam-2017	152	16	its	its	PRON
ejpam-2017	152	17	transition	transition	NOUN
ejpam-2017	152	18	”	"	PUNCT
ejpam-2017	152	19	for	for	ADP
ejpam-2017	152	20	the	the	DET
ejpam-2017	152	21	commutative	commutative	ADJ
ejpam-2017	152	22	law	law	NOUN
ejpam-2017	152	23	for	for	ADP
ejpam-2017	152	24	multiplication	multiplication	NOUN
ejpam-2017	152	25	.	.	PUNCT
ejpam-2017	153	1	this	this	DET
ejpam-2017	153	2	view	view	NOUN
ejpam-2017	153	3	indicates	indicate	VERB
ejpam-2017	153	4	that	that	SCONJ
ejpam-2017	153	5	we	we	PRON
ejpam-2017	153	6	can	can	AUX
ejpam-2017	153	7	unify	unify	VERB
ejpam-2017	153	8	a	a	DET
ejpam-2017	153	9	rule	rule	NOUN
ejpam-2017	153	10	of	of	ADP
ejpam-2017	153	11	matrix	matrix	NOUN
ejpam-2017	153	12	arithmetic	arithmetic	ADJ
ejpam-2017	153	13	and	and	CCONJ
ejpam-2017	153	14	that	that	PRON
ejpam-2017	153	15	of	of	ADP
ejpam-2017	153	16	real	real	ADJ
ejpam-2017	153	17	number	number	NOUN
ejpam-2017	153	18	algebra	algebra	NOUN
ejpam-2017	153	19	to	to	PART
ejpam-2017	153	20	avoid	avoid	VERB
ejpam-2017	153	21	the	the	DET
ejpam-2017	153	22	exception	exception	NOUN
ejpam-2017	153	23	.	.	PUNCT
ejpam-2017	154	1	from	from	ADP
ejpam-2017	154	2	this	this	DET
ejpam-2017	154	3	point	point	NOUN
ejpam-2017	154	4	of	of	ADP
ejpam-2017	154	5	view	view	NOUN
ejpam-2017	154	6	,	,	PUNCT
ejpam-2017	154	7	the	the	DET
ejpam-2017	154	8	right	right	ADJ
ejpam-2017	154	9	multiplication	multiplication	NOUN
ejpam-2017	154	10	of	of	ADP
ejpam-2017	154	11	a	a	DET
ejpam-2017	154	12	column	column	NOUN
ejpam-2017	154	13	vector	vector	NOUN
ejpam-2017	154	14	with	with	ADP
ejpam-2017	154	15	a	a	DET
ejpam-2017	154	16	scalar	scalar	NOUN
ejpam-2017	154	17	is	be	AUX
ejpam-2017	154	18	the	the	DET
ejpam-2017	154	19	matrix	matrix	NOUN
ejpam-2017	154	20	multiplication	multiplication	NOUN
ejpam-2017	154	21	of	of	ADP
ejpam-2017	154	22	a	a	DET
ejpam-2017	154	23	n	n	NUM
ejpam-2017	154	24	×	×	NOUN
ejpam-2017	154	25	1	1	NUM
ejpam-2017	154	26	matrix	matrix	NOUN
ejpam-2017	154	27	and	and	CCONJ
ejpam-2017	154	28	a	a	DET
ejpam-2017	154	29	1	1	NUM
ejpam-2017	154	30	×	×	NOUN
ejpam-2017	154	31	1	1	NUM
ejpam-2017	154	32	matrix	matrix	NOUN
ejpam-2017	154	33	,	,	PUNCT
ejpam-2017	154	34	which	which	PRON
ejpam-2017	154	35	is	be	AUX
ejpam-2017	154	36	compatible	compatible	ADJ
ejpam-2017	154	37	with	with	ADP
ejpam-2017	154	38	the	the	DET
ejpam-2017	154	39	definition	definition	NOUN
ejpam-2017	154	40	of	of	ADP
ejpam-2017	154	41	matrix	matrix	NOUN
ejpam-2017	154	42	multiplication	multiplication	NOUN
ejpam-2017	154	43	in	in	ADP
ejpam-2017	154	44	contrast	contrast	NOUN
ejpam-2017	154	45	to	to	ADP
ejpam-2017	154	46	the	the	DET
ejpam-2017	154	47	left	left	ADJ
ejpam-2017	154	48	multiplication	multiplication	NOUN
ejpam-2017	154	49	of	of	ADP
ejpam-2017	154	50	a	a	DET
ejpam-2017	154	51	column	column	NOUN
ejpam-2017	154	52	vector	vector	NOUN
ejpam-2017	154	53	with	with	ADP
ejpam-2017	154	54	a	a	DET
ejpam-2017	154	55	scalar	scalar	NOUN
ejpam-2017	154	56	.	.	PUNCT
ejpam-2017	155	1	for	for	ADP
ejpam-2017	155	2	example	example	NOUN
ejpam-2017	155	3	,	,	PUNCT
ejpam-2017	155	4	as	as	SCONJ
ejpam-2017	155	5	shown	show	VERB
ejpam-2017	155	6	in	in	ADP
ejpam-2017	155	7	section	section	NOUN
ejpam-2017	155	8	4	4	NUM
ejpam-2017	155	9	,	,	PUNCT
ejpam-2017	155	10	the	the	DET
ejpam-2017	155	11	process	process	NOUN
ejpam-2017	155	12	of	of	ADP
ejpam-2017	155	13	finding	find	VERB
ejpam-2017	155	14	a	a	DET
ejpam-2017	155	15	corresponding	correspond	VERB
ejpam-2017	155	16	diagonal	diagonal	ADJ
ejpam-2017	155	17	matrix	matrix	NOUN
ejpam-2017	155	18	for	for	ADP
ejpam-2017	155	19	a	a	DET
ejpam-2017	155	20	diagonalizable	diagonalizable	ADJ
ejpam-2017	155	21	matrix	matrix	NOUN
ejpam-2017	155	22	becomes	become	VERB
ejpam-2017	155	23	clear	clear	ADJ
ejpam-2017	155	24	by	by	ADP
ejpam-2017	155	25	considering	consider	VERB
ejpam-2017	155	26	a	a	DET
ejpam-2017	155	27	scalar	scalar	ADJ
ejpam-2017	155	28	multiple	multiple	NOUN
ejpam-2017	155	29	the	the	DET
ejpam-2017	155	30	right	right	ADJ
ejpam-2017	155	31	multiplication	multiplication	NOUN
ejpam-2017	155	32	of	of	ADP
ejpam-2017	155	33	a	a	DET
ejpam-2017	155	34	column	column	NOUN
ejpam-2017	155	35	vector	vector	NOUN
ejpam-2017	155	36	with	with	ADP
ejpam-2017	155	37	a	a	DET
ejpam-2017	155	38	scalar	scalar	NOUN
ejpam-2017	155	39	.	.	PUNCT
ejpam-2017	156	1	if	if	SCONJ
ejpam-2017	156	2	we	we	PRON
ejpam-2017	156	3	omit	omit	VERB
ejpam-2017	156	4	the	the	DET
ejpam-2017	156	5	brackets	bracket	NOUN
ejpam-2017	156	6	on	on	ADP
ejpam-2017	156	7	a	a	DET
ejpam-2017	156	8	1×1	1×1	NUM
ejpam-2017	156	9	matrix	matrix	NOUN
ejpam-2017	156	10	,	,	PUNCT
ejpam-2017	156	11	it	it	PRON
ejpam-2017	156	12	is	be	AUX
ejpam-2017	156	13	impossible	impossible	ADJ
ejpam-2017	156	14	to	to	PART
ejpam-2017	156	15	distinguish	distinguish	VERB
ejpam-2017	156	16	between	between	ADP
ejpam-2017	156	17	the	the	DET
ejpam-2017	156	18	number	number	NOUN
ejpam-2017	156	19	and	and	CCONJ
ejpam-2017	156	20	the	the	DET
ejpam-2017	156	21	1×	1×	NUM
ejpam-2017	156	22	1	1	NUM
ejpam-2017	156	23	matrix	matrix	NOUN
ejpam-2017	156	24	whose	whose	DET
ejpam-2017	156	25	entry	entry	NOUN
ejpam-2017	156	26	takes	take	VERB
ejpam-2017	156	27	the	the	DET
ejpam-2017	156	28	same	same	ADJ
ejpam-2017	156	29	value	value	NOUN
ejpam-2017	156	30	as	as	ADP
ejpam-2017	156	31	the	the	DET
ejpam-2017	156	32	number	number	NOUN
ejpam-2017	156	33	.	.	PUNCT
ejpam-2017	157	1	however	however	ADV
ejpam-2017	157	2	,	,	PUNCT
ejpam-2017	157	3	it	it	PRON
ejpam-2017	157	4	is	be	AUX
ejpam-2017	157	5	usually	usually	ADV
ejpam-2017	157	6	possible	possible	ADJ
ejpam-2017	157	7	to	to	PART
ejpam-2017	157	8	tell	tell	VERB
ejpam-2017	157	9	which	which	PRON
ejpam-2017	157	10	is	be	AUX
ejpam-2017	157	11	meant	mean	VERB
ejpam-2017	157	12	from	from	ADP
ejpam-2017	157	13	the	the	DET
ejpam-2017	157	14	context	context	NOUN
ejpam-2017	157	15	in	in	ADP
ejpam-2017	157	16	which	which	PRON
ejpam-2017	157	17	the	the	DET
ejpam-2017	157	18	symbol	symbol	NOUN
ejpam-2017	157	19	appears	appear	VERB
ejpam-2017	157	20	[	[	X
ejpam-2017	157	21	1	1	NUM
ejpam-2017	157	22	]	]	PUNCT
ejpam-2017	157	23	.	.	PUNCT
ejpam-2017	158	1	scalar	scalar	ADJ
ejpam-2017	158	2	multiplication	multiplication	NOUN
ejpam-2017	158	3	implies	imply	VERB
ejpam-2017	158	4	homothety	homothety	NOUN
ejpam-2017	158	5	,	,	PUNCT
ejpam-2017	158	6	and	and	CCONJ
ejpam-2017	158	7	thus	thus	ADV
ejpam-2017	158	8	the	the	DET
ejpam-2017	158	9	scalar	scalar	NOUN
ejpam-2017	158	10	can	can	AUX
ejpam-2017	158	11	be	be	AUX
ejpam-2017	158	12	regarded	regard	VERB
ejpam-2017	158	13	as	as	ADP
ejpam-2017	158	14	a	a	DET
ejpam-2017	158	15	1×	1×	NUM
ejpam-2017	158	16	1	1	NUM
ejpam-2017	158	17	matrix	matrix	NOUN
ejpam-2017	158	18	or	or	CCONJ
ejpam-2017	158	19	an	an	DET
ejpam-2017	158	20	abbreviation	abbreviation	NOUN
ejpam-2017	158	21	of	of	ADP
ejpam-2017	158	22	a	a	DET
ejpam-2017	158	23	scalar	scalar	ADJ
ejpam-2017	158	24	matrix	matrix	NOUN
ejpam-2017	158	25	as	as	SCONJ
ejpam-2017	158	26	shown	show	VERB
ejpam-2017	158	27	in	in	ADP
ejpam-2017	158	28	section	section	NOUN
ejpam-2017	158	29	3	3	NUM
ejpam-2017	159	1	.	.	PUNCT
ejpam-2017	159	2	references	reference	NOUN
ejpam-2017	159	3	[	[	X
ejpam-2017	159	4	1	1	NUM
ejpam-2017	159	5	]	]	PUNCT
ejpam-2017	159	6	h	h	NOUN
ejpam-2017	159	7	anton	anton	NOUN
ejpam-2017	159	8	and	and	CCONJ
ejpam-2017	159	9	c	c	NOUN
ejpam-2017	159	10	rorres	rorre	NOUN
ejpam-2017	159	11	.	.	PUNCT
ejpam-2017	160	1	elementary	elementary	ADJ
ejpam-2017	160	2	linear	linear	PROPN
ejpam-2017	160	3	algebra	algebra	PROPN
ejpam-2017	160	4	applications	application	NOUN
ejpam-2017	160	5	version	version	NOUN
ejpam-2017	160	6	.	.	PUNCT
ejpam-2017	161	1	john	john	PROPN
ejpam-2017	161	2	wiley	wiley	PROPN
ejpam-2017	161	3	&	&	CCONJ
ejpam-2017	161	4	sons	son	NOUN
ejpam-2017	161	5	,	,	PUNCT
ejpam-2017	161	6	new	new	PROPN
ejpam-2017	161	7	york	york	PROPN
ejpam-2017	161	8	,	,	PUNCT
ejpam-2017	161	9	1994	1994	NUM
ejpam-2017	161	10	.	.	PUNCT
ejpam-2017	162	1	[	[	X
ejpam-2017	162	2	2	2	NUM
ejpam-2017	162	3	]	]	X
ejpam-2017	162	4	e	e	X
ejpam-2017	162	5	e	e	X
ejpam-2017	162	6	escultura	escultura	PROPN
ejpam-2017	162	7	.	.	PROPN
ejpam-2017	162	8	creative	creative	ADJ
ejpam-2017	162	9	mathematics	mathematic	NOUN
ejpam-2017	162	10	education	education	NOUN
ejpam-2017	162	11	.	.	PUNCT
ejpam-2017	163	1	creative	creative	ADJ
ejpam-2017	163	2	education	education	NOUN
ejpam-2017	163	3	,	,	PUNCT
ejpam-2017	163	4	3	3	NUM
ejpam-2017	163	5	,	,	PUNCT
ejpam-2017	163	6	45	45	NUM
ejpam-2017	163	7	-	-	SYM
ejpam-2017	163	8	54	54	NUM
ejpam-2017	163	9	(	(	PUNCT
ejpam-2017	163	10	2012	2012	NUM
ejpam-2017	163	11	)	)	PUNCT
ejpam-2017	163	12	.	.	PUNCT
ejpam-2017	164	1	[	[	X
ejpam-2017	164	2	3	3	X
ejpam-2017	164	3	]	]	X
ejpam-2017	164	4	y	y	PROPN
ejpam-2017	164	5	itagaki	itagaki	PROPN
ejpam-2017	164	6	.	.	PUNCT
ejpam-2017	165	1	the	the	DET
ejpam-2017	165	2	concept	concept	NOUN
ejpam-2017	165	3	of	of	ADP
ejpam-2017	165	4	rational	rational	ADJ
ejpam-2017	165	5	numbers	number	NOUN
ejpam-2017	165	6	:	:	PUNCT
ejpam-2017	165	7	a	a	DET
ejpam-2017	165	8	study	study	NOUN
ejpam-2017	165	9	of	of	ADP
ejpam-2017	165	10	the	the	DET
ejpam-2017	165	11	view	view	NOUN
ejpam-2017	165	12	on	on	ADP
ejpam-2017	165	13	the	the	DET
ejpam-2017	165	14	principle	principle	NOUN
ejpam-2017	165	15	of	of	ADP
ejpam-2017	165	16	the	the	DET
ejpam-2017	165	17	permanence	permanence	NOUN
ejpam-2017	165	18	of	of	ADP
ejpam-2017	165	19	form	form	NOUN
ejpam-2017	165	20	and	and	CCONJ
ejpam-2017	165	21	its	its	PRON
ejpam-2017	165	22	transition	transition	NOUN
ejpam-2017	165	23	.	.	PUNCT
ejpam-2017	166	1	journal	journal	PROPN
ejpam-2017	166	2	of	of	ADP
ejpam-2017	166	3	japan	japan	PROPN
ejpam-2017	166	4	society	society	PROPN
ejpam-2017	166	5	of	of	ADP
ejpam-2017	166	6	mathematical	mathematical	ADJ
ejpam-2017	166	7	education	education	NOUN
ejpam-2017	166	8	,	,	PUNCT
ejpam-2017	166	9	67	67	NUM
ejpam-2017	166	10	,	,	PUNCT
ejpam-2017	166	11	114	114	NUM
ejpam-2017	166	12	-	-	SYM
ejpam-2017	166	13	121	121	NUM
ejpam-2017	166	14	(	(	PUNCT
ejpam-2017	166	15	1985	1985	NUM
ejpam-2017	166	16	)	)	PUNCT
ejpam-2017	167	1	[	[	X
ejpam-2017	167	2	in	in	ADP
ejpam-2017	167	3	japanese	japanese	PROPN
ejpam-2017	167	4	]	]	PUNCT
ejpam-2017	167	5	.	.	PUNCT