id	sid	tid	token	lemma	pos
ejpam-1624	1	1	5_xie.dvi	5_xie.dvi	NUM
ejpam-1624	1	2	european	european	ADJ
ejpam-1624	1	3	journal	journal	PROPN
ejpam-1624	1	4	of	of	ADP
ejpam-1624	1	5	pure	pure	ADJ
ejpam-1624	1	6	and	and	CCONJ
ejpam-1624	1	7	applied	apply	VERB
ejpam-1624	1	8	mathematics	mathematic	NOUN
ejpam-1624	1	9	vol	vol	NOUN
ejpam-1624	1	10	.	.	PROPN
ejpam-1624	1	11	5	5	NUM
ejpam-1624	1	12	,	,	PUNCT
ejpam-1624	1	13	no	no	INTJ
ejpam-1624	1	14	.	.	NOUN
ejpam-1624	1	15	4	4	NUM
ejpam-1624	1	16	,	,	PUNCT
ejpam-1624	1	17	2012	2012	NUM
ejpam-1624	1	18	,	,	PUNCT
ejpam-1624	1	19	480	480	NUM
ejpam-1624	1	20	-	-	SYM
ejpam-1624	1	21	491	491	NUM
ejpam-1624	1	22	issn	issn	PROPN
ejpam-1624	1	23	1307	1307	NUM
ejpam-1624	1	24	-	-	SYM
ejpam-1624	1	25	5543	5543	NUM
ejpam-1624	1	26	–	–	PUNCT
ejpam-1624	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1624	1	28	the	the	DET
ejpam-1624	1	29	drazin	drazin	PROPN
ejpam-1624	1	30	inverses	inverse	NOUN
ejpam-1624	1	31	of	of	ADP
ejpam-1624	1	32	combinations	combination	NOUN
ejpam-1624	1	33	of	of	ADP
ejpam-1624	1	34	two	two	NUM
ejpam-1624	1	35	idempotents	idempotent	NOUN
ejpam-1624	1	36	tao	tao	PROPN
ejpam-1624	1	37	xie∗	xie∗	PROPN
ejpam-1624	1	38	,	,	PUNCT
ejpam-1624	1	39	kezheng	kezheng	PROPN
ejpam-1624	1	40	zuo	zuo	PROPN
ejpam-1624	1	41	math	math	PROPN
ejpam-1624	1	42	department	department	PROPN
ejpam-1624	1	43	,	,	PUNCT
ejpam-1624	1	44	hubei	hubei	PROPN
ejpam-1624	1	45	normal	normal	ADJ
ejpam-1624	1	46	university	university	PROPN
ejpam-1624	1	47	,	,	PUNCT
ejpam-1624	1	48	hubei	hubei	PROPN
ejpam-1624	1	49	,	,	PUNCT
ejpam-1624	1	50	huangshi	huangshi	NOUN
ejpam-1624	1	51	,	,	PUNCT
ejpam-1624	1	52	435002	435002	NUM
ejpam-1624	1	53	,	,	PUNCT
ejpam-1624	1	54	china	china	PROPN
ejpam-1624	1	55	abstract	abstract	NOUN
ejpam-1624	1	56	.	.	PUNCT
ejpam-1624	2	1	by	by	ADP
ejpam-1624	2	2	using	use	VERB
ejpam-1624	2	3	the	the	DET
ejpam-1624	2	4	methods	method	NOUN
ejpam-1624	2	5	of	of	ADP
ejpam-1624	2	6	splitting	splitting	NOUN
ejpam-1624	2	7	operator	operator	NOUN
ejpam-1624	2	8	’s	’s	PART
ejpam-1624	2	9	matrix	matrix	NOUN
ejpam-1624	2	10	into	into	ADP
ejpam-1624	2	11	blocks	block	NOUN
ejpam-1624	2	12	and	and	CCONJ
ejpam-1624	2	13	space	space	NOUN
ejpam-1624	2	14	decompositions	decomposition	NOUN
ejpam-1624	2	15	,	,	PUNCT
ejpam-1624	2	16	the	the	DET
ejpam-1624	2	17	existence	existence	NOUN
ejpam-1624	2	18	and	and	CCONJ
ejpam-1624	2	19	calculation	calculation	NOUN
ejpam-1624	2	20	formulas	formula	NOUN
ejpam-1624	2	21	of	of	ADP
ejpam-1624	2	22	drazin	drazin	PROPN
ejpam-1624	2	23	inverse	inverse	NOUN
ejpam-1624	2	24	of	of	ADP
ejpam-1624	2	25	the	the	DET
ejpam-1624	2	26	combinations	combination	NOUN
ejpam-1624	2	27	ap	ap	PROPN
ejpam-1624	2	28	+	+	CCONJ
ejpam-1624	2	29	bq+	bq+	NOUN
ejpam-1624	2	30	cpq+	cpq+	ADP
ejpam-1624	2	31	dqp	dqp	NOUN
ejpam-1624	2	32	of	of	ADP
ejpam-1624	2	33	two	two	NUM
ejpam-1624	2	34	idempotent	idempotent	ADJ
ejpam-1624	2	35	operators	operator	NOUN
ejpam-1624	2	36	p	p	NOUN
ejpam-1624	2	37	and	and	CCONJ
ejpam-1624	2	38	q	q	NOUN
ejpam-1624	2	39	on	on	ADP
ejpam-1624	2	40	a	a	DET
ejpam-1624	2	41	hilbert	hilbert	NOUN
ejpam-1624	2	42	space	space	NOUN
ejpam-1624	2	43	are	be	AUX
ejpam-1624	2	44	obtained	obtain	VERB
ejpam-1624	2	45	under	under	ADP
ejpam-1624	2	46	the	the	DET
ejpam-1624	2	47	conditions	condition	NOUN
ejpam-1624	2	48	pqp	pqp	NOUN
ejpam-1624	2	49	=	=	SYM
ejpam-1624	2	50	0	0	NUM
ejpam-1624	2	51	,	,	PUNCT
ejpam-1624	2	52	pqp	pqp	NOUN
ejpam-1624	2	53	=	=	SYM
ejpam-1624	2	54	p	p	NOUN
ejpam-1624	2	55	and	and	CCONJ
ejpam-1624	2	56	pqp	pqp	NOUN
ejpam-1624	3	1	=	=	SYM
ejpam-1624	3	2	pq	pq	X
ejpam-1624	3	3	respectively	respectively	ADV
ejpam-1624	3	4	.	.	PUNCT
ejpam-1624	4	1	these	these	PRON
ejpam-1624	4	2	generalized	generalize	VERB
ejpam-1624	4	3	the	the	DET
ejpam-1624	4	4	related	related	ADJ
ejpam-1624	4	5	results	result	NOUN
ejpam-1624	4	6	of	of	ADP
ejpam-1624	4	7	deng	deng	PROPN
ejpam-1624	4	8	’s	’s	PART
ejpam-1624	4	9	work	work	NOUN
ejpam-1624	4	10	,	,	PUNCT
ejpam-1624	4	11	which	which	PRON
ejpam-1624	4	12	characterized	characterize	VERB
ejpam-1624	4	13	the	the	DET
ejpam-1624	4	14	drazin	drazin	PROPN
ejpam-1624	4	15	inverse	inverse	NOUN
ejpam-1624	4	16	of	of	ADP
ejpam-1624	4	17	the	the	DET
ejpam-1624	4	18	sum	sum	NOUN
ejpam-1624	4	19	and	and	CCONJ
ejpam-1624	4	20	difference	difference	NOUN
ejpam-1624	4	21	of	of	ADP
ejpam-1624	4	22	two	two	NUM
ejpam-1624	4	23	idempotents	idempotent	NOUN
ejpam-1624	4	24	.	.	PUNCT
ejpam-1624	5	1	2010	2010	NUM
ejpam-1624	5	2	mathematics	mathematic	NOUN
ejpam-1624	5	3	subject	subject	NOUN
ejpam-1624	5	4	classifications	classification	NOUN
ejpam-1624	5	5	:	:	PUNCT
ejpam-1624	5	6	15a09	15a09	NUM
ejpam-1624	5	7	,	,	PUNCT
ejpam-1624	5	8	47a05	47a05	NUM
ejpam-1624	5	9	key	key	ADJ
ejpam-1624	5	10	words	word	NOUN
ejpam-1624	5	11	and	and	CCONJ
ejpam-1624	5	12	phrases	phrase	NOUN
ejpam-1624	5	13	:	:	PUNCT
ejpam-1624	5	14	idempotent	idempotent	ADJ
ejpam-1624	5	15	operator	operator	NOUN
ejpam-1624	5	16	;	;	PUNCT
ejpam-1624	5	17	drazin	drazin	PROPN
ejpam-1624	5	18	inverse	inverse	NOUN
ejpam-1624	5	19	;	;	PUNCT
ejpam-1624	5	20	combination	combination	NOUN
ejpam-1624	5	21	1	1	NUM
ejpam-1624	5	22	.	.	PUNCT
ejpam-1624	6	1	preliminaries	preliminary	NOUN
ejpam-1624	6	2	let	let	VERB
ejpam-1624	6	3	h	h	NOUN
ejpam-1624	6	4	be	be	AUX
ejpam-1624	6	5	a	a	DET
ejpam-1624	6	6	hilbert	hilbert	NOUN
ejpam-1624	6	7	space	space	NOUN
ejpam-1624	6	8	,	,	PUNCT
ejpam-1624	6	9	the	the	DET
ejpam-1624	6	10	set	set	NOUN
ejpam-1624	6	11	of	of	ADP
ejpam-1624	6	12	all	all	DET
ejpam-1624	6	13	bounded	bound	VERB
ejpam-1624	6	14	linear	linear	PROPN
ejpam-1624	6	15	operators	operator	NOUN
ejpam-1624	6	16	on	on	ADP
ejpam-1624	6	17	h	h	NOUN
ejpam-1624	6	18	is	be	AUX
ejpam-1624	6	19	denoted	denote	VERB
ejpam-1624	6	20	by	by	ADP
ejpam-1624	6	21	b(h	b(h	PROPN
ejpam-1624	6	22	)	)	PUNCT
ejpam-1624	6	23	.	.	PUNCT
ejpam-1624	7	1	for	for	ADP
ejpam-1624	7	2	an	an	DET
ejpam-1624	7	3	operator	operator	NOUN
ejpam-1624	7	4	t	t	PROPN
ejpam-1624	7	5	∈	∈	PROPN
ejpam-1624	7	6	b(h	b(h	PROPN
ejpam-1624	7	7	)	)	PUNCT
ejpam-1624	7	8	,	,	PUNCT
ejpam-1624	7	9	n	n	PROPN
ejpam-1624	7	10	(	(	PUNCT
ejpam-1624	7	11	t	t	PROPN
ejpam-1624	7	12	)	)	PUNCT
ejpam-1624	7	13	and	and	CCONJ
ejpam-1624	7	14	r(t	r(t	NOUN
ejpam-1624	7	15	)	)	PUNCT
ejpam-1624	7	16	denote	denote	VERB
ejpam-1624	7	17	the	the	DET
ejpam-1624	7	18	null	null	ADJ
ejpam-1624	7	19	space	space	NOUN
ejpam-1624	7	20	and	and	CCONJ
ejpam-1624	7	21	the	the	DET
ejpam-1624	7	22	range	range	NOUN
ejpam-1624	7	23	of	of	ADP
ejpam-1624	7	24	t	t	PROPN
ejpam-1624	7	25	,	,	PUNCT
ejpam-1624	7	26	respectively	respectively	ADV
ejpam-1624	7	27	.	.	PUNCT
ejpam-1624	8	1	an	an	DET
ejpam-1624	8	2	operator	operator	NOUN
ejpam-1624	8	3	p	p	NOUN
ejpam-1624	8	4	∈	∈	PROPN
ejpam-1624	8	5	b(h	b(h	PROPN
ejpam-1624	8	6	)	)	PUNCT
ejpam-1624	8	7	is	be	AUX
ejpam-1624	8	8	said	say	VERB
ejpam-1624	8	9	to	to	PART
ejpam-1624	8	10	be	be	AUX
ejpam-1624	8	11	idempotent	idempotent	ADJ
ejpam-1624	8	12	if	if	SCONJ
ejpam-1624	8	13	p2	p2	PROPN
ejpam-1624	8	14	=	=	PUNCT
ejpam-1624	9	1	p.	p.	NOUN
ejpam-1624	9	2	if	if	SCONJ
ejpam-1624	9	3	p	p	NOUN
ejpam-1624	9	4	satisfies	satisfy	VERB
ejpam-1624	9	5	p2	p2	X
ejpam-1624	9	6	=	=	SYM
ejpam-1624	10	1	p	p	NOUN
ejpam-1624	10	2	=	=	PUNCT
ejpam-1624	10	3	p∗	p∗	NOUN
ejpam-1624	10	4	then	then	ADV
ejpam-1624	10	5	p	p	NOUN
ejpam-1624	10	6	is	be	AUX
ejpam-1624	10	7	called	call	VERB
ejpam-1624	10	8	orthogonal	orthogonal	ADJ
ejpam-1624	10	9	projector	projector	NOUN
ejpam-1624	10	10	,	,	PUNCT
ejpam-1624	10	11	where	where	SCONJ
ejpam-1624	10	12	p∗	p∗	PROPN
ejpam-1624	10	13	is	be	AUX
ejpam-1624	10	14	the	the	DET
ejpam-1624	10	15	conjugate	conjugate	ADJ
ejpam-1624	10	16	operator	operator	NOUN
ejpam-1624	10	17	of	of	ADP
ejpam-1624	10	18	p	p	PROPN
ejpam-1624	10	19	∈	∈	PROPN
ejpam-1624	10	20	b(h	b(h	PROPN
ejpam-1624	10	21	)	)	PUNCT
ejpam-1624	10	22	.	.	PUNCT
ejpam-1624	11	1	let	let	VERB
ejpam-1624	11	2	t	t	PROPN
ejpam-1624	11	3	∈	∈	PROPN
ejpam-1624	11	4	b(h	b(h	PROPN
ejpam-1624	11	5	)	)	PUNCT
ejpam-1624	11	6	,	,	PUNCT
ejpam-1624	11	7	if	if	SCONJ
ejpam-1624	11	8	there	there	PRON
ejpam-1624	11	9	exists	exist	VERB
ejpam-1624	11	10	an	an	DET
ejpam-1624	11	11	operator	operator	NOUN
ejpam-1624	11	12	t	t	PROPN
ejpam-1624	11	13	d	d	PROPN
ejpam-1624	11	14	∈	∈	PROPN
ejpam-1624	11	15	b(h	b(h	PROPN
ejpam-1624	11	16	)	)	PUNCT
ejpam-1624	11	17	and	and	CCONJ
ejpam-1624	11	18	nonnegative	nonnegative	ADJ
ejpam-1624	11	19	integer	integer	NOUN
ejpam-1624	11	20	k	k	PROPN
ejpam-1624	12	1	such	such	ADJ
ejpam-1624	12	2	that	that	SCONJ
ejpam-1624	12	3	t	t	NOUN
ejpam-1624	12	4	t	t	NOUN
ejpam-1624	13	1	d	d	PROPN
ejpam-1624	13	2	=	=	SYM
ejpam-1624	13	3	t	t	PROPN
ejpam-1624	13	4	dt	dt	PROPN
ejpam-1624	13	5	,	,	PUNCT
ejpam-1624	13	6	t	t	PROPN
ejpam-1624	14	1	dt	dt	X
ejpam-1624	14	2	t	t	PROPN
ejpam-1624	15	1	d	d	PROPN
ejpam-1624	15	2	=	=	SYM
ejpam-1624	15	3	t	t	PROPN
ejpam-1624	15	4	d	d	PROPN
ejpam-1624	15	5	,	,	PUNCT
ejpam-1624	15	6	t	t	PROPN
ejpam-1624	15	7	k+1	k+1	PROPN
ejpam-1624	15	8	t	t	X
ejpam-1624	15	9	d	d	NOUN
ejpam-1624	15	10	=	=	PROPN
ejpam-1624	15	11	t	t	PROPN
ejpam-1624	15	12	k	k	NOUN
ejpam-1624	15	13	,	,	PUNCT
ejpam-1624	15	14	then	then	ADV
ejpam-1624	15	15	t	t	PROPN
ejpam-1624	15	16	d	d	PROPN
ejpam-1624	15	17	is	be	AUX
ejpam-1624	15	18	called	call	VERB
ejpam-1624	15	19	a	a	DET
ejpam-1624	15	20	drazin	drazin	NOUN
ejpam-1624	15	21	inverse	inverse	NOUN
ejpam-1624	15	22	of	of	ADP
ejpam-1624	15	23	t	t	PROPN
ejpam-1624	15	24	.	.	PUNCT
ejpam-1624	16	1	the	the	DET
ejpam-1624	16	2	least	least	ADJ
ejpam-1624	16	3	integer	integer	NOUN
ejpam-1624	16	4	k	k	PROPN
ejpam-1624	16	5	such	such	ADJ
ejpam-1624	16	6	that	that	SCONJ
ejpam-1624	16	7	the	the	DET
ejpam-1624	16	8	above	above	ADJ
ejpam-1624	16	9	identities	identity	NOUN
ejpam-1624	16	10	are	be	AUX
ejpam-1624	16	11	hold	hold	NOUN
ejpam-1624	16	12	is	be	AUX
ejpam-1624	16	13	called	call	VERB
ejpam-1624	16	14	the	the	DET
ejpam-1624	16	15	index	index	NOUN
ejpam-1624	16	16	of	of	ADP
ejpam-1624	16	17	t	t	PROPN
ejpam-1624	16	18	,	,	PUNCT
ejpam-1624	16	19	which	which	PRON
ejpam-1624	16	20	is	be	AUX
ejpam-1624	16	21	denoted	denote	VERB
ejpam-1624	16	22	by	by	ADP
ejpam-1624	16	23	ind(t	ind(t	ADJ
ejpam-1624	16	24	)	)	PUNCT
ejpam-1624	17	1	=	=	VERB
ejpam-1624	17	2	k.	k.	PROPN
ejpam-1624	18	1	specifically	specifically	ADV
ejpam-1624	18	2	,	,	PUNCT
ejpam-1624	18	3	if	if	SCONJ
ejpam-1624	18	4	k	k	PROPN
ejpam-1624	18	5	=	=	SYM
ejpam-1624	18	6	0	0	PROPN
ejpam-1624	18	7	,	,	PUNCT
ejpam-1624	18	8	then	then	ADV
ejpam-1624	18	9	t	t	PROPN
ejpam-1624	18	10	is	be	AUX
ejpam-1624	18	11	invertible	invertible	ADJ
ejpam-1624	18	12	and	and	CCONJ
ejpam-1624	18	13	t	t	NOUN
ejpam-1624	18	14	d	d	X
ejpam-1624	18	15	=	=	SYM
ejpam-1624	18	16	t−1	t−1	PROPN
ejpam-1624	18	17	.	.	PUNCT
ejpam-1624	19	1	for	for	ADP
ejpam-1624	19	2	drazin	drazin	PROPN
ejpam-1624	19	3	invertible	invertible	ADJ
ejpam-1624	19	4	operator	operator	NOUN
ejpam-1624	19	5	t	t	PROPN
ejpam-1624	19	6	∈	∈	PROPN
ejpam-1624	19	7	b(h	b(h	PROPN
ejpam-1624	19	8	)	)	PUNCT
ejpam-1624	19	9	,	,	PUNCT
ejpam-1624	19	10	the	the	DET
ejpam-1624	19	11	drazin	drazin	PROPN
ejpam-1624	19	12	inverse	inverse	PROPN
ejpam-1624	19	13	t	t	PROPN
ejpam-1624	19	14	d	d	PROPN
ejpam-1624	19	15	of	of	ADP
ejpam-1624	19	16	t	t	PROPN
ejpam-1624	19	17	is	be	AUX
ejpam-1624	19	18	unique	unique	ADJ
ejpam-1624	19	19	[	[	X
ejpam-1624	19	20	13	13	NUM
ejpam-1624	19	21	]	]	PUNCT
ejpam-1624	19	22	.	.	PUNCT
ejpam-1624	20	1	the	the	DET
ejpam-1624	20	2	set	set	NOUN
ejpam-1624	20	3	of	of	ADP
ejpam-1624	20	4	all	all	DET
ejpam-1624	20	5	idempotents	idempotent	NOUN
ejpam-1624	20	6	in	in	ADP
ejpam-1624	20	7	b(h	b(h	PROPN
ejpam-1624	20	8	)	)	PUNCT
ejpam-1624	20	9	is	be	AUX
ejpam-1624	20	10	invariant	invariant	ADJ
ejpam-1624	20	11	under	under	ADP
ejpam-1624	20	12	similarity	similarity	NOUN
ejpam-1624	20	13	,	,	PUNCT
ejpam-1624	20	14	that	that	ADV
ejpam-1624	20	15	is	is	ADV
ejpam-1624	20	16	,	,	PUNCT
ejpam-1624	20	17	if	if	SCONJ
ejpam-1624	20	18	p	p	NOUN
ejpam-1624	20	19	is	be	AUX
ejpam-1624	20	20	an	an	DET
ejpam-1624	20	21	idempotent	idempotent	ADJ
ejpam-1624	20	22	operator	operator	NOUN
ejpam-1624	20	23	and	and	CCONJ
ejpam-1624	20	24	s	s	NOUN
ejpam-1624	20	25	∈	∈	PROPN
ejpam-1624	20	26	b(h	b(h	PROPN
ejpam-1624	20	27	)	)	PUNCT
ejpam-1624	20	28	is	be	AUX
ejpam-1624	20	29	an	an	DET
ejpam-1624	20	30	invertible	invertible	ADJ
ejpam-1624	20	31	operator	operator	NOUN
ejpam-1624	20	32	,	,	PUNCT
ejpam-1624	20	33	then	then	ADV
ejpam-1624	20	34	s−1ps	s−1ps	NOUN
ejpam-1624	20	35	is	be	AUX
ejpam-1624	20	36	also	also	ADV
ejpam-1624	20	37	an	an	DET
ejpam-1624	20	38	idempotent	idempotent	ADJ
ejpam-1624	20	39	operator	operator	NOUN
ejpam-1624	20	40	.	.	PUNCT
ejpam-1624	21	1	moreover	moreover	ADV
ejpam-1624	21	2	the	the	DET
ejpam-1624	21	3	drazin	drazin	PROPN
ejpam-1624	21	4	invertibility	invertibility	NOUN
ejpam-1624	21	5	is	be	AUX
ejpam-1624	21	6	also	also	ADV
ejpam-1624	21	7	invariant	invariant	ADJ
ejpam-1624	21	8	under	under	ADP
ejpam-1624	21	9	similarity	similarity	NOUN
ejpam-1624	21	10	,	,	PUNCT
ejpam-1624	21	11	that	that	ADV
ejpam-1624	21	12	is	is	ADV
ejpam-1624	21	13	,	,	PUNCT
ejpam-1624	21	14	if	if	SCONJ
ejpam-1624	21	15	t	t	PROPN
ejpam-1624	21	16	is	be	AUX
ejpam-1624	21	17	drazin	drazin	PROPN
ejpam-1624	21	18	invertible	invertible	ADJ
ejpam-1624	21	19	and	and	CCONJ
ejpam-1624	21	20	s	s	NOUN
ejpam-1624	21	21	is	be	AUX
ejpam-1624	21	22	invertible	invertible	ADJ
ejpam-1624	21	23	,	,	PUNCT
ejpam-1624	21	24	then	then	ADV
ejpam-1624	21	25	s−1ts	s−1ts	PROPN
ejpam-1624	21	26	is	be	AUX
ejpam-1624	21	27	drazin	drazin	PROPN
ejpam-1624	21	28	invertible	invertible	ADJ
ejpam-1624	21	29	and	and	CCONJ
ejpam-1624	21	30	(	(	PUNCT
ejpam-1624	21	31	s−1ts)d	s−1ts)d	NOUN
ejpam-1624	21	32	=	=	SYM
ejpam-1624	21	33	s−1	s−1	PROPN
ejpam-1624	21	34	t	t	NOUN
ejpam-1624	21	35	dt	dt	NOUN
ejpam-1624	21	36	.	.	PUNCT
ejpam-1624	22	1	two	two	NUM
ejpam-1624	22	2	facts	fact	NOUN
ejpam-1624	22	3	are	be	AUX
ejpam-1624	22	4	well	well	ADV
ejpam-1624	22	5	known	known	ADJ
ejpam-1624	22	6	on	on	ADP
ejpam-1624	22	7	a	a	DET
ejpam-1624	22	8	hilbert	hilbert	NOUN
ejpam-1624	22	9	space	space	NOUN
ejpam-1624	22	10	,	,	PUNCT
ejpam-1624	22	11	one	one	NUM
ejpam-1624	22	12	is	be	AUX
ejpam-1624	22	13	that	that	SCONJ
ejpam-1624	22	14	the	the	DET
ejpam-1624	22	15	orthogonal	orthogonal	ADJ
ejpam-1624	22	16	operator	operator	NOUN
ejpam-1624	22	17	p	p	NOUN
ejpam-1624	22	18	is	be	AUX
ejpam-1624	22	19	drazin	drazin	PROPN
ejpam-1624	22	20	invertible	invertible	ADJ
ejpam-1624	22	21	and	and	CCONJ
ejpam-1624	22	22	pd	pd	NOUN
ejpam-1624	22	23	=	=	SYM
ejpam-1624	22	24	p	p	PROPN
ejpam-1624	22	25	,	,	PUNCT
ejpam-1624	22	26	another	another	PRON
ejpam-1624	22	27	is	be	AUX
ejpam-1624	22	28	that	that	SCONJ
ejpam-1624	22	29	for	for	ADP
ejpam-1624	22	30	any	any	DET
ejpam-1624	22	31	idempotent	idempotent	ADJ
ejpam-1624	22	32	operator	operator	NOUN
ejpam-1624	22	33	p	p	NOUN
ejpam-1624	22	34	,	,	PUNCT
ejpam-1624	22	35	there	there	PRON
ejpam-1624	22	36	exists	exist	VERB
ejpam-1624	22	37	an	an	DET
ejpam-1624	22	38	invertible	invertible	ADJ
ejpam-1624	22	39	∗corresponding	∗corresponde	VERB
ejpam-1624	22	40	author	author	NOUN
ejpam-1624	22	41	.	.	PUNCT
ejpam-1624	23	1	email	email	NOUN
ejpam-1624	23	2	addresses	address	NOUN
ejpam-1624	23	3	:	:	PUNCT
ejpam-1624	23	4	xietao_1294	xietao_1294	PROPN
ejpam-1624	23	5	�	�	PROPN
ejpam-1624	23	6	163	163	NUM
ejpam-1624	23	7	.	.	PUNCT
ejpam-1624	24	1	om	om	PROPN
ejpam-1624	24	2	(	(	PUNCT
ejpam-1624	24	3	t.	t.	PROPN
ejpam-1624	24	4	xie	xie	PROPN
ejpam-1624	24	5	)	)	PUNCT
ejpam-1624	24	6	,	,	PUNCT
ejpam-1624	24	7	xiangzuo28	xiangzuo28	PROPN
ejpam-1624	24	8	�	�	PROPN
ejpam-1624	24	9	yahoo	yahoo	PROPN
ejpam-1624	24	10	.	.	PUNCT
ejpam-1624	25	1	n	n	PROPN
ejpam-1624	25	2	(	(	PUNCT
ejpam-1624	25	3	k.	k.	NOUN
ejpam-1624	25	4	zuo	zuo	PROPN
ejpam-1624	25	5	)	)	PUNCT
ejpam-1624	25	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1624	26	1	480	480	NUM
ejpam-1624	27	1	c	c	X
ejpam-1624	27	2	©	©	PROPN
ejpam-1624	27	3	2012	2012	NUM
ejpam-1624	27	4	ejpam	ejpam	VERB
ejpam-1624	27	5	all	all	DET
ejpam-1624	27	6	rights	right	NOUN
ejpam-1624	27	7	reserved	reserve	VERB
ejpam-1624	27	8	.	.	PUNCT
ejpam-1624	28	1	t.	t.	PROPN
ejpam-1624	28	2	xie	xie	PROPN
ejpam-1624	28	3	,	,	PUNCT
ejpam-1624	28	4	k.	k.	PROPN
ejpam-1624	28	5	zuo	zuo	PROPN
ejpam-1624	28	6	/	/	SYM
ejpam-1624	28	7	eur	eur	PROPN
ejpam-1624	28	8	.	.	PUNCT
ejpam-1624	29	1	j.	j.	PROPN
ejpam-1624	29	2	pure	pure	PROPN
ejpam-1624	29	3	appl	appl	PROPN
ejpam-1624	29	4	.	.	PROPN
ejpam-1624	29	5	math	math	PROPN
ejpam-1624	29	6	,	,	PUNCT
ejpam-1624	29	7	5	5	NUM
ejpam-1624	29	8	(	(	PUNCT
ejpam-1624	29	9	2012	2012	NUM
ejpam-1624	29	10	)	)	PUNCT
ejpam-1624	29	11	,	,	PUNCT
ejpam-1624	29	12	480	480	NUM
ejpam-1624	29	13	-	-	SYM
ejpam-1624	29	14	491	491	NUM
ejpam-1624	29	15	481	481	NUM
ejpam-1624	29	16	operator	operator	NOUN
ejpam-1624	29	17	s	s	PRON
ejpam-1624	29	18	such	such	ADJ
ejpam-1624	29	19	that	that	SCONJ
ejpam-1624	29	20	s−1ps	s−1ps	NOUN
ejpam-1624	29	21	is	be	AUX
ejpam-1624	29	22	an	an	DET
ejpam-1624	29	23	orthogonal	orthogonal	ADJ
ejpam-1624	29	24	projector	projector	NOUN
ejpam-1624	29	25	[	[	X
ejpam-1624	29	26	13	13	NUM
ejpam-1624	29	27	]	]	PUNCT
ejpam-1624	29	28	.	.	PUNCT
ejpam-1624	30	1	in	in	ADP
ejpam-1624	30	2	the	the	DET
ejpam-1624	30	3	following	follow	VERB
ejpam-1624	30	4	discussion	discussion	NOUN
ejpam-1624	30	5	,	,	PUNCT
ejpam-1624	30	6	given	give	VERB
ejpam-1624	30	7	two	two	NUM
ejpam-1624	30	8	idempotent	idempotent	ADJ
ejpam-1624	30	9	operators	operator	NOUN
ejpam-1624	30	10	p	p	NOUN
ejpam-1624	30	11	and	and	CCONJ
ejpam-1624	30	12	q	q	PROPN
ejpam-1624	30	13	onh	onh	PROPN
ejpam-1624	30	14	,	,	PUNCT
ejpam-1624	30	15	without	without	ADP
ejpam-1624	30	16	loss	loss	NOUN
ejpam-1624	30	17	of	of	ADP
ejpam-1624	30	18	generality	generality	NOUN
ejpam-1624	30	19	,	,	PUNCT
ejpam-1624	30	20	we	we	PRON
ejpam-1624	30	21	may	may	AUX
ejpam-1624	30	22	assume	assume	VERB
ejpam-1624	30	23	that	that	SCONJ
ejpam-1624	30	24	p	p	NOUN
ejpam-1624	30	25	is	be	AUX
ejpam-1624	30	26	orthogonal	orthogonal	ADJ
ejpam-1624	30	27	.	.	PUNCT
ejpam-1624	31	1	the	the	DET
ejpam-1624	31	2	concept	concept	NOUN
ejpam-1624	31	3	of	of	ADP
ejpam-1624	31	4	a	a	DET
ejpam-1624	31	5	drazin	drazin	PROPN
ejpam-1624	31	6	inverse	inverse	NOUN
ejpam-1624	31	7	was	be	AUX
ejpam-1624	31	8	shown	show	VERB
ejpam-1624	31	9	to	to	PART
ejpam-1624	31	10	be	be	AUX
ejpam-1624	31	11	very	very	ADV
ejpam-1624	31	12	useful	useful	ADJ
ejpam-1624	31	13	in	in	ADP
ejpam-1624	31	14	various	various	ADJ
ejpam-1624	31	15	applied	apply	VERB
ejpam-1624	31	16	mathematical	mathematical	ADJ
ejpam-1624	31	17	settings	setting	NOUN
ejpam-1624	31	18	which	which	PRON
ejpam-1624	31	19	can	can	AUX
ejpam-1624	31	20	be	be	AUX
ejpam-1624	31	21	found	find	VERB
ejpam-1624	31	22	in	in	ADP
ejpam-1624	31	23	references	reference	NOUN
ejpam-1624	31	24	[	[	X
ejpam-1624	31	25	2	2	NUM
ejpam-1624	31	26	,	,	PUNCT
ejpam-1624	31	27	7	7	NUM
ejpam-1624	31	28	,	,	PUNCT
ejpam-1624	31	29	9	9	NUM
ejpam-1624	31	30	,	,	PUNCT
ejpam-1624	31	31	10	10	NUM
ejpam-1624	31	32	]	]	PUNCT
ejpam-1624	31	33	.	.	PUNCT
ejpam-1624	32	1	the	the	DET
ejpam-1624	32	2	problem	problem	NOUN
ejpam-1624	32	3	of	of	ADP
ejpam-1624	32	4	finding	find	VERB
ejpam-1624	32	5	the	the	DET
ejpam-1624	32	6	drazin	drazin	PROPN
ejpam-1624	32	7	inverse	inverse	NOUN
ejpam-1624	32	8	(	(	PUNCT
ejpam-1624	32	9	p	p	NOUN
ejpam-1624	32	10	±	±	PROPN
ejpam-1624	32	11	q)d	q)d	NOUN
ejpam-1624	32	12	of	of	ADP
ejpam-1624	32	13	the	the	DET
ejpam-1624	32	14	sum	sum	NOUN
ejpam-1624	32	15	and	and	CCONJ
ejpam-1624	32	16	difference	difference	NOUN
ejpam-1624	32	17	of	of	ADP
ejpam-1624	32	18	two	two	NUM
ejpam-1624	32	19	idempotents	idempotent	NOUN
ejpam-1624	32	20	p	p	NOUN
ejpam-1624	32	21	and	and	CCONJ
ejpam-1624	32	22	q	q	PROPN
ejpam-1624	32	23	was	be	AUX
ejpam-1624	32	24	first	first	ADV
ejpam-1624	32	25	considered	consider	VERB
ejpam-1624	32	26	by	by	ADP
ejpam-1624	32	27	drazin	drazin	PROPN
ejpam-1624	32	28	in	in	ADP
ejpam-1624	32	29	1958	1958	NUM
ejpam-1624	32	30	in	in	ADP
ejpam-1624	32	31	his	his	PRON
ejpam-1624	32	32	celebrated	celebrated	ADJ
ejpam-1624	32	33	paper	paper	NOUN
ejpam-1624	32	34	[	[	X
ejpam-1624	32	35	3	3	NUM
ejpam-1624	32	36	]	]	PUNCT
ejpam-1624	32	37	.	.	PUNCT
ejpam-1624	33	1	herein	herein	PROPN
ejpam-1624	33	2	,	,	PUNCT
ejpam-1624	33	3	it	it	PRON
ejpam-1624	33	4	was	be	AUX
ejpam-1624	33	5	proved	prove	VERB
ejpam-1624	33	6	that	that	SCONJ
ejpam-1624	33	7	(	(	PUNCT
ejpam-1624	33	8	p	p	X
ejpam-1624	33	9	+	+	NOUN
ejpam-1624	33	10	q)d	q)d	NOUN
ejpam-1624	33	11	=	=	SYM
ejpam-1624	33	12	pd	pd	X
ejpam-1624	33	13	+	+	PROPN
ejpam-1624	33	14	qd	qd	NOUN
ejpam-1624	33	15	provided	provide	VERB
ejpam-1624	33	16	pq	pq	NOUN
ejpam-1624	33	17	=	=	SYM
ejpam-1624	33	18	qp	qp	PROPN
ejpam-1624	33	19	=	=	SYM
ejpam-1624	33	20	0	0	X
ejpam-1624	33	21	.	.	PUNCT
ejpam-1624	34	1	the	the	DET
ejpam-1624	34	2	general	general	ADJ
ejpam-1624	34	3	question	question	NOUN
ejpam-1624	34	4	of	of	ADP
ejpam-1624	34	5	how	how	SCONJ
ejpam-1624	34	6	to	to	PART
ejpam-1624	34	7	express	express	VERB
ejpam-1624	34	8	(	(	PUNCT
ejpam-1624	34	9	p+q)d	p+q)d	X
ejpam-1624	34	10	as	as	ADP
ejpam-1624	34	11	a	a	DET
ejpam-1624	34	12	function	function	NOUN
ejpam-1624	34	13	of	of	ADP
ejpam-1624	34	14	p	p	X
ejpam-1624	34	15	,	,	PUNCT
ejpam-1624	34	16	q	q	ADJ
ejpam-1624	34	17	,	,	PUNCT
ejpam-1624	34	18	pd	pd	PROPN
ejpam-1624	34	19	,	,	PUNCT
ejpam-1624	34	20	qd	qd	PROPN
ejpam-1624	34	21	,	,	PUNCT
ejpam-1624	34	22	without	without	ADP
ejpam-1624	34	23	side	side	NOUN
ejpam-1624	34	24	condition	condition	NOUN
ejpam-1624	34	25	,	,	PUNCT
ejpam-1624	34	26	is	be	AUX
ejpam-1624	34	27	very	very	ADV
ejpam-1624	34	28	difficult	difficult	ADJ
ejpam-1624	34	29	and	and	CCONJ
ejpam-1624	34	30	remains	remain	VERB
ejpam-1624	34	31	open	open	ADJ
ejpam-1624	34	32	[	[	X
ejpam-1624	34	33	8	8	NUM
ejpam-1624	34	34	]	]	PUNCT
ejpam-1624	34	35	.	.	PUNCT
ejpam-1624	35	1	in	in	ADP
ejpam-1624	35	2	2009	2009	NUM
ejpam-1624	35	3	,	,	PUNCT
ejpam-1624	35	4	deng	deng	PROPN
ejpam-1624	35	5	extended	extend	VERB
ejpam-1624	35	6	drazin	drazin	PROPN
ejpam-1624	35	7	’s	’s	PART
ejpam-1624	35	8	result	result	NOUN
ejpam-1624	35	9	to	to	ADP
ejpam-1624	35	10	the	the	DET
ejpam-1624	35	11	three	three	NUM
ejpam-1624	35	12	different	different	ADJ
ejpam-1624	35	13	cases	case	NOUN
ejpam-1624	35	14	(	(	PUNCT
ejpam-1624	35	15	i)pqp	i)pqp	PROPN
ejpam-1624	35	16	=	=	SYM
ejpam-1624	35	17	0	0	NUM
ejpam-1624	35	18	;	;	PUNCT
ejpam-1624	35	19	(	(	PUNCT
ejpam-1624	35	20	ii)pqp	ii)pqp	X
ejpam-1624	35	21	=	=	SYM
ejpam-1624	35	22	p	p	X
ejpam-1624	35	23	;	;	PUNCT
ejpam-1624	35	24	(	(	PUNCT
ejpam-1624	35	25	iii)pqp	iii)pqp	PROPN
ejpam-1624	35	26	=	=	SYM
ejpam-1624	35	27	pq	pq	PROPN
ejpam-1624	35	28	,	,	PUNCT
ejpam-1624	35	29	see	see	VERB
ejpam-1624	35	30	[	[	X
ejpam-1624	35	31	4	4	NUM
ejpam-1624	35	32	]	]	PUNCT
ejpam-1624	35	33	.	.	PUNCT
ejpam-1624	36	1	these	these	DET
ejpam-1624	36	2	cases	case	NOUN
ejpam-1624	36	3	are	be	AUX
ejpam-1624	36	4	useful	useful	ADJ
ejpam-1624	36	5	in	in	ADP
ejpam-1624	36	6	several	several	ADJ
ejpam-1624	36	7	applications	application	NOUN
ejpam-1624	36	8	,	,	PUNCT
ejpam-1624	36	9	such	such	ADJ
ejpam-1624	36	10	as	as	ADP
ejpam-1624	36	11	in	in	ADP
ejpam-1624	36	12	the	the	DET
ejpam-1624	36	13	splitting	splitting	NOUN
ejpam-1624	36	14	of	of	ADP
ejpam-1624	36	15	operators	operator	NOUN
ejpam-1624	36	16	and	and	CCONJ
ejpam-1624	36	17	iteration	iteration	NOUN
ejpam-1624	36	18	theory	theory	NOUN
ejpam-1624	36	19	.	.	PUNCT
ejpam-1624	37	1	zhang	zhang	PROPN
ejpam-1624	37	2	and	and	CCONJ
ejpam-1624	37	3	wu	wu	PROPN
ejpam-1624	37	4	discussed	discuss	VERB
ejpam-1624	37	5	the	the	DET
ejpam-1624	37	6	drazin	drazin	PROPN
ejpam-1624	37	7	inverse	inverse	NOUN
ejpam-1624	37	8	of	of	ADP
ejpam-1624	37	9	the	the	DET
ejpam-1624	37	10	linear	linear	ADJ
ejpam-1624	37	11	combinations	combination	NOUN
ejpam-1624	37	12	of	of	ADP
ejpam-1624	37	13	two	two	NUM
ejpam-1624	37	14	idempotents	idempotent	NOUN
ejpam-1624	37	15	in	in	ADP
ejpam-1624	37	16	a	a	DET
ejpam-1624	37	17	banach	banach	NOUN
ejpam-1624	37	18	algebras	algebras	NOUN
ejpam-1624	37	19	and	and	CCONJ
ejpam-1624	37	20	represent	represent	VERB
ejpam-1624	37	21	the	the	DET
ejpam-1624	37	22	drazin	drazin	PROPN
ejpam-1624	37	23	inverse	inverse	NOUN
ejpam-1624	37	24	as	as	ADP
ejpam-1624	37	25	a	a	DET
ejpam-1624	37	26	function	function	NOUN
ejpam-1624	37	27	of	of	ADP
ejpam-1624	37	28	p	p	X
ejpam-1624	37	29	,	,	PUNCT
ejpam-1624	37	30	q	q	ADJ
ejpam-1624	37	31	,	,	PUNCT
ejpam-1624	37	32	pq	pq	PROPN
ejpam-1624	37	33	,	,	PUNCT
ejpam-1624	37	34	qp	qp	ADP
ejpam-1624	37	35	,	,	PUNCT
ejpam-1624	37	36	pqp	pqp	NOUN
ejpam-1624	37	37	,	,	PUNCT
ejpam-1624	37	38	qpq	qpq	VERB
ejpam-1624	38	1	[	[	X
ejpam-1624	38	2	14	14	NUM
ejpam-1624	38	3	]	]	PUNCT
ejpam-1624	38	4	.	.	PUNCT
ejpam-1624	39	1	in	in	ADP
ejpam-1624	39	2	2010	2010	NUM
ejpam-1624	39	3	,	,	PUNCT
ejpam-1624	39	4	zuo	zuo	PROPN
ejpam-1624	39	5	considered	consider	VERB
ejpam-1624	39	6	a	a	DET
ejpam-1624	39	7	special	special	ADJ
ejpam-1624	39	8	combination	combination	NOUN
ejpam-1624	39	9	ap+	ap+	NOUN
ejpam-1624	39	10	bq−	bq−	PUNCT
ejpam-1624	39	11	cpq	cpq	NOUN
ejpam-1624	39	12	of	of	ADP
ejpam-1624	39	13	two	two	NUM
ejpam-1624	39	14	idempotent	idempotent	ADJ
ejpam-1624	39	15	matrices	matrix	NOUN
ejpam-1624	39	16	over	over	ADP
ejpam-1624	39	17	complex	complex	ADJ
ejpam-1624	39	18	numbers	number	NOUN
ejpam-1624	39	19	,	,	PUNCT
ejpam-1624	39	20	and	and	CCONJ
ejpam-1624	39	21	obtained	obtain	VERB
ejpam-1624	39	22	that	that	DET
ejpam-1624	39	23	r(ap	r(ap	PROPN
ejpam-1624	39	24	+	+	CCONJ
ejpam-1624	39	25	bq−	bq−	NUM
ejpam-1624	39	26	cpq	cpq	NOUN
ejpam-1624	39	27	)	)	PUNCT
ejpam-1624	39	28	=	=	SYM
ejpam-1624	39	29	(	(	PUNCT
ejpam-1624	39	30	r(p	r(p	NOUN
ejpam-1624	39	31	−q	−q	NOUN
ejpam-1624	39	32	)	)	PUNCT
ejpam-1624	39	33	,	,	PUNCT
ejpam-1624	39	34	whenc	whenc	NOUN
ejpam-1624	39	35	=	=	SYM
ejpam-1624	39	36	a+	a+	PUNCT
ejpam-1624	39	37	b	b	X
ejpam-1624	39	38	r(p	r(p	PROPN
ejpam-1624	39	39	+	+	NOUN
ejpam-1624	39	40	q	q	NOUN
ejpam-1624	39	41	)	)	PUNCT
ejpam-1624	39	42	,	,	PUNCT
ejpam-1624	39	43	whenc	whenc	NOUN
ejpam-1624	39	44	6=	6=	PROPN
ejpam-1624	39	45	a+	a+	PRON
ejpam-1624	39	46	b	b	NOUN
ejpam-1624	39	47	,	,	PUNCT
ejpam-1624	39	48	where	where	SCONJ
ejpam-1624	39	49	r(a	r(a	NUM
ejpam-1624	39	50	)	)	PUNCT
ejpam-1624	39	51	represents	represent	VERB
ejpam-1624	39	52	the	the	DET
ejpam-1624	39	53	rank	rank	NOUN
ejpam-1624	39	54	of	of	ADP
ejpam-1624	39	55	the	the	DET
ejpam-1624	39	56	matrix	matrix	NOUN
ejpam-1624	40	1	a	a	DET
ejpam-1624	40	2	[	[	X
ejpam-1624	40	3	15	15	NUM
ejpam-1624	40	4	]	]	PUNCT
ejpam-1624	40	5	.	.	PUNCT
ejpam-1624	41	1	later	later	ADV
ejpam-1624	41	2	,	,	PUNCT
ejpam-1624	41	3	xie	xie	PROPN
ejpam-1624	41	4	and	and	CCONJ
ejpam-1624	41	5	zuo	zuo	PROPN
ejpam-1624	41	6	found	find	VERB
ejpam-1624	41	7	that	that	SCONJ
ejpam-1624	41	8	the	the	DET
ejpam-1624	41	9	fredholmness	fredholmness	NOUN
ejpam-1624	41	10	of	of	ADP
ejpam-1624	41	11	ap	ap	PROPN
ejpam-1624	41	12	+	+	PUNCT
ejpam-1624	41	13	bq−	bq−	PUNCT
ejpam-1624	41	14	cpq	cpq	PROPN
ejpam-1624	41	15	is	be	AUX
ejpam-1624	41	16	independent	independent	ADJ
ejpam-1624	41	17	of	of	ADP
ejpam-1624	41	18	choices	choice	NOUN
ejpam-1624	41	19	of	of	ADP
ejpam-1624	41	20	scalars	scalar	NOUN
ejpam-1624	41	21	a	a	DET
ejpam-1624	41	22	,	,	PUNCT
ejpam-1624	41	23	b	b	NOUN
ejpam-1624	41	24	,	,	PUNCT
ejpam-1624	41	25	c	c	PROPN
ejpam-1624	41	26	∈	∈	PROPN
ejpam-1624	41	27	c	c	PROPN
ejpam-1624	41	28	with	with	ADP
ejpam-1624	41	29	ab	ab	PROPN
ejpam-1624	41	30	6=	6=	ADP
ejpam-1624	41	31	0	0	NUM
ejpam-1624	42	1	[	[	X
ejpam-1624	42	2	12	12	NUM
ejpam-1624	42	3	]	]	PUNCT
ejpam-1624	42	4	.	.	PUNCT
ejpam-1624	43	1	after	after	ADP
ejpam-1624	43	2	that	that	PRON
ejpam-1624	43	3	,	,	PUNCT
ejpam-1624	43	4	liu	liu	PROPN
ejpam-1624	43	5	,	,	PUNCT
ejpam-1624	43	6	wu	wu	PROPN
ejpam-1624	43	7	and	and	CCONJ
ejpam-1624	43	8	yu	yu	PROPN
ejpam-1624	43	9	discussed	discuss	VERB
ejpam-1624	43	10	the	the	DET
ejpam-1624	43	11	group	group	NOUN
ejpam-1624	43	12	invertibility	invertibility	NOUN
ejpam-1624	43	13	of	of	ADP
ejpam-1624	43	14	combinations	combination	NOUN
ejpam-1624	43	15	of	of	ADP
ejpam-1624	43	16	two	two	NUM
ejpam-1624	43	17	idempotents	idempotent	NOUN
ejpam-1624	43	18	and	and	CCONJ
ejpam-1624	43	19	represent	represent	VERB
ejpam-1624	43	20	the	the	DET
ejpam-1624	43	21	group	group	NOUN
ejpam-1624	43	22	inverse	inverse	NOUN
ejpam-1624	43	23	as	as	ADP
ejpam-1624	43	24	a	a	DET
ejpam-1624	43	25	function	function	NOUN
ejpam-1624	43	26	of	of	ADP
ejpam-1624	43	27	p	p	X
ejpam-1624	43	28	,	,	PUNCT
ejpam-1624	43	29	q	q	ADJ
ejpam-1624	43	30	,	,	PUNCT
ejpam-1624	43	31	pq	pq	PROPN
ejpam-1624	43	32	,	,	PUNCT
ejpam-1624	43	33	qp	qp	ADP
ejpam-1624	43	34	,	,	PUNCT
ejpam-1624	43	35	pqp	pqp	NOUN
ejpam-1624	43	36	,	,	PUNCT
ejpam-1624	43	37	qpq	qpq	VERB
ejpam-1624	44	1	[	[	X
ejpam-1624	44	2	11	11	NUM
ejpam-1624	44	3	]	]	PUNCT
ejpam-1624	44	4	.	.	PUNCT
ejpam-1624	45	1	under	under	ADP
ejpam-1624	45	2	the	the	DET
ejpam-1624	45	3	above	above	ADJ
ejpam-1624	45	4	works	work	NOUN
ejpam-1624	45	5	,	,	PUNCT
ejpam-1624	45	6	we	we	PRON
ejpam-1624	45	7	consider	consider	VERB
ejpam-1624	45	8	the	the	DET
ejpam-1624	45	9	drazin	drazin	PROPN
ejpam-1624	45	10	invertibility	invertibility	NOUN
ejpam-1624	45	11	of	of	ADP
ejpam-1624	45	12	combinations	combination	NOUN
ejpam-1624	45	13	ap	ap	PROPN
ejpam-1624	46	1	+	+	NUM
ejpam-1624	46	2	bq	bq	X
ejpam-1624	46	3	+	+	NUM
ejpam-1624	46	4	cpq	cpq	PROPN
ejpam-1624	46	5	+	+	CCONJ
ejpam-1624	46	6	dqp	dqp	NOUN
ejpam-1624	46	7	of	of	ADP
ejpam-1624	46	8	two	two	NUM
ejpam-1624	46	9	idempotent	idempotent	ADJ
ejpam-1624	46	10	operators	operator	NOUN
ejpam-1624	46	11	p	p	NOUN
ejpam-1624	46	12	and	and	CCONJ
ejpam-1624	46	13	q	q	NOUN
ejpam-1624	46	14	on	on	ADP
ejpam-1624	46	15	h	h	NOUN
ejpam-1624	46	16	.	.	PUNCT
ejpam-1624	47	1	under	under	ADP
ejpam-1624	47	2	the	the	DET
ejpam-1624	47	3	conditions	condition	NOUN
ejpam-1624	47	4	pqp	pqp	NOUN
ejpam-1624	47	5	=	=	SYM
ejpam-1624	47	6	0	0	NUM
ejpam-1624	47	7	,	,	PUNCT
ejpam-1624	47	8	pqp	pqp	NOUN
ejpam-1624	47	9	=	=	SYM
ejpam-1624	47	10	p	p	NOUN
ejpam-1624	47	11	and	and	CCONJ
ejpam-1624	47	12	pqp	pqp	NOUN
ejpam-1624	47	13	=	=	PROPN
ejpam-1624	47	14	pq	pq	PROPN
ejpam-1624	47	15	,	,	PUNCT
ejpam-1624	47	16	the	the	DET
ejpam-1624	47	17	representations	representation	NOUN
ejpam-1624	47	18	for	for	ADP
ejpam-1624	47	19	the	the	DET
ejpam-1624	47	20	drazin	drazin	PROPN
ejpam-1624	47	21	inverse	inverse	NOUN
ejpam-1624	47	22	of	of	ADP
ejpam-1624	47	23	ap	ap	PROPN
ejpam-1624	47	24	+	+	CCONJ
ejpam-1624	47	25	bq+	bq+	PROPN
ejpam-1624	47	26	cpq+	cpq+	PROPN
ejpam-1624	47	27	dqp	dqp	NOUN
ejpam-1624	47	28	as	as	ADP
ejpam-1624	47	29	a	a	DET
ejpam-1624	47	30	functions	function	NOUN
ejpam-1624	47	31	of	of	ADP
ejpam-1624	47	32	p	p	X
ejpam-1624	47	33	,	,	PUNCT
ejpam-1624	47	34	q	q	ADJ
ejpam-1624	47	35	,	,	PUNCT
ejpam-1624	47	36	pq	pq	PROPN
ejpam-1624	47	37	,	,	PUNCT
ejpam-1624	47	38	qp	qp	ADP
ejpam-1624	47	39	,	,	PUNCT
ejpam-1624	47	40	pqp	pqp	NOUN
ejpam-1624	47	41	,	,	PUNCT
ejpam-1624	47	42	qpq	qpq	X
ejpam-1624	47	43	are	be	AUX
ejpam-1624	47	44	obtained	obtain	VERB
ejpam-1624	47	45	by	by	ADP
ejpam-1624	47	46	using	use	VERB
ejpam-1624	47	47	the	the	DET
ejpam-1624	47	48	technique	technique	NOUN
ejpam-1624	47	49	of	of	ADP
ejpam-1624	47	50	splitting	splitting	NOUN
ejpam-1624	47	51	matrices	matrix	NOUN
ejpam-1624	47	52	into	into	ADP
ejpam-1624	47	53	blocks	block	NOUN
ejpam-1624	47	54	and	and	CCONJ
ejpam-1624	47	55	space	space	NOUN
ejpam-1624	47	56	decompositions	decomposition	NOUN
ejpam-1624	47	57	.	.	PUNCT
ejpam-1624	48	1	the	the	DET
ejpam-1624	48	2	following	follow	VERB
ejpam-1624	48	3	two	two	NUM
ejpam-1624	48	4	lemmas	lemma	NOUN
ejpam-1624	48	5	which	which	PRON
ejpam-1624	48	6	were	be	AUX
ejpam-1624	48	7	proved	prove	VERB
ejpam-1624	48	8	for	for	ADP
ejpam-1624	48	9	a	a	DET
ejpam-1624	48	10	bounded	bounded	ADJ
ejpam-1624	48	11	linear	linear	ADJ
ejpam-1624	48	12	operator	operator	NOUN
ejpam-1624	48	13	[	[	X
ejpam-1624	48	14	5	5	NUM
ejpam-1624	48	15	]	]	PUNCT
ejpam-1624	48	16	and	and	CCONJ
ejpam-1624	48	17	for	for	ADP
ejpam-1624	48	18	arbitrary	arbitrary	ADJ
ejpam-1624	48	19	elements	element	NOUN
ejpam-1624	48	20	in	in	ADP
ejpam-1624	48	21	a	a	DET
ejpam-1624	48	22	banach	banach	NOUN
ejpam-1624	48	23	algebra	algebra	NOUN
ejpam-1624	48	24	[	[	X
ejpam-1624	48	25	1	1	NUM
ejpam-1624	48	26	]	]	PUNCT
ejpam-1624	48	27	.	.	PUNCT
ejpam-1624	49	1	lemma	lemma	PROPN
ejpam-1624	49	2	1	1	X
ejpam-1624	49	3	.	.	PUNCT
ejpam-1624	50	1	let	let	VERB
ejpam-1624	50	2	a∈	a∈	PROPN
ejpam-1624	50	3	b(x	b(x	PROPN
ejpam-1624	50	4	)	)	PUNCT
ejpam-1624	50	5	,	,	PUNCT
ejpam-1624	50	6	b	b	X
ejpam-1624	50	7	∈	∈	PROPN
ejpam-1624	50	8	b(y	b(y	PROPN
ejpam-1624	50	9	)	)	PUNCT
ejpam-1624	50	10	and	and	CCONJ
ejpam-1624	50	11	c	c	PROPN
ejpam-1624	50	12	∈	∈	PROPN
ejpam-1624	50	13	b(y	b(y	PROPN
ejpam-1624	50	14	,	,	PUNCT
ejpam-1624	50	15	x	x	PUNCT
ejpam-1624	50	16	)	)	PUNCT
ejpam-1624	50	17	.	.	PUNCT
ejpam-1624	51	1	if	if	SCONJ
ejpam-1624	51	2	a	a	PRON
ejpam-1624	51	3	and	and	CCONJ
ejpam-1624	51	4	b	b	NOUN
ejpam-1624	51	5	are	be	AUX
ejpam-1624	51	6	drazin	drazin	PROPN
ejpam-1624	51	7	invertible	invertible	ADJ
ejpam-1624	51	8	,	,	PUNCT
ejpam-1624	51	9	then	then	ADV
ejpam-1624	51	10	m	m	VERB
ejpam-1624	51	11	=	=	VERB
ejpam-1624	51	12	�	�	PROPN
ejpam-1624	52	1	a	a	DET
ejpam-1624	52	2	c	c	PROPN
ejpam-1624	52	3	0	0	SYM
ejpam-1624	52	4	b	b	PROPN
ejpam-1624	52	5	�	�	PROPN
ejpam-1624	52	6	,	,	PUNCT
ejpam-1624	52	7	n	n	PROPN
ejpam-1624	52	8	=	=	SYM
ejpam-1624	52	9	�	�	PROPN
ejpam-1624	52	10	b	b	PROPN
ejpam-1624	52	11	0	0	PROPN
ejpam-1624	52	12	c	c	PROPN
ejpam-1624	52	13	a	a	DET
ejpam-1624	52	14	�	�	PROPN
ejpam-1624	52	15	t.	t.	PROPN
ejpam-1624	52	16	xie	xie	PROPN
ejpam-1624	52	17	,	,	PUNCT
ejpam-1624	52	18	k.	k.	PROPN
ejpam-1624	52	19	zuo	zuo	PROPN
ejpam-1624	52	20	/	/	SYM
ejpam-1624	52	21	eur	eur	PROPN
ejpam-1624	52	22	.	.	PUNCT
ejpam-1624	53	1	j.	j.	PROPN
ejpam-1624	53	2	pure	pure	PROPN
ejpam-1624	53	3	appl	appl	PROPN
ejpam-1624	53	4	.	.	PROPN
ejpam-1624	53	5	math	math	PROPN
ejpam-1624	53	6	,	,	PUNCT
ejpam-1624	53	7	5	5	NUM
ejpam-1624	53	8	(	(	PUNCT
ejpam-1624	53	9	2012	2012	NUM
ejpam-1624	53	10	)	)	PUNCT
ejpam-1624	53	11	,	,	PUNCT
ejpam-1624	53	12	480	480	NUM
ejpam-1624	53	13	-	-	SYM
ejpam-1624	53	14	491	491	NUM
ejpam-1624	53	15	482	482	NUM
ejpam-1624	53	16	are	be	AUX
ejpam-1624	53	17	drazin	drazin	NOUN
ejpam-1624	53	18	invertible	invertible	ADJ
ejpam-1624	53	19	and	and	CCONJ
ejpam-1624	53	20	m	m	ADJ
ejpam-1624	53	21	d	d	X
ejpam-1624	53	22	=	=	SYM
ejpam-1624	53	23	�	�	PROPN
ejpam-1624	53	24	ad	ad	NOUN
ejpam-1624	53	25	x	x	SYM
ejpam-1624	53	26	0	0	NUM
ejpam-1624	53	27	bd	bd	PROPN
ejpam-1624	53	28	�	�	PROPN
ejpam-1624	53	29	,	,	PUNCT
ejpam-1624	53	30	n	n	PROPN
ejpam-1624	53	31	d	d	NOUN
ejpam-1624	53	32	=	=	SYM
ejpam-1624	53	33	�	�	PROPN
ejpam-1624	53	34	bd	bd	PROPN
ejpam-1624	53	35	0	0	NUM
ejpam-1624	53	36	x	x	SYM
ejpam-1624	53	37	ad	ad	NOUN
ejpam-1624	53	38	�	�	PROPN
ejpam-1624	53	39	,	,	PUNCT
ejpam-1624	53	40	where	where	SCONJ
ejpam-1624	53	41	x	x	X
ejpam-1624	53	42	=	=	PRON
ejpam-1624	53	43	(	(	PUNCT
ejpam-1624	53	44	ad)2	ad)2	PROPN
ejpam-1624	53	45	[	[	PUNCT
ejpam-1624	53	46	∑∞	∑∞	NOUN
ejpam-1624	53	47	i=0(a	i=0(a	PROPN
ejpam-1624	53	48	d)icbi](i	d)icbi](i	PROPN
ejpam-1624	53	49	−	−	PROPN
ejpam-1624	53	50	bbd	bbd	PROPN
ejpam-1624	53	51	)	)	PUNCT
ejpam-1624	54	1	+	+	CCONJ
ejpam-1624	54	2	(	(	PUNCT
ejpam-1624	54	3	i	i	PRON
ejpam-1624	54	4	−aad	−aad	ADV
ejpam-1624	54	5	)	)	PUNCT
ejpam-1624	54	6	[	[	PUNCT
ejpam-1624	54	7	∑∞	∑∞	X
ejpam-1624	54	8	i=0	i=0	VERB
ejpam-1624	54	9	aic(bd)i](bd)2	aic(bd)i](bd)2	ADJ
ejpam-1624	54	10	−adcbd	−adcbd	NOUN
ejpam-1624	54	11	.	.	PUNCT
ejpam-1624	55	1	lemma	lemma	PROPN
ejpam-1624	55	2	2	2	X
ejpam-1624	55	3	.	.	PUNCT
ejpam-1624	55	4	let	let	VERB
ejpam-1624	55	5	a∈	a∈	PROPN
ejpam-1624	55	6	b(x	b(x	PROPN
ejpam-1624	55	7	)	)	PUNCT
ejpam-1624	55	8	,	,	PUNCT
ejpam-1624	55	9	b	b	X
ejpam-1624	55	10	∈	∈	PROPN
ejpam-1624	55	11	b(y	b(y	PROPN
ejpam-1624	55	12	)	)	PUNCT
ejpam-1624	55	13	and	and	CCONJ
ejpam-1624	55	14	c	c	PROPN
ejpam-1624	55	15	∈	∈	PROPN
ejpam-1624	55	16	b(y	b(y	PROPN
ejpam-1624	55	17	,	,	PUNCT
ejpam-1624	55	18	x	x	PUNCT
ejpam-1624	55	19	)	)	PUNCT
ejpam-1624	55	20	.	.	PUNCT
ejpam-1624	56	1	if	if	SCONJ
ejpam-1624	56	2	a	a	PRON
ejpam-1624	56	3	is	be	AUX
ejpam-1624	56	4	invertible	invertible	ADJ
ejpam-1624	56	5	and	and	CCONJ
ejpam-1624	56	6	bk	bk	VERB
ejpam-1624	56	7	=	=	SYM
ejpam-1624	56	8	0	0	NUM
ejpam-1624	56	9	,	,	PUNCT
ejpam-1624	56	10	then	then	ADV
ejpam-1624	56	11	m	m	VERB
ejpam-1624	56	12	=	=	VERB
ejpam-1624	56	13	�	�	PROPN
ejpam-1624	56	14	a	a	PRON
ejpam-1624	56	15	0	0	NUM
ejpam-1624	56	16	c	c	NOUN
ejpam-1624	56	17	b	b	X
ejpam-1624	56	18	�	�	PROPN
ejpam-1624	56	19	are	be	AUX
ejpam-1624	56	20	drazin	drazin	PROPN
ejpam-1624	56	21	invertible	invertible	ADJ
ejpam-1624	56	22	and	and	CCONJ
ejpam-1624	56	23	m	m	ADJ
ejpam-1624	56	24	d	d	X
ejpam-1624	56	25	=	=	SYM
ejpam-1624	56	26	�	�	PROPN
ejpam-1624	56	27	a−1	a−1	PROPN
ejpam-1624	56	28	0	0	NUM
ejpam-1624	56	29	x	x	SYM
ejpam-1624	56	30	0	0	NUM
ejpam-1624	56	31	�	�	PROPN
ejpam-1624	56	32	,	,	PUNCT
ejpam-1624	56	33	where	where	SCONJ
ejpam-1624	56	34	x	x	X
ejpam-1624	56	35	=	=	PUNCT
ejpam-1624	56	36	∑k−1	∑k−1	PROPN
ejpam-1624	56	37	i=0	i=0	PROPN
ejpam-1624	56	38	bk−1−icai−k−1	bk−1−icai−k−1	PROPN
ejpam-1624	56	39	.	.	PUNCT
ejpam-1624	57	1	lemma	lemma	PROPN
ejpam-1624	57	2	3	3	NUM
ejpam-1624	57	3	(	(	PUNCT
ejpam-1624	57	4	see	see	VERB
ejpam-1624	57	5	[	[	X
ejpam-1624	57	6	6	6	NUM
ejpam-1624	57	7	]	]	NUM
ejpam-1624	57	8	)	)	PUNCT
ejpam-1624	57	9	.	.	PUNCT
ejpam-1624	58	1	let	let	VERB
ejpam-1624	58	2	a	a	DET
ejpam-1624	58	3	,	,	PUNCT
ejpam-1624	58	4	b	b	PROPN
ejpam-1624	58	5	∈	∈	PROPN
ejpam-1624	58	6	b(h	b(h	PROPN
ejpam-1624	58	7	)	)	PUNCT
ejpam-1624	58	8	.	.	PUNCT
ejpam-1624	59	1	then	then	ADV
ejpam-1624	59	2	the	the	DET
ejpam-1624	59	3	following	follow	VERB
ejpam-1624	59	4	conditions	condition	NOUN
ejpam-1624	59	5	are	be	AUX
ejpam-1624	59	6	equivalent	equivalent	ADJ
ejpam-1624	59	7	.	.	PUNCT
ejpam-1624	60	1	(	(	PUNCT
ejpam-1624	60	2	i	i	NOUN
ejpam-1624	60	3	)	)	PUNCT
ejpam-1624	60	4	r(b	r(b	PROPN
ejpam-1624	60	5	)	)	PUNCT
ejpam-1624	60	6	⊆r(a	⊆r(a	PROPN
ejpam-1624	60	7	)	)	PUNCT
ejpam-1624	60	8	;	;	PUNCT
ejpam-1624	60	9	(	(	PUNCT
ejpam-1624	60	10	ii	ii	NOUN
ejpam-1624	60	11	)	)	PUNCT
ejpam-1624	60	12	there	there	PRON
ejpam-1624	60	13	exists	exist	VERB
ejpam-1624	60	14	d	d	PROPN
ejpam-1624	60	15	∈	∈	PROPN
ejpam-1624	60	16	b(h	b(h	PROPN
ejpam-1624	60	17	)	)	PUNCT
ejpam-1624	60	18	such	such	ADJ
ejpam-1624	60	19	that	that	DET
ejpam-1624	60	20	b	b	NOUN
ejpam-1624	60	21	=	=	SYM
ejpam-1624	60	22	ad	ad	NOUN
ejpam-1624	60	23	.	.	NOUN
ejpam-1624	61	1	2	2	X
ejpam-1624	61	2	.	.	X
ejpam-1624	61	3	main	main	ADJ
ejpam-1624	61	4	results	result	NOUN
ejpam-1624	61	5	theorem	theorem	VERB
ejpam-1624	61	6	1	1	NUM
ejpam-1624	61	7	.	.	PUNCT
ejpam-1624	62	1	let	let	VERB
ejpam-1624	62	2	p	p	NOUN
ejpam-1624	62	3	and	and	CCONJ
ejpam-1624	62	4	q	q	NOUN
ejpam-1624	62	5	be	be	AUX
ejpam-1624	62	6	two	two	NUM
ejpam-1624	62	7	idempotents	idempotent	NOUN
ejpam-1624	62	8	in	in	ADP
ejpam-1624	62	9	b(h	b(h	PROPN
ejpam-1624	62	10	)	)	PUNCT
ejpam-1624	62	11	,	,	PUNCT
ejpam-1624	62	12	and	and	CCONJ
ejpam-1624	62	13	a	a	DET
ejpam-1624	62	14	,	,	PUNCT
ejpam-1624	62	15	b	b	NOUN
ejpam-1624	62	16	,	,	PUNCT
ejpam-1624	62	17	c	c	NOUN
ejpam-1624	62	18	,	,	PUNCT
ejpam-1624	62	19	d	d	PROPN
ejpam-1624	62	20	∈	∈	PROPN
ejpam-1624	62	21	c	c	X
ejpam-1624	62	22	,	,	PUNCT
ejpam-1624	62	23	ab	ab	PROPN
ejpam-1624	62	24	6=	6=	ADP
ejpam-1624	62	25	0	0	NUM
ejpam-1624	62	26	.	.	PUNCT
ejpam-1624	63	1	if	if	SCONJ
ejpam-1624	63	2	pqp	pqp	NOUN
ejpam-1624	63	3	=	=	SYM
ejpam-1624	63	4	0	0	NUM
ejpam-1624	63	5	,	,	PUNCT
ejpam-1624	63	6	then	then	ADV
ejpam-1624	63	7	ap	ap	PROPN
ejpam-1624	63	8	+	+	CCONJ
ejpam-1624	63	9	bq+	bq+	PROPN
ejpam-1624	63	10	cpq+	cpq+	PROPN
ejpam-1624	63	11	dqp	dqp	NOUN
ejpam-1624	63	12	is	be	AUX
ejpam-1624	63	13	drazin	drazin	PROPN
ejpam-1624	63	14	invertible	invertible	ADJ
ejpam-1624	64	1	and	and	CCONJ
ejpam-1624	65	1	(	(	PUNCT
ejpam-1624	65	2	ap	ap	PROPN
ejpam-1624	65	3	+	+	NUM
ejpam-1624	65	4	bq+	bq+	NOUN
ejpam-1624	65	5	cpq+	cpq+	ADP
ejpam-1624	65	6	dqp)d	dqp)d	PROPN
ejpam-1624	65	7	=	=	PUNCT
ejpam-1624	65	8	1	1	NUM
ejpam-1624	65	9	a	a	DET
ejpam-1624	65	10	p	p	X
ejpam-1624	65	11	+	+	NOUN
ejpam-1624	65	12	1	1	NUM
ejpam-1624	65	13	b	b	X
ejpam-1624	65	14	q−	q−	PROPN
ejpam-1624	65	15	(	(	PUNCT
ejpam-1624	65	16	1	1	NUM
ejpam-1624	65	17	a	a	DET
ejpam-1624	65	18	+	+	NUM
ejpam-1624	65	19	1	1	NUM
ejpam-1624	65	20	b	b	NOUN
ejpam-1624	65	21	+	+	NUM
ejpam-1624	65	22	c	c	PROPN
ejpam-1624	65	23	ab	ab	PROPN
ejpam-1624	65	24	)	)	PUNCT
ejpam-1624	65	25	pq−	pq−	PROPN
ejpam-1624	65	26	(	(	PUNCT
ejpam-1624	65	27	1	1	NUM
ejpam-1624	65	28	a	a	DET
ejpam-1624	65	29	+	+	NUM
ejpam-1624	65	30	1	1	NUM
ejpam-1624	65	31	b	b	NOUN
ejpam-1624	65	32	+	+	CCONJ
ejpam-1624	65	33	d	d	PROPN
ejpam-1624	65	34	ab	ab	PROPN
ejpam-1624	65	35	)	)	PUNCT
ejpam-1624	65	36	qp	qp	VERB
ejpam-1624	66	1	+	+	PUNCT
ejpam-1624	66	2	(	(	PUNCT
ejpam-1624	66	3	1	1	NUM
ejpam-1624	66	4	a	a	DET
ejpam-1624	66	5	+	+	NUM
ejpam-1624	66	6	2	2	NUM
ejpam-1624	66	7	b	b	NOUN
ejpam-1624	66	8	+	+	NUM
ejpam-1624	66	9	c	c	NOUN
ejpam-1624	66	10	ab	ab	NOUN
ejpam-1624	67	1	+	+	PROPN
ejpam-1624	67	2	d	d	PROPN
ejpam-1624	67	3	ab	ab	PROPN
ejpam-1624	67	4	+	+	PROPN
ejpam-1624	67	5	cd	cd	PROPN
ejpam-1624	67	6	ab2	ab2	NOUN
ejpam-1624	67	7	)	)	PUNCT
ejpam-1624	67	8	qpq	qpq	ADJ
ejpam-1624	67	9	.	.	PUNCT
ejpam-1624	68	1	proof	proof	NOUN
ejpam-1624	68	2	.	.	PUNCT
ejpam-1624	69	1	let	let	VERB
ejpam-1624	69	2	p	p	NOUN
ejpam-1624	69	3	and	and	CCONJ
ejpam-1624	69	4	q	q	NOUN
ejpam-1624	69	5	be	be	AUX
ejpam-1624	69	6	two	two	NUM
ejpam-1624	69	7	idempotent	idempotent	ADJ
ejpam-1624	69	8	operators	operator	NOUN
ejpam-1624	69	9	in	in	ADP
ejpam-1624	69	10	b(h	b(h	PROPN
ejpam-1624	69	11	)	)	PUNCT
ejpam-1624	69	12	.	.	PUNCT
ejpam-1624	70	1	with	with	ADP
ejpam-1624	70	2	out	out	ADP
ejpam-1624	70	3	loss	loss	NOUN
ejpam-1624	70	4	of	of	ADP
ejpam-1624	70	5	generality	generality	NOUN
ejpam-1624	70	6	,	,	PUNCT
ejpam-1624	70	7	we	we	PRON
ejpam-1624	70	8	assume	assume	VERB
ejpam-1624	70	9	that	that	SCONJ
ejpam-1624	70	10	p	p	NOUN
ejpam-1624	70	11	is	be	AUX
ejpam-1624	70	12	an	an	DET
ejpam-1624	70	13	orthogonal	orthogonal	ADJ
ejpam-1624	70	14	projector	projector	NOUN
ejpam-1624	70	15	.	.	PUNCT
ejpam-1624	71	1	by	by	ADP
ejpam-1624	71	2	lemma	lemma	PROPN
ejpam-1624	71	3	3	3	NUM
ejpam-1624	71	4	,	,	PUNCT
ejpam-1624	71	5	the	the	DET
ejpam-1624	71	6	condition	condition	NOUN
ejpam-1624	71	7	pqp	pqp	NOUN
ejpam-1624	71	8	=	=	SYM
ejpam-1624	71	9	0	0	NUM
ejpam-1624	71	10	implies	imply	VERB
ejpam-1624	71	11	that	that	SCONJ
ejpam-1624	71	12	r(qp)⊆n	r(qp)⊆n	PROPN
ejpam-1624	71	13	(	(	PUNCT
ejpam-1624	71	14	p	p	NOUN
ejpam-1624	71	15	)	)	PUNCT
ejpam-1624	71	16	and	and	CCONJ
ejpam-1624	71	17	r(qp)⊆r(q	r(qp)⊆r(q	NOUN
ejpam-1624	71	18	)	)	PUNCT
ejpam-1624	71	19	.	.	PUNCT
ejpam-1624	72	1	observing	observe	VERB
ejpam-1624	72	2	that	that	DET
ejpam-1624	72	3	q(r(qp)⊕r(p))⊆r(qp	q(r(qp)⊕r(p))⊆r(qp	NOUN
ejpam-1624	72	4	)	)	PUNCT
ejpam-1624	72	5	,	,	PUNCT
ejpam-1624	72	6	the	the	DET
ejpam-1624	72	7	space	space	NOUN
ejpam-1624	72	8	h	h	NOUN
ejpam-1624	72	9	can	can	AUX
ejpam-1624	72	10	be	be	AUX
ejpam-1624	72	11	decomposed	decompose	VERB
ejpam-1624	72	12	as	as	ADP
ejpam-1624	72	13	h	h	NOUN
ejpam-1624	72	14	=	=	NOUN
ejpam-1624	72	15	r(qp)⊕r(p)⊕	r(qp)⊕r(p)⊕	NOUN
ejpam-1624	72	16	(	(	PUNCT
ejpam-1624	72	17	r(qp)⊥⊖r(p	r(qp)⊥⊖r(p	NOUN
ejpam-1624	72	18	)	)	PUNCT
ejpam-1624	72	19	)	)	PUNCT
ejpam-1624	72	20	.	.	PUNCT
ejpam-1624	73	1	then	then	ADV
ejpam-1624	73	2	p	p	PROPN
ejpam-1624	73	3	and	and	CCONJ
ejpam-1624	73	4	q	q	NOUN
ejpam-1624	73	5	can	can	AUX
ejpam-1624	73	6	be	be	AUX
ejpam-1624	73	7	represented	represent	VERB
ejpam-1624	73	8	as	as	ADP
ejpam-1624	73	9	p	p	NOUN
ejpam-1624	73	10	=	=	PUNCT
ejpam-1624	73	11			NOUN
ejpam-1624	73	12			NOUN
ejpam-1624	73	13			NOUN
ejpam-1624	73	14	0	0	NUM
ejpam-1624	73	15	0	0	NUM
ejpam-1624	73	16	0	0	NUM
ejpam-1624	73	17	0	0	NUM
ejpam-1624	74	1	i	i	NOUN
ejpam-1624	74	2	0	0	NUM
ejpam-1624	74	3	0	0	NUM
ejpam-1624	74	4	0	0	NUM
ejpam-1624	74	5	0	0	NUM
ejpam-1624	74	6			NOUN
ejpam-1624	74	7			NOUN
ejpam-1624	74	8			PUNCT
ejpam-1624	74	9	,	,	PUNCT
ejpam-1624	74	10	q	q	NOUN
ejpam-1624	74	11	=	=	NOUN
ejpam-1624	74	12			NOUN
ejpam-1624	74	13			NOUN
ejpam-1624	74	14			NOUN
ejpam-1624	75	1	i	i	PRON
ejpam-1624	75	2	q12	q12	NOUN
ejpam-1624	75	3	q13	q13	PROPN
ejpam-1624	75	4	0	0	NUM
ejpam-1624	75	5	0	0	NUM
ejpam-1624	75	6	q23	q23	VERB
ejpam-1624	75	7	0	0	NUM
ejpam-1624	75	8	0	0	NUM
ejpam-1624	75	9	q33	q33	NOUN
ejpam-1624	75	10			NOUN
ejpam-1624	75	11			NOUN
ejpam-1624	75	12			PUNCT
ejpam-1624	75	13	,	,	PUNCT
ejpam-1624	75	14	t.	t.	PROPN
ejpam-1624	75	15	xie	xie	PROPN
ejpam-1624	75	16	,	,	PUNCT
ejpam-1624	75	17	k.	k.	PROPN
ejpam-1624	75	18	zuo	zuo	PROPN
ejpam-1624	75	19	/	/	SYM
ejpam-1624	75	20	eur	eur	PROPN
ejpam-1624	75	21	.	.	PUNCT
ejpam-1624	76	1	j.	j.	PROPN
ejpam-1624	76	2	pure	pure	PROPN
ejpam-1624	76	3	appl	appl	PROPN
ejpam-1624	76	4	.	.	PROPN
ejpam-1624	76	5	math	math	PROPN
ejpam-1624	76	6	,	,	PUNCT
ejpam-1624	76	7	5	5	NUM
ejpam-1624	76	8	(	(	PUNCT
ejpam-1624	76	9	2012	2012	NUM
ejpam-1624	76	10	)	)	PUNCT
ejpam-1624	76	11	,	,	PUNCT
ejpam-1624	76	12	480	480	NUM
ejpam-1624	76	13	-	-	SYM
ejpam-1624	76	14	491	491	NUM
ejpam-1624	76	15	483	483	NUM
ejpam-1624	76	16	where	where	SCONJ
ejpam-1624	76	17	r(qp	r(qp	NOUN
ejpam-1624	76	18	)	)	PUNCT
ejpam-1624	76	19	denotes	denote	VERB
ejpam-1624	76	20	the	the	DET
ejpam-1624	76	21	closure	closure	NOUN
ejpam-1624	76	22	ofr(qp	ofr(qp	NOUN
ejpam-1624	76	23	)	)	PUNCT
ejpam-1624	76	24	.	.	PUNCT
ejpam-1624	77	1	on	on	ADP
ejpam-1624	77	2	the	the	DET
ejpam-1624	77	3	other	other	ADJ
ejpam-1624	77	4	hand	hand	NOUN
ejpam-1624	77	5	,	,	PUNCT
ejpam-1624	77	6	q2	q2	NOUN
ejpam-1624	77	7	=	=	SYM
ejpam-1624	78	1	q	q	PROPN
ejpam-1624	78	2	gives	give	VERB
ejpam-1624	78	3	that	that	DET
ejpam-1624	78	4	q2	q2	NOUN
ejpam-1624	78	5	33	33	NUM
ejpam-1624	78	6	=	=	SYM
ejpam-1624	78	7	q33	q33	NOUN
ejpam-1624	78	8	and	and	CCONJ
ejpam-1624	78	9	r(qp)⊥⊖r(p	r(qp)⊥⊖r(p	NOUN
ejpam-1624	78	10	)	)	PUNCT
ejpam-1624	79	1	=	=	NOUN
ejpam-1624	79	2	r(q33)⊕r(q33	r(q33)⊕r(q33	NOUN
ejpam-1624	79	3	)	)	PUNCT
ejpam-1624	79	4	⊥.	⊥.	NUM
ejpam-1624	79	5	it	it	PRON
ejpam-1624	79	6	follows	follow	VERB
ejpam-1624	79	7	that	that	SCONJ
ejpam-1624	79	8	p	p	PROPN
ejpam-1624	79	9	and	and	CCONJ
ejpam-1624	79	10	q	q	NOUN
ejpam-1624	79	11	can	can	AUX
ejpam-1624	79	12	be	be	AUX
ejpam-1624	79	13	written	write	VERB
ejpam-1624	79	14	as	as	ADP
ejpam-1624	79	15	p	p	NOUN
ejpam-1624	79	16	=	=	PUNCT
ejpam-1624	79	17			PROPN
ejpam-1624	79	18			NOUN
ejpam-1624	79	19			NOUN
ejpam-1624	79	20			NOUN
ejpam-1624	79	21			NOUN
ejpam-1624	79	22	0	0	NUM
ejpam-1624	80	1	0	0	NUM
ejpam-1624	80	2	0	0	NUM
ejpam-1624	80	3	0	0	NUM
ejpam-1624	80	4	0	0	NUM
ejpam-1624	81	1	i	i	NOUN
ejpam-1624	81	2	0	0	NUM
ejpam-1624	81	3	0	0	NUM
ejpam-1624	81	4	0	0	NUM
ejpam-1624	81	5	0	0	NUM
ejpam-1624	81	6	0	0	NUM
ejpam-1624	81	7	0	0	NUM
ejpam-1624	81	8	0	0	NUM
ejpam-1624	81	9	0	0	NUM
ejpam-1624	81	10	0	0	NUM
ejpam-1624	81	11	0	0	NUM
ejpam-1624	81	12			NOUN
ejpam-1624	81	13			NOUN
ejpam-1624	81	14			VERB
ejpam-1624	81	15			NOUN
ejpam-1624	81	16			PUNCT
ejpam-1624	81	17	,	,	PUNCT
ejpam-1624	81	18	q	q	NOUN
ejpam-1624	81	19	=	=	SYM
ejpam-1624	81	20			PROPN
ejpam-1624	81	21			NOUN
ejpam-1624	81	22			NOUN
ejpam-1624	81	23			NOUN
ejpam-1624	81	24			NOUN
ejpam-1624	82	1	i	i	PRON
ejpam-1624	82	2	q12	q12	VERB
ejpam-1624	82	3	q′13	q′13	NOUN
ejpam-1624	82	4	q′′13	q′′13	PROPN
ejpam-1624	82	5	0	0	NUM
ejpam-1624	82	6	0	0	NUM
ejpam-1624	82	7	q′23	q′23	PROPN
ejpam-1624	82	8	q′′23	q′′23	PROPN
ejpam-1624	82	9	0	0	NUM
ejpam-1624	82	10	0	0	NUM
ejpam-1624	83	1	i	i	PRON
ejpam-1624	83	2	q′′33	q′′33	VERB
ejpam-1624	83	3	0	0	NUM
ejpam-1624	83	4	0	0	NUM
ejpam-1624	83	5	0	0	NUM
ejpam-1624	83	6	0	0	NUM
ejpam-1624	83	7			NOUN
ejpam-1624	83	8			NOUN
ejpam-1624	83	9			VERB
ejpam-1624	83	10			NOUN
ejpam-1624	83	11			X
ejpam-1624	83	12	,	,	PUNCT
ejpam-1624	83	13	under	under	ADP
ejpam-1624	83	14	the	the	DET
ejpam-1624	83	15	space	space	NOUN
ejpam-1624	83	16	decompositionh	decompositionh	NOUN
ejpam-1624	83	17	=	=	NOUN
ejpam-1624	83	18	r(qp)⊕r(p)⊕r(q33)r(q33	r(qp)⊕r(p)⊕r(q33)r(q33	NOUN
ejpam-1624	83	19	)	)	PUNCT
ejpam-1624	83	20	⊥.	⊥.	NUM
ejpam-1624	83	21	the	the	DET
ejpam-1624	83	22	idempotency	idempotency	NOUN
ejpam-1624	83	23	of	of	ADP
ejpam-1624	83	24	q	q	NOUN
ejpam-1624	83	25	implies	imply	VERB
ejpam-1624	83	26	that	that	SCONJ
ejpam-1624	83	27	q′23q′′33	q′23q′′33	PROPN
ejpam-1624	83	28	=	=	SYM
ejpam-1624	83	29	q′′23	q′′23	PROPN
ejpam-1624	83	30	,	,	PUNCT
ejpam-1624	83	31	q12q′23	q12q′23	PROPN
ejpam-1624	83	32	+	+	ADJ
ejpam-1624	83	33	q′13	q′13	NOUN
ejpam-1624	83	34	=	=	SYM
ejpam-1624	83	35	0	0	NUM
ejpam-1624	83	36	,	,	PUNCT
ejpam-1624	83	37	q12q′′23	q12q′′23	PROPN
ejpam-1624	83	38	+	+	PROPN
ejpam-1624	83	39	q′13q′′33	q′13q′′33	ADJ
ejpam-1624	83	40	=	=	SYM
ejpam-1624	83	41	0	0	X
ejpam-1624	83	42	.	.	PUNCT
ejpam-1624	84	1	direct	direct	ADJ
ejpam-1624	84	2	calculations	calculation	NOUN
ejpam-1624	84	3	show	show	VERB
ejpam-1624	84	4	that	that	SCONJ
ejpam-1624	84	5	ap	ap	PROPN
ejpam-1624	84	6	+	+	CCONJ
ejpam-1624	84	7	bq+	bq+	NOUN
ejpam-1624	84	8	cpq+	cpq+	ADP
ejpam-1624	84	9	dqp	dqp	NOUN
ejpam-1624	84	10	=	=	SYM
ejpam-1624	84	11			PROPN
ejpam-1624	84	12			NOUN
ejpam-1624	84	13			NOUN
ejpam-1624	84	14			NOUN
ejpam-1624	84	15			ADJ
ejpam-1624	84	16	bi	bi	NOUN
ejpam-1624	84	17	(	(	PUNCT
ejpam-1624	84	18	b+	b+	X
ejpam-1624	84	19	d)q12	d)q12	X
ejpam-1624	84	20	bq′13	bq′13	ADP
ejpam-1624	84	21	bq′′13	bq′′13	NOUN
ejpam-1624	84	22	0	0	NUM
ejpam-1624	84	23	ai	ai	NOUN
ejpam-1624	84	24	(	(	PUNCT
ejpam-1624	84	25	b+	b+	X
ejpam-1624	84	26	c)q′23	c)q′23	PROPN
ejpam-1624	84	27	(	(	PUNCT
ejpam-1624	84	28	b+	b+	X
ejpam-1624	84	29	c)q′′23	c)q′′23	NUM
ejpam-1624	84	30	0	0	NUM
ejpam-1624	84	31	0	0	NUM
ejpam-1624	84	32	bi	bi	NOUN
ejpam-1624	84	33	bq′′33	bq′′33	NOUN
ejpam-1624	84	34	0	0	PUNCT
ejpam-1624	84	35	0	0	NUM
ejpam-1624	84	36	0	0	NUM
ejpam-1624	84	37	0	0	NUM
ejpam-1624	84	38			NOUN
ejpam-1624	84	39			NOUN
ejpam-1624	84	40			VERB
ejpam-1624	84	41			NOUN
ejpam-1624	84	42			PUNCT
ejpam-1624	85	1	it	it	PRON
ejpam-1624	85	2	is	be	AUX
ejpam-1624	85	3	clear	clear	ADJ
ejpam-1624	85	4	that	that	SCONJ
ejpam-1624	85	5	the	the	DET
ejpam-1624	85	6	condition	condition	NOUN
ejpam-1624	85	7	a	a	PRON
ejpam-1624	85	8	,	,	PUNCT
ejpam-1624	85	9	b	b	PROPN
ejpam-1624	85	10	6=	6=	ADP
ejpam-1624	85	11	0	0	NUM
ejpam-1624	85	12	implies	imply	VERB
ejpam-1624	85	13	the	the	DET
ejpam-1624	85	14	invertibility	invertibility	NOUN
ejpam-1624	85	15	of	of	ADP
ejpam-1624	85	16			NOUN
ejpam-1624	85	17			NOUN
ejpam-1624	85	18			ADJ
ejpam-1624	85	19	bi	bi	NOUN
ejpam-1624	85	20	(	(	PUNCT
ejpam-1624	85	21	b+	b+	X
ejpam-1624	85	22	d)q12	d)q12	X
ejpam-1624	85	23	bq′13	bq′13	ADP
ejpam-1624	85	24	0	0	NUM
ejpam-1624	85	25	ai	ai	NOUN
ejpam-1624	85	26	(	(	PUNCT
ejpam-1624	85	27	b+	b+	X
ejpam-1624	85	28	c)q′23	c)q′23	PROPN
ejpam-1624	85	29	0	0	NUM
ejpam-1624	85	30	0	0	NUM
ejpam-1624	85	31	bi	bi	NOUN
ejpam-1624	85	32			PROPN
ejpam-1624	85	33			NOUN
ejpam-1624	85	34			PUNCT
ejpam-1624	86	1	on	on	ADP
ejpam-1624	86	2	r(qp)⊕r(p)⊕r(q33	r(qp)⊕r(p)⊕r(q33	NUM
ejpam-1624	86	3	)	)	PUNCT
ejpam-1624	86	4	and	and	CCONJ
ejpam-1624	86	5	its	its	PRON
ejpam-1624	86	6	inverse	inverse	NOUN
ejpam-1624	86	7	is	be	AUX
ejpam-1624	86	8			NOUN
ejpam-1624	86	9			NOUN
ejpam-1624	86	10			NOUN
ejpam-1624	86	11			NOUN
ejpam-1624	86	12	1	1	NUM
ejpam-1624	86	13	b	b	NOUN
ejpam-1624	86	14	i	i	PRON
ejpam-1624	86	15	−	−	PROPN
ejpam-1624	86	16	b+d	b+d	PROPN
ejpam-1624	86	17	ab	ab	PROPN
ejpam-1624	86	18	q12	q12	NOUN
ejpam-1624	86	19	−	−	PROPN
ejpam-1624	86	20	[	[	PUNCT
ejpam-1624	86	21	(	(	PUNCT
ejpam-1624	86	22	b+c)(b+d)+ab	b+c)(b+d)+ab	PROPN
ejpam-1624	86	23	ab2	ab2	NOUN
ejpam-1624	86	24	]	]	X
ejpam-1624	86	25	q′13	q′13	NOUN
ejpam-1624	86	26	0	0	NUM
ejpam-1624	86	27	1	1	NUM
ejpam-1624	86	28	a	a	PRON
ejpam-1624	87	1	i	i	PRON
ejpam-1624	87	2	−	−	PROPN
ejpam-1624	87	3	b+c	b+c	PROPN
ejpam-1624	87	4	ab	ab	PROPN
ejpam-1624	87	5	q′23	q′23	PROPN
ejpam-1624	87	6	0	0	NUM
ejpam-1624	87	7	0	0	NUM
ejpam-1624	87	8	1	1	NUM
ejpam-1624	87	9	b	b	NOUN
ejpam-1624	88	1	i	i	PRON
ejpam-1624	88	2			PROPN
ejpam-1624	88	3			NOUN
ejpam-1624	88	4			VERB
ejpam-1624	88	5			PUNCT
ejpam-1624	88	6	.	.	PUNCT
ejpam-1624	89	1	moreover	moreover	ADV
ejpam-1624	89	2	,	,	PUNCT
ejpam-1624	89	3			NOUN
ejpam-1624	89	4			NOUN
ejpam-1624	89	5			NOUN
ejpam-1624	89	6			NOUN
ejpam-1624	89	7	1	1	NUM
ejpam-1624	89	8	b	b	NOUN
ejpam-1624	89	9	i	i	PRON
ejpam-1624	89	10	−	−	PROPN
ejpam-1624	89	11	b+d	b+d	PROPN
ejpam-1624	89	12	ab	ab	PROPN
ejpam-1624	89	13	q12	q12	NOUN
ejpam-1624	89	14	−	−	PROPN
ejpam-1624	89	15	[	[	PUNCT
ejpam-1624	89	16	(	(	PUNCT
ejpam-1624	89	17	b+c)(b+d)+ab	b+c)(b+d)+ab	PROPN
ejpam-1624	89	18	ab2	ab2	NOUN
ejpam-1624	89	19	]	]	X
ejpam-1624	89	20	q′13	q′13	NOUN
ejpam-1624	89	21	0	0	NUM
ejpam-1624	89	22	1	1	NUM
ejpam-1624	89	23	a	a	PRON
ejpam-1624	90	1	i	i	PRON
ejpam-1624	90	2	−	−	PROPN
ejpam-1624	90	3	b+c	b+c	PROPN
ejpam-1624	90	4	ab	ab	PROPN
ejpam-1624	90	5	q′23	q′23	PROPN
ejpam-1624	90	6	0	0	NUM
ejpam-1624	90	7	0	0	NUM
ejpam-1624	90	8	1	1	NUM
ejpam-1624	90	9	b	b	NOUN
ejpam-1624	91	1	i	i	PRON
ejpam-1624	91	2			PROPN
ejpam-1624	91	3			NOUN
ejpam-1624	91	4			VERB
ejpam-1624	91	5			PUNCT
ejpam-1624	92	1	2	2	NUM
ejpam-1624	92	2			NOUN
ejpam-1624	92	3			NOUN
ejpam-1624	92	4	bq′′13	bq′′13	NOUN
ejpam-1624	92	5	(	(	PUNCT
ejpam-1624	92	6	b+	b+	X
ejpam-1624	92	7	c)q′′23	c)q′′23	NUM
ejpam-1624	92	8	bq′′33	bq′′33	NOUN
ejpam-1624	92	9			NOUN
ejpam-1624	92	10			NOUN
ejpam-1624	92	11			PUNCT
ejpam-1624	93	1	=	=	PUNCT
ejpam-1624	93	2			PROPN
ejpam-1624	93	3			NOUN
ejpam-1624	93	4			NOUN
ejpam-1624	93	5			NOUN
ejpam-1624	93	6	1	1	NUM
ejpam-1624	93	7	b	b	NOUN
ejpam-1624	93	8	q′′13	q′′13	ADP
ejpam-1624	93	9	−	−	NOUN
ejpam-1624	93	10	[	[	PUNCT
ejpam-1624	93	11	(	(	PUNCT
ejpam-1624	93	12	b+c)(b+d	b+c)(b+d	PROPN
ejpam-1624	93	13	)	)	PUNCT
ejpam-1624	93	14	ab2	ab2	NOUN
ejpam-1624	94	1	+	+	CCONJ
ejpam-1624	94	2	2	2	NUM
ejpam-1624	94	3	b	b	NOUN
ejpam-1624	94	4	]	]	PUNCT
ejpam-1624	94	5	q′13q′′33	q′13q′′33	NUM
ejpam-1624	94	6	−	−	PROPN
ejpam-1624	94	7	(	(	PUNCT
ejpam-1624	94	8	1	1	NUM
ejpam-1624	94	9	a	a	PRON
ejpam-1624	94	10	+	+	NOUN
ejpam-1624	94	11	c	c	NOUN
ejpam-1624	94	12	ab	ab	NOUN
ejpam-1624	94	13	)	)	PUNCT
ejpam-1624	94	14	q′′23	q′′23	PROPN
ejpam-1624	94	15	1	1	NUM
ejpam-1624	94	16	b	b	X
ejpam-1624	94	17	q′′33	q′′33	ADJ
ejpam-1624	94	18			NOUN
ejpam-1624	94	19			NOUN
ejpam-1624	94	20			VERB
ejpam-1624	94	21			PUNCT
ejpam-1624	94	22	.	.	PUNCT
ejpam-1624	95	1	applying	apply	VERB
ejpam-1624	95	2	b	b	NOUN
ejpam-1624	95	3	=	=	NOUN
ejpam-1624	95	4	0	0	NUM
ejpam-1624	95	5	to	to	ADP
ejpam-1624	95	6	the	the	DET
ejpam-1624	95	7	formula	formula	NOUN
ejpam-1624	95	8	of	of	ADP
ejpam-1624	95	9	representing	represent	VERB
ejpam-1624	95	10	drazin	drazin	PROPN
ejpam-1624	95	11	inverse	inverse	NOUN
ejpam-1624	95	12	of	of	ADP
ejpam-1624	95	13	upper	upper	ADJ
ejpam-1624	95	14	triangle	triangle	NOUN
ejpam-1624	95	15	block	block	NOUN
ejpam-1624	95	16	matrix	matrix	NOUN
ejpam-1624	95	17	in	in	ADP
ejpam-1624	95	18	lemma	lemma	PROPN
ejpam-1624	95	19	1	1	NUM
ejpam-1624	95	20	,	,	PUNCT
ejpam-1624	95	21	we	we	PRON
ejpam-1624	95	22	have	have	VERB
ejpam-1624	95	23	(	(	PUNCT
ejpam-1624	95	24	ap	ap	NOUN
ejpam-1624	95	25	+	+	NUM
ejpam-1624	95	26	bq+	bq+	NOUN
ejpam-1624	95	27	cpq+	cpq+	ADP
ejpam-1624	95	28	dqp)d	dqp)d	PROPN
ejpam-1624	95	29	=	=	SYM
ejpam-1624	95	30	t.	t.	PROPN
ejpam-1624	95	31	xie	xie	PROPN
ejpam-1624	95	32	,	,	PUNCT
ejpam-1624	95	33	k.	k.	PROPN
ejpam-1624	95	34	zuo	zuo	PROPN
ejpam-1624	95	35	/	/	SYM
ejpam-1624	95	36	eur	eur	PROPN
ejpam-1624	95	37	.	.	PUNCT
ejpam-1624	96	1	j.	j.	PROPN
ejpam-1624	96	2	pure	pure	PROPN
ejpam-1624	96	3	appl	appl	PROPN
ejpam-1624	96	4	.	.	PROPN
ejpam-1624	96	5	math	math	PROPN
ejpam-1624	96	6	,	,	PUNCT
ejpam-1624	96	7	5	5	NUM
ejpam-1624	96	8	(	(	PUNCT
ejpam-1624	96	9	2012	2012	NUM
ejpam-1624	96	10	)	)	PUNCT
ejpam-1624	96	11	,	,	PUNCT
ejpam-1624	96	12	480	480	NUM
ejpam-1624	96	13	-	-	SYM
ejpam-1624	96	14	491	491	NUM
ejpam-1624	96	15	484	484	NUM
ejpam-1624	96	16			NOUN
ejpam-1624	96	17			NOUN
ejpam-1624	96	18			NOUN
ejpam-1624	96	19			NOUN
ejpam-1624	96	20			NOUN
ejpam-1624	96	21			NOUN
ejpam-1624	96	22	1	1	NUM
ejpam-1624	96	23	b	b	NOUN
ejpam-1624	97	1	i	i	PRON
ejpam-1624	97	2	−	−	PROPN
ejpam-1624	97	3	b+d	b+d	PROPN
ejpam-1624	97	4	ab	ab	PROPN
ejpam-1624	97	5	q12	q12	NOUN
ejpam-1624	97	6	−	−	PROPN
ejpam-1624	97	7	(	(	PUNCT
ejpam-1624	97	8	b+c)(b+d)+ab	b+c)(b+d)+ab	PROPN
ejpam-1624	97	9	ab2	ab2	PROPN
ejpam-1624	97	10	q′13	q′13	PROPN
ejpam-1624	97	11	1	1	NUM
ejpam-1624	97	12	b	b	NOUN
ejpam-1624	97	13	q′′13	q′′13	ADP
ejpam-1624	97	14	−	−	NOUN
ejpam-1624	97	15	[	[	PUNCT
ejpam-1624	97	16	(	(	PUNCT
ejpam-1624	97	17	b+c)(b+d	b+c)(b+d	PROPN
ejpam-1624	97	18	)	)	PUNCT
ejpam-1624	97	19	ab2	ab2	NOUN
ejpam-1624	98	1	+	+	CCONJ
ejpam-1624	98	2	2	2	NUM
ejpam-1624	98	3	b	b	NOUN
ejpam-1624	98	4	]	]	PUNCT
ejpam-1624	98	5	q′13q′′33	q′13q′′33	NUM
ejpam-1624	98	6	0	0	NUM
ejpam-1624	98	7	1	1	NUM
ejpam-1624	98	8	a	a	PRON
ejpam-1624	98	9	i	i	PRON
ejpam-1624	98	10	−	−	PROPN
ejpam-1624	98	11	b+c	b+c	PROPN
ejpam-1624	98	12	ab	ab	PROPN
ejpam-1624	98	13	q′23	q′23	PROPN
ejpam-1624	98	14	−	−	PROPN
ejpam-1624	98	15	b+c	b+c	PROPN
ejpam-1624	98	16	ab	ab	PROPN
ejpam-1624	99	1	q′′23	q′′23	PROPN
ejpam-1624	99	2	0	0	NUM
ejpam-1624	99	3	0	0	NUM
ejpam-1624	99	4	1	1	NUM
ejpam-1624	99	5	b	b	X
ejpam-1624	99	6	i	i	PRON
ejpam-1624	99	7	1	1	NUM
ejpam-1624	99	8	b	b	X
ejpam-1624	99	9	q′′33	q′′33	ADJ
ejpam-1624	99	10	0	0	NUM
ejpam-1624	99	11	0	0	NUM
ejpam-1624	99	12	0	0	NUM
ejpam-1624	99	13	0	0	NUM
ejpam-1624	99	14			NOUN
ejpam-1624	99	15			NOUN
ejpam-1624	99	16			VERB
ejpam-1624	99	17			NOUN
ejpam-1624	99	18			NOUN
ejpam-1624	99	19			PUNCT
ejpam-1624	99	20	.	.	PUNCT
ejpam-1624	100	1	moreover	moreover	ADV
ejpam-1624	100	2	,	,	PUNCT
ejpam-1624	100	3	through	through	ADP
ejpam-1624	100	4	direct	direct	ADJ
ejpam-1624	100	5	calculations	calculation	NOUN
ejpam-1624	100	6	,	,	PUNCT
ejpam-1624	100	7	we	we	PRON
ejpam-1624	100	8	have	have	VERB
ejpam-1624	100	9	pq	pq	NOUN
ejpam-1624	100	10	=	=	SYM
ejpam-1624	100	11			PROPN
ejpam-1624	100	12			NOUN
ejpam-1624	100	13			NOUN
ejpam-1624	100	14			NOUN
ejpam-1624	100	15			NOUN
ejpam-1624	100	16	0	0	NUM
ejpam-1624	100	17	0	0	NUM
ejpam-1624	100	18	0	0	NUM
ejpam-1624	100	19	0	0	NUM
ejpam-1624	100	20	0	0	NUM
ejpam-1624	100	21	0	0	NUM
ejpam-1624	100	22	q′23	q′23	PROPN
ejpam-1624	100	23	q′′23	q′′23	PROPN
ejpam-1624	100	24	0	0	NUM
ejpam-1624	100	25	0	0	NUM
ejpam-1624	100	26	0	0	NUM
ejpam-1624	100	27	0	0	NUM
ejpam-1624	100	28	0	0	NUM
ejpam-1624	100	29	0	0	NUM
ejpam-1624	100	30	0	0	NUM
ejpam-1624	100	31	0	0	NUM
ejpam-1624	100	32			NOUN
ejpam-1624	100	33			NOUN
ejpam-1624	100	34			VERB
ejpam-1624	100	35			NOUN
ejpam-1624	100	36			X
ejpam-1624	100	37	,	,	PUNCT
ejpam-1624	100	38	qp	qp	NOUN
ejpam-1624	101	1	=	=	SYM
ejpam-1624	101	2			PROPN
ejpam-1624	101	3			NOUN
ejpam-1624	101	4			NOUN
ejpam-1624	101	5			NOUN
ejpam-1624	101	6			NOUN
ejpam-1624	101	7	0	0	NUM
ejpam-1624	101	8	q12	q12	NOUN
ejpam-1624	101	9	0	0	NUM
ejpam-1624	101	10	0	0	NUM
ejpam-1624	101	11	0	0	NUM
ejpam-1624	101	12	0	0	NUM
ejpam-1624	101	13	0	0	NUM
ejpam-1624	101	14	0	0	NUM
ejpam-1624	101	15	0	0	NUM
ejpam-1624	101	16	0	0	NUM
ejpam-1624	101	17	0	0	NUM
ejpam-1624	101	18	0	0	NUM
ejpam-1624	101	19	0	0	NUM
ejpam-1624	101	20	0	0	NUM
ejpam-1624	101	21	0	0	NUM
ejpam-1624	101	22	0	0	NUM
ejpam-1624	101	23			NOUN
ejpam-1624	101	24			NOUN
ejpam-1624	101	25			VERB
ejpam-1624	101	26			NOUN
ejpam-1624	101	27			PUNCT
ejpam-1624	101	28	,	,	PUNCT
ejpam-1624	101	29	and	and	CCONJ
ejpam-1624	101	30	qpq	qpq	ADJ
ejpam-1624	101	31	=	=	SYM
ejpam-1624	101	32			PROPN
ejpam-1624	101	33			NOUN
ejpam-1624	101	34			NOUN
ejpam-1624	101	35			NOUN
ejpam-1624	101	36			NOUN
ejpam-1624	101	37	0	0	NUM
ejpam-1624	101	38	0	0	NUM
ejpam-1624	102	1	q12q′23	q12q′23	CCONJ
ejpam-1624	102	2	q12q′′23	q12q′′23	PROPN
ejpam-1624	102	3	0	0	NUM
ejpam-1624	102	4	0	0	NUM
ejpam-1624	102	5	0	0	NUM
ejpam-1624	102	6	0	0	NUM
ejpam-1624	102	7	0	0	NUM
ejpam-1624	102	8	0	0	NUM
ejpam-1624	102	9	0	0	NUM
ejpam-1624	102	10	0	0	NUM
ejpam-1624	102	11	0	0	NUM
ejpam-1624	102	12	0	0	NUM
ejpam-1624	102	13	0	0	NUM
ejpam-1624	102	14	0	0	NUM
ejpam-1624	102	15			NOUN
ejpam-1624	102	16			NOUN
ejpam-1624	102	17			VERB
ejpam-1624	102	18			NOUN
ejpam-1624	102	19			PUNCT
ejpam-1624	102	20	.	.	PUNCT
ejpam-1624	103	1	therefore	therefore	ADV
ejpam-1624	103	2	,	,	PUNCT
ejpam-1624	103	3	(	(	PUNCT
ejpam-1624	103	4	ap	ap	PROPN
ejpam-1624	103	5	+	+	NUM
ejpam-1624	103	6	bq+	bq+	NOUN
ejpam-1624	103	7	cpq+	cpq+	ADP
ejpam-1624	103	8	dqp)d	dqp)d	PROPN
ejpam-1624	103	9	=	=	PUNCT
ejpam-1624	103	10	1	1	NUM
ejpam-1624	103	11	a	a	DET
ejpam-1624	103	12	p	p	X
ejpam-1624	103	13	+	+	NOUN
ejpam-1624	103	14	1	1	NUM
ejpam-1624	103	15	b	b	X
ejpam-1624	103	16	q−	q−	PROPN
ejpam-1624	103	17	(	(	PUNCT
ejpam-1624	103	18	1	1	NUM
ejpam-1624	103	19	a	a	DET
ejpam-1624	103	20	+	+	NUM
ejpam-1624	103	21	1	1	NUM
ejpam-1624	103	22	b	b	NOUN
ejpam-1624	103	23	+	+	NUM
ejpam-1624	103	24	c	c	PROPN
ejpam-1624	103	25	ab	ab	PROPN
ejpam-1624	103	26	)	)	PUNCT
ejpam-1624	103	27	pq−	pq−	PROPN
ejpam-1624	103	28	(	(	PUNCT
ejpam-1624	103	29	1	1	NUM
ejpam-1624	103	30	a	a	PRON
ejpam-1624	103	31	+	+	NUM
ejpam-1624	103	32	1	1	NUM
ejpam-1624	103	33	b	b	NOUN
ejpam-1624	103	34	+	+	CCONJ
ejpam-1624	103	35	d	d	PROPN
ejpam-1624	103	36	ab	ab	PROPN
ejpam-1624	103	37	)	)	PUNCT
ejpam-1624	103	38	qp	qp	VERB
ejpam-1624	104	1	+	+	NOUN
ejpam-1624	104	2	(	(	PUNCT
ejpam-1624	104	3	1	1	NUM
ejpam-1624	104	4	a	a	DET
ejpam-1624	104	5	+	+	NUM
ejpam-1624	104	6	2	2	NUM
ejpam-1624	104	7	b	b	NOUN
ejpam-1624	104	8	+	+	NUM
ejpam-1624	104	9	c	c	NOUN
ejpam-1624	104	10	ab	ab	NOUN
ejpam-1624	105	1	+	+	PROPN
ejpam-1624	105	2	d	d	PROPN
ejpam-1624	105	3	ab	ab	PROPN
ejpam-1624	105	4	+	+	PROPN
ejpam-1624	105	5	cd	cd	PROPN
ejpam-1624	105	6	ab2	ab2	NOUN
ejpam-1624	105	7	)	)	PUNCT
ejpam-1624	105	8	qpq	qpq	INTJ
ejpam-1624	105	9	.	.	PUNCT
ejpam-1624	106	1	now	now	ADV
ejpam-1624	106	2	we	we	PRON
ejpam-1624	106	3	can	can	AUX
ejpam-1624	106	4	derive	derive	VERB
ejpam-1624	106	5	some	some	DET
ejpam-1624	106	6	special	special	ADJ
ejpam-1624	106	7	cases	case	NOUN
ejpam-1624	106	8	from	from	ADP
ejpam-1624	106	9	theorem	theorem	ADJ
ejpam-1624	106	10	1	1	NUM
ejpam-1624	106	11	.	.	PUNCT
ejpam-1624	107	1	these	these	DET
ejpam-1624	107	2	results	result	NOUN
ejpam-1624	107	3	are	be	AUX
ejpam-1624	107	4	also	also	ADV
ejpam-1624	107	5	the	the	DET
ejpam-1624	107	6	cases	case	NOUN
ejpam-1624	107	7	of	of	ADP
ejpam-1624	107	8	theorem	theorem	NOUN
ejpam-1624	107	9	2.1	2.1	NUM
ejpam-1624	107	10	in	in	ADP
ejpam-1624	107	11	[	[	X
ejpam-1624	107	12	4	4	NUM
ejpam-1624	107	13	]	]	PUNCT
ejpam-1624	107	14	.	.	PUNCT
ejpam-1624	108	1	corollary	corollary	ADJ
ejpam-1624	108	2	1	1	NUM
ejpam-1624	108	3	.	.	PUNCT
ejpam-1624	109	1	let	let	VERB
ejpam-1624	109	2	p	p	NOUN
ejpam-1624	109	3	and	and	CCONJ
ejpam-1624	109	4	q	q	NOUN
ejpam-1624	109	5	be	be	AUX
ejpam-1624	109	6	two	two	NUM
ejpam-1624	109	7	idempotents	idempotent	NOUN
ejpam-1624	109	8	in	in	ADP
ejpam-1624	109	9	b(h	b(h	PROPN
ejpam-1624	109	10	)	)	PUNCT
ejpam-1624	109	11	.	.	PUNCT
ejpam-1624	110	1	assume	assume	VERB
ejpam-1624	110	2	that	that	SCONJ
ejpam-1624	110	3	pqp	pqp	NOUN
ejpam-1624	110	4	=	=	NOUN
ejpam-1624	110	5	0	0	NUM
ejpam-1624	110	6	,	,	PUNCT
ejpam-1624	110	7	then	then	ADV
ejpam-1624	110	8	the	the	DET
ejpam-1624	110	9	following	follow	VERB
ejpam-1624	110	10	statements	statement	NOUN
ejpam-1624	110	11	hold	hold	VERB
ejpam-1624	110	12	.	.	PUNCT
ejpam-1624	111	1	(	(	PUNCT
ejpam-1624	111	2	i	i	NOUN
ejpam-1624	111	3	)	)	PUNCT
ejpam-1624	111	4	(	(	PUNCT
ejpam-1624	111	5	p	p	NOUN
ejpam-1624	111	6	+	+	NOUN
ejpam-1624	111	7	q)d	q)d	NOUN
ejpam-1624	111	8	=	=	NOUN
ejpam-1624	111	9	p	p	X
ejpam-1624	112	1	+	+	NOUN
ejpam-1624	112	2	q−	q−	PROPN
ejpam-1624	112	3	2(pq+qp	2(pq+qp	NUM
ejpam-1624	112	4	)	)	PUNCT
ejpam-1624	113	1	+	+	CCONJ
ejpam-1624	113	2	3qpq	3qpq	X
ejpam-1624	113	3	.	.	PUNCT
ejpam-1624	114	1	(	(	PUNCT
ejpam-1624	114	2	ii	ii	NOUN
ejpam-1624	114	3	)	)	PUNCT
ejpam-1624	114	4	(	(	PUNCT
ejpam-1624	114	5	p	p	NOUN
ejpam-1624	114	6	−q)d	−q)d	VERB
ejpam-1624	114	7	=	=	PROPN
ejpam-1624	114	8	p	p	X
ejpam-1624	115	1	−q−qpq	−q−qpq	PROPN
ejpam-1624	115	2	.	.	PUNCT
ejpam-1624	116	1	if	if	SCONJ
ejpam-1624	116	2	either	either	PRON
ejpam-1624	116	3	of	of	ADP
ejpam-1624	116	4	the	the	DET
ejpam-1624	116	5	stronger	strong	ADJ
ejpam-1624	116	6	condition	condition	NOUN
ejpam-1624	116	7	pq	pq	NOUN
ejpam-1624	116	8	=	=	SYM
ejpam-1624	116	9	0	0	NUM
ejpam-1624	116	10	or	or	CCONJ
ejpam-1624	116	11	qp	qp	ADV
ejpam-1624	116	12	=	=	SYM
ejpam-1624	116	13	0	0	NUM
ejpam-1624	116	14	is	be	AUX
ejpam-1624	116	15	satisfied	satisfied	ADJ
ejpam-1624	116	16	,	,	PUNCT
ejpam-1624	116	17	then	then	ADV
ejpam-1624	116	18	by	by	ADP
ejpam-1624	116	19	theorem	theorem	NOUN
ejpam-1624	116	20	1	1	NUM
ejpam-1624	116	21	,	,	PUNCT
ejpam-1624	116	22	we	we	PRON
ejpam-1624	116	23	obtain	obtain	VERB
ejpam-1624	116	24	the	the	DET
ejpam-1624	116	25	following	follow	VERB
ejpam-1624	116	26	results	result	NOUN
ejpam-1624	116	27	.	.	PUNCT
ejpam-1624	117	1	corollary	corollary	ADJ
ejpam-1624	117	2	2	2	NUM
ejpam-1624	117	3	.	.	PUNCT
ejpam-1624	118	1	let	let	VERB
ejpam-1624	118	2	p	p	NOUN
ejpam-1624	118	3	and	and	CCONJ
ejpam-1624	118	4	q	q	NOUN
ejpam-1624	118	5	be	be	AUX
ejpam-1624	118	6	two	two	NUM
ejpam-1624	118	7	idempotents	idempotent	NOUN
ejpam-1624	118	8	in	in	ADP
ejpam-1624	118	9	b(h	b(h	PROPN
ejpam-1624	118	10	)	)	PUNCT
ejpam-1624	118	11	and	and	CCONJ
ejpam-1624	118	12	a	a	DET
ejpam-1624	118	13	,	,	PUNCT
ejpam-1624	118	14	b	b	X
ejpam-1624	118	15	∈	∈	PROPN
ejpam-1624	118	16	c	c	X
ejpam-1624	118	17	,	,	PUNCT
ejpam-1624	118	18	ab	ab	PROPN
ejpam-1624	118	19	6=	6=	ADP
ejpam-1624	118	20	0	0	NUM
ejpam-1624	118	21	.	.	PUNCT
ejpam-1624	119	1	then	then	ADV
ejpam-1624	119	2	the	the	DET
ejpam-1624	119	3	following	follow	VERB
ejpam-1624	119	4	statements	statement	NOUN
ejpam-1624	119	5	hold	hold	VERB
ejpam-1624	119	6	.	.	PUNCT
ejpam-1624	120	1	(	(	PUNCT
ejpam-1624	120	2	i	i	NOUN
ejpam-1624	120	3	)	)	PUNCT
ejpam-1624	120	4	if	if	SCONJ
ejpam-1624	120	5	qp	qp	ADV
ejpam-1624	120	6	=	=	SYM
ejpam-1624	120	7	0	0	NUM
ejpam-1624	120	8	,	,	PUNCT
ejpam-1624	120	9	then	then	ADV
ejpam-1624	120	10	(	(	PUNCT
ejpam-1624	120	11	ap	ap	PROPN
ejpam-1624	120	12	+	+	CCONJ
ejpam-1624	121	1	bq)d	bq)d	PROPN
ejpam-1624	121	2	=	=	SYM
ejpam-1624	121	3	1	1	NUM
ejpam-1624	121	4	a	a	DET
ejpam-1624	121	5	p	p	X
ejpam-1624	121	6	+	+	NOUN
ejpam-1624	121	7	1	1	NUM
ejpam-1624	121	8	b	b	X
ejpam-1624	121	9	q−	q−	PROPN
ejpam-1624	121	10	(	(	PUNCT
ejpam-1624	121	11	1	1	NUM
ejpam-1624	121	12	a	a	DET
ejpam-1624	121	13	+	+	NUM
ejpam-1624	121	14	1	1	NUM
ejpam-1624	121	15	b	b	NOUN
ejpam-1624	121	16	)	)	PUNCT
ejpam-1624	121	17	pq	pq	NOUN
ejpam-1624	121	18	.	.	PUNCT
ejpam-1624	121	19	(	(	PUNCT
ejpam-1624	121	20	ii	ii	NOUN
ejpam-1624	121	21	)	)	PUNCT
ejpam-1624	121	22	if	if	SCONJ
ejpam-1624	121	23	pq	pq	NOUN
ejpam-1624	121	24	=	=	SYM
ejpam-1624	121	25	0	0	PROPN
ejpam-1624	121	26	,	,	PUNCT
ejpam-1624	121	27	then	then	ADV
ejpam-1624	121	28	(	(	PUNCT
ejpam-1624	121	29	ap	ap	PROPN
ejpam-1624	122	1	+	+	CCONJ
ejpam-1624	122	2	bq)d	bq)d	PROPN
ejpam-1624	122	3	=	=	SYM
ejpam-1624	122	4	1	1	NUM
ejpam-1624	122	5	a	a	DET
ejpam-1624	122	6	p	p	X
ejpam-1624	122	7	+	+	NOUN
ejpam-1624	122	8	1	1	NUM
ejpam-1624	122	9	b	b	X
ejpam-1624	122	10	q−	q−	PROPN
ejpam-1624	122	11	(	(	PUNCT
ejpam-1624	122	12	1	1	NUM
ejpam-1624	122	13	a	a	DET
ejpam-1624	122	14	+	+	NUM
ejpam-1624	122	15	1	1	NUM
ejpam-1624	122	16	b	b	NOUN
ejpam-1624	122	17	)	)	PUNCT
ejpam-1624	122	18	qp	qp	PROPN
ejpam-1624	122	19	.	.	PUNCT
ejpam-1624	123	1	next	next	ADV
ejpam-1624	123	2	we	we	PRON
ejpam-1624	123	3	discuss	discuss	VERB
ejpam-1624	123	4	the	the	DET
ejpam-1624	123	5	drazin	drazin	PROPN
ejpam-1624	123	6	inverse	inverse	NOUN
ejpam-1624	123	7	of	of	ADP
ejpam-1624	123	8	ap	ap	PROPN
ejpam-1624	123	9	+	+	CCONJ
ejpam-1624	123	10	bq+	bq+	PROPN
ejpam-1624	123	11	cpq	cpq	PROPN
ejpam-1624	123	12	+	+	CCONJ
ejpam-1624	123	13	dqp	dqp	NOUN
ejpam-1624	123	14	under	under	ADP
ejpam-1624	123	15	the	the	DET
ejpam-1624	123	16	assumption	assumption	NOUN
ejpam-1624	123	17	that	that	SCONJ
ejpam-1624	123	18	pqp	pqp	NOUN
ejpam-1624	123	19	=	=	PUNCT
ejpam-1624	124	1	p.	p.	NOUN
ejpam-1624	124	2	t.	t.	PROPN
ejpam-1624	124	3	xie	xie	PROPN
ejpam-1624	124	4	,	,	PUNCT
ejpam-1624	124	5	k.	k.	PROPN
ejpam-1624	124	6	zuo	zuo	PROPN
ejpam-1624	124	7	/	/	SYM
ejpam-1624	124	8	eur	eur	PROPN
ejpam-1624	124	9	.	.	PUNCT
ejpam-1624	125	1	j.	j.	PROPN
ejpam-1624	125	2	pure	pure	PROPN
ejpam-1624	125	3	appl	appl	PROPN
ejpam-1624	125	4	.	.	PROPN
ejpam-1624	125	5	math	math	PROPN
ejpam-1624	125	6	,	,	PUNCT
ejpam-1624	125	7	5	5	NUM
ejpam-1624	125	8	(	(	PUNCT
ejpam-1624	125	9	2012	2012	NUM
ejpam-1624	125	10	)	)	PUNCT
ejpam-1624	125	11	,	,	PUNCT
ejpam-1624	125	12	480	480	NUM
ejpam-1624	125	13	-	-	SYM
ejpam-1624	125	14	491	491	NUM
ejpam-1624	125	15	485	485	NUM
ejpam-1624	125	16	theorem	theorem	NOUN
ejpam-1624	125	17	2	2	NUM
ejpam-1624	125	18	.	.	PUNCT
ejpam-1624	126	1	let	let	VERB
ejpam-1624	126	2	p	p	NOUN
ejpam-1624	126	3	and	and	CCONJ
ejpam-1624	126	4	q	q	NOUN
ejpam-1624	126	5	be	be	AUX
ejpam-1624	126	6	two	two	NUM
ejpam-1624	126	7	idempotents	idempotent	NOUN
ejpam-1624	126	8	in	in	ADP
ejpam-1624	126	9	b(h	b(h	PROPN
ejpam-1624	126	10	)	)	PUNCT
ejpam-1624	127	1	,	,	PUNCT
ejpam-1624	127	2	then	then	ADV
ejpam-1624	127	3	for	for	ADP
ejpam-1624	127	4	any	any	DET
ejpam-1624	127	5	a	a	DET
ejpam-1624	127	6	,	,	PUNCT
ejpam-1624	127	7	b	b	NOUN
ejpam-1624	127	8	,	,	PUNCT
ejpam-1624	127	9	c	c	NOUN
ejpam-1624	127	10	,	,	PUNCT
ejpam-1624	127	11	d	d	PROPN
ejpam-1624	127	12	∈	∈	PROPN
ejpam-1624	127	13	c	c	X
ejpam-1624	127	14	,	,	PUNCT
ejpam-1624	127	15	ab	ab	PROPN
ejpam-1624	127	16	6=	6=	PROPN
ejpam-1624	127	17	0	0	NUM
ejpam-1624	127	18	,	,	PUNCT
ejpam-1624	127	19	the	the	DET
ejpam-1624	127	20	combinations	combination	NOUN
ejpam-1624	127	21	ap	ap	PROPN
ejpam-1624	127	22	+	+	NUM
ejpam-1624	127	23	bq+	bq+	PROPN
ejpam-1624	127	24	cpq	cpq	PROPN
ejpam-1624	127	25	+	+	CCONJ
ejpam-1624	127	26	dqp	dqp	PROPN
ejpam-1624	127	27	are	be	AUX
ejpam-1624	127	28	drazin	drazin	PROPN
ejpam-1624	127	29	invertible	invertible	ADJ
ejpam-1624	127	30	under	under	ADP
ejpam-1624	127	31	the	the	DET
ejpam-1624	127	32	condition	condition	NOUN
ejpam-1624	127	33	pqp	pqp	NOUN
ejpam-1624	127	34	=	=	PUNCT
ejpam-1624	128	1	p.	p.	NOUN
ejpam-1624	128	2	the	the	DET
ejpam-1624	128	3	drazin	drazin	PROPN
ejpam-1624	128	4	inverses	inverses	PROPN
ejpam-1624	128	5	of	of	ADP
ejpam-1624	128	6	ap	ap	PROPN
ejpam-1624	128	7	+	+	CCONJ
ejpam-1624	128	8	bq+	bq+	PROPN
ejpam-1624	128	9	cpq+	cpq+	PROPN
ejpam-1624	128	10	dqp	dqp	NOUN
ejpam-1624	128	11	can	can	AUX
ejpam-1624	128	12	be	be	AUX
ejpam-1624	128	13	represented	represent	VERB
ejpam-1624	128	14	as	as	ADP
ejpam-1624	128	15	following	follow	VERB
ejpam-1624	128	16	:	:	PUNCT
ejpam-1624	128	17	(	(	PUNCT
ejpam-1624	128	18	i	i	NOUN
ejpam-1624	128	19	)	)	PUNCT
ejpam-1624	128	20	if	if	SCONJ
ejpam-1624	128	21	a+	a+	X
ejpam-1624	128	22	b+	b+	X
ejpam-1624	128	23	c	c	X
ejpam-1624	129	1	+	+	SYM
ejpam-1624	129	2	d	d	X
ejpam-1624	129	3	6=	6=	NUM
ejpam-1624	129	4	0	0	NUM
ejpam-1624	129	5	,	,	PUNCT
ejpam-1624	129	6	then	then	ADV
ejpam-1624	129	7	(	(	PUNCT
ejpam-1624	129	8	ap	ap	PROPN
ejpam-1624	129	9	+	+	NUM
ejpam-1624	129	10	bq+	bq+	NOUN
ejpam-1624	129	11	cpq+	cpq+	ADP
ejpam-1624	129	12	dqp)d	dqp)d	PROPN
ejpam-1624	129	13	=	=	PUNCT
ejpam-1624	129	14	(	(	PUNCT
ejpam-1624	129	15	a+	a+	X
ejpam-1624	129	16	c)(a+	c)(a+	NOUN
ejpam-1624	129	17	d	d	PROPN
ejpam-1624	129	18	)	)	PUNCT
ejpam-1624	129	19	(	(	PUNCT
ejpam-1624	129	20	a+	a+	X
ejpam-1624	129	21	b+	b+	X
ejpam-1624	129	22	c	c	X
ejpam-1624	129	23	+	+	PUNCT
ejpam-1624	129	24	d)3	d)3	NOUN
ejpam-1624	129	25	p	p	NOUN
ejpam-1624	129	26	+	+	NOUN
ejpam-1624	129	27	1	1	NUM
ejpam-1624	129	28	b	b	NOUN
ejpam-1624	129	29	q+	q+	X
ejpam-1624	129	30	(	(	PUNCT
ejpam-1624	129	31	b+	b+	X
ejpam-1624	129	32	c)(a+	c)(a+	NOUN
ejpam-1624	129	33	c	c	NOUN
ejpam-1624	129	34	)	)	PUNCT
ejpam-1624	129	35	(	(	PUNCT
ejpam-1624	129	36	a+	a+	X
ejpam-1624	129	37	b+	b+	X
ejpam-1624	129	38	c	c	X
ejpam-1624	129	39	+	+	PUNCT
ejpam-1624	129	40	d)3	d)3	PROPN
ejpam-1624	129	41	pq	pq	NOUN
ejpam-1624	129	42	+	+	CCONJ
ejpam-1624	129	43	(	(	PUNCT
ejpam-1624	129	44	a+	a+	X
ejpam-1624	129	45	d)(b+	d)(b+	NOUN
ejpam-1624	129	46	d	d	NOUN
ejpam-1624	129	47	)	)	PUNCT
ejpam-1624	129	48	(	(	PUNCT
ejpam-1624	129	49	a+	a+	X
ejpam-1624	129	50	b+	b+	X
ejpam-1624	129	51	c	c	X
ejpam-1624	129	52	+	+	PUNCT
ejpam-1624	129	53	d)3	d)3	NOUN
ejpam-1624	129	54	qp	qp	ADP
ejpam-1624	129	55	+	+	X
ejpam-1624	129	56	[	[	PUNCT
ejpam-1624	129	57	(	(	PUNCT
ejpam-1624	129	58	b+	b+	X
ejpam-1624	129	59	c)(b+	c)(b+	X
ejpam-1624	129	60	d	d	X
ejpam-1624	129	61	)	)	PUNCT
ejpam-1624	129	62	(	(	PUNCT
ejpam-1624	129	63	a+	a+	X
ejpam-1624	129	64	b+	b+	X
ejpam-1624	129	65	c	c	X
ejpam-1624	129	66	+	+	PUNCT
ejpam-1624	129	67	d)3	d)3	VERB
ejpam-1624	129	68	−	−	PROPN
ejpam-1624	129	69	1	1	NUM
ejpam-1624	129	70	b	b	NOUN
ejpam-1624	129	71	]	]	X
ejpam-1624	129	72	qpq	qpq	NOUN
ejpam-1624	129	73	.	.	PUNCT
ejpam-1624	130	1	(	(	PUNCT
ejpam-1624	130	2	ii	ii	NOUN
ejpam-1624	130	3	)	)	PUNCT
ejpam-1624	130	4	if	if	SCONJ
ejpam-1624	130	5	a+	a+	X
ejpam-1624	130	6	b+	b+	X
ejpam-1624	130	7	c	c	X
ejpam-1624	131	1	+	+	SYM
ejpam-1624	131	2	d	d	X
ejpam-1624	131	3	=	=	SYM
ejpam-1624	131	4	0	0	NUM
ejpam-1624	131	5	,	,	PUNCT
ejpam-1624	131	6	then	then	ADV
ejpam-1624	131	7	(	(	PUNCT
ejpam-1624	131	8	ap	ap	PROPN
ejpam-1624	131	9	+	+	NUM
ejpam-1624	131	10	bq+	bq+	NOUN
ejpam-1624	131	11	cpq+	cpq+	ADP
ejpam-1624	131	12	dqp)d	dqp)d	PROPN
ejpam-1624	131	13	=	=	SYM
ejpam-1624	131	14	1	1	NUM
ejpam-1624	131	15	b	b	X
ejpam-1624	131	16	(	(	PUNCT
ejpam-1624	131	17	q−qpq	q−qpq	PROPN
ejpam-1624	131	18	)	)	PUNCT
ejpam-1624	131	19	.	.	PUNCT
ejpam-1624	132	1	proof	proof	NOUN
ejpam-1624	132	2	.	.	PUNCT
ejpam-1624	133	1	if	if	SCONJ
ejpam-1624	133	2	pqp	pqp	NOUN
ejpam-1624	133	3	=	=	SYM
ejpam-1624	133	4	p	p	X
ejpam-1624	133	5	,	,	PUNCT
ejpam-1624	133	6	then	then	ADV
ejpam-1624	133	7	p	p	NOUN
ejpam-1624	133	8	and	and	CCONJ
ejpam-1624	133	9	q	q	NOUN
ejpam-1624	133	10	can	can	AUX
ejpam-1624	133	11	be	be	AUX
ejpam-1624	133	12	written	write	VERB
ejpam-1624	133	13	as	as	ADP
ejpam-1624	133	14	p	p	PROPN
ejpam-1624	133	15	=	=	PROPN
ejpam-1624	133	16	�	�	PROPN
ejpam-1624	133	17	i	i	NOUN
ejpam-1624	133	18	0	0	NUM
ejpam-1624	133	19	0	0	SYM
ejpam-1624	133	20	0	0	NUM
ejpam-1624	133	21	�	�	PROPN
ejpam-1624	133	22	,	,	PUNCT
ejpam-1624	133	23	q	q	NOUN
ejpam-1624	133	24	=	=	PUNCT
ejpam-1624	133	25	�	�	PROPN
ejpam-1624	133	26	i	i	PRON
ejpam-1624	133	27	q1	q1	PROPN
ejpam-1624	133	28	q2	q2	PROPN
ejpam-1624	133	29	q3	q3	PROPN
ejpam-1624	133	30	�	�	PROPN
ejpam-1624	133	31	under	under	ADP
ejpam-1624	133	32	the	the	DET
ejpam-1624	133	33	space	space	NOUN
ejpam-1624	133	34	decomposition	decomposition	NOUN
ejpam-1624	133	35	of	of	ADP
ejpam-1624	133	36	h	h	NOUN
ejpam-1624	133	37	=	=	PUNCT
ejpam-1624	133	38	r(p)⊕r(p)⊥.	r(p)⊕r(p)⊥.	ADP
ejpam-1624	133	39	the	the	DET
ejpam-1624	133	40	idempotency	idempotency	NOUN
ejpam-1624	133	41	of	of	ADP
ejpam-1624	133	42	q	q	NOUN
ejpam-1624	133	43	yields	yield	NOUN
ejpam-1624	134	1	that	that	PRON
ejpam-1624	134	2	q1q2	q1q2	AUX
ejpam-1624	134	3	=	=	SYM
ejpam-1624	134	4	0	0	NUM
ejpam-1624	134	5	,	,	PUNCT
ejpam-1624	134	6	q1q3	q1q3	ADP
ejpam-1624	134	7	=	=	SYM
ejpam-1624	134	8	0	0	NUM
ejpam-1624	134	9	,	,	PUNCT
ejpam-1624	134	10	q3q2	q3q2	NOUN
ejpam-1624	134	11	=	=	SYM
ejpam-1624	134	12	0	0	PUNCT
ejpam-1624	134	13	and	and	CCONJ
ejpam-1624	134	14	q2q1	q2q1	PROPN
ejpam-1624	134	15	+	+	NUM
ejpam-1624	134	16	q2	q2	NOUN
ejpam-1624	134	17	3	3	NUM
ejpam-1624	134	18	=	=	SYM
ejpam-1624	134	19	q3	q3	PROPN
ejpam-1624	134	20	.	.	PUNCT
ejpam-1624	135	1	it	it	PRON
ejpam-1624	135	2	follows	follow	VERB
ejpam-1624	135	3	that	that	DET
ejpam-1624	135	4	r(q2	r(q2	NOUN
ejpam-1624	135	5	)	)	PUNCT
ejpam-1624	136	1	⊆	⊆	NUM
ejpam-1624	136	2	n	n	NUM
ejpam-1624	136	3	(	(	PUNCT
ejpam-1624	136	4	q1	q1	PROPN
ejpam-1624	136	5	)	)	PUNCT
ejpam-1624	136	6	,	,	PUNCT
ejpam-1624	136	7	r(q2)⊆n	r(q2)⊆n	PROPN
ejpam-1624	136	8	(	(	PUNCT
ejpam-1624	136	9	q3	q3	PROPN
ejpam-1624	136	10	)	)	PUNCT
ejpam-1624	136	11	,	,	PUNCT
ejpam-1624	136	12	r(q3)⊆n	r(q3)⊆n	PROPN
ejpam-1624	136	13	(	(	PUNCT
ejpam-1624	136	14	q1	q1	PROPN
ejpam-1624	136	15	)	)	PUNCT
ejpam-1624	136	16	.	.	PUNCT
ejpam-1624	137	1	with	with	ADP
ejpam-1624	137	2	respect	respect	NOUN
ejpam-1624	137	3	to	to	ADP
ejpam-1624	137	4	the	the	DET
ejpam-1624	137	5	space	space	NOUN
ejpam-1624	137	6	decomposition	decomposition	NOUN
ejpam-1624	137	7	h	h	NOUN
ejpam-1624	137	8	=	=	SYM
ejpam-1624	137	9	r(q1)⊕r(q1	r(q1)⊕r(q1	PROPN
ejpam-1624	137	10	)	)	PUNCT
ejpam-1624	138	1	⊥	⊥	NOUN
ejpam-1624	138	2	⊕r(q2)⊕r(q2	⊕r(q2)⊕r(q2	NOUN
ejpam-1624	138	3	)	)	PUNCT
ejpam-1624	139	1	⊥	⊥	NOUN
ejpam-1624	139	2	,	,	PUNCT
ejpam-1624	139	3	p	p	NOUN
ejpam-1624	139	4	and	and	CCONJ
ejpam-1624	139	5	q	q	NOUN
ejpam-1624	139	6	can	can	AUX
ejpam-1624	139	7	be	be	AUX
ejpam-1624	139	8	represented	represent	VERB
ejpam-1624	139	9	as	as	ADP
ejpam-1624	139	10	p	p	NOUN
ejpam-1624	139	11	=	=	PUNCT
ejpam-1624	139	12			PROPN
ejpam-1624	139	13			NOUN
ejpam-1624	139	14			NOUN
ejpam-1624	139	15			NOUN
ejpam-1624	139	16			NOUN
ejpam-1624	139	17	i	i	PRON
ejpam-1624	139	18	0	0	NUM
ejpam-1624	139	19	0	0	NUM
ejpam-1624	139	20	0	0	NUM
ejpam-1624	139	21	0	0	NUM
ejpam-1624	140	1	i	i	NOUN
ejpam-1624	140	2	0	0	NUM
ejpam-1624	140	3	0	0	NUM
ejpam-1624	140	4	0	0	NUM
ejpam-1624	140	5	0	0	NUM
ejpam-1624	140	6	0	0	NUM
ejpam-1624	140	7	0	0	NUM
ejpam-1624	140	8	0	0	NUM
ejpam-1624	140	9	0	0	NUM
ejpam-1624	140	10	0	0	NUM
ejpam-1624	140	11	0	0	NUM
ejpam-1624	140	12			NOUN
ejpam-1624	140	13			NOUN
ejpam-1624	140	14			VERB
ejpam-1624	140	15			NOUN
ejpam-1624	140	16			PUNCT
ejpam-1624	140	17	,	,	PUNCT
ejpam-1624	140	18	q	q	NOUN
ejpam-1624	140	19	=	=	SYM
ejpam-1624	140	20			PROPN
ejpam-1624	140	21			NOUN
ejpam-1624	140	22			NOUN
ejpam-1624	140	23			NOUN
ejpam-1624	140	24			NOUN
ejpam-1624	141	1	i	i	PRON
ejpam-1624	141	2	0	0	NUM
ejpam-1624	141	3	0	0	NUM
ejpam-1624	142	1	q′11	q′11	NOUN
ejpam-1624	142	2	0	0	PUNCT
ejpam-1624	143	1	i	i	NOUN
ejpam-1624	143	2	0	0	NUM
ejpam-1624	143	3	0	0	NUM
ejpam-1624	143	4	q21	q21	NOUN
ejpam-1624	143	5	q22	q22	NOUN
ejpam-1624	143	6	0	0	NUM
ejpam-1624	143	7	q31	q31	ADJ
ejpam-1624	143	8	0	0	NUM
ejpam-1624	143	9	0	0	NUM
ejpam-1624	143	10	0	0	NUM
ejpam-1624	143	11	q32	q32	NOUN
ejpam-1624	143	12			PROPN
ejpam-1624	143	13			NOUN
ejpam-1624	143	14			VERB
ejpam-1624	143	15			NOUN
ejpam-1624	143	16			PUNCT
ejpam-1624	144	1	,	,	PUNCT
ejpam-1624	144	2	where	where	SCONJ
ejpam-1624	144	3	q11q32	q11q32	VERB
ejpam-1624	144	4	=	=	SYM
ejpam-1624	144	5	0,q2	0,q2	NUM
ejpam-1624	144	6	32	32	NUM
ejpam-1624	144	7	=	=	NOUN
ejpam-1624	144	8	q32	q32	NOUN
ejpam-1624	144	9	and	and	CCONJ
ejpam-1624	144	10	q21q11+q31q32	q21q11+q31q32	PROPN
ejpam-1624	144	11	=	=	SYM
ejpam-1624	144	12	q31	q31	PROPN
ejpam-1624	144	13	.	.	PUNCT
ejpam-1624	145	1	so	so	ADV
ejpam-1624	145	2	,	,	PUNCT
ejpam-1624	145	3	under	under	ADP
ejpam-1624	145	4	the	the	DET
ejpam-1624	145	5	space	space	NOUN
ejpam-1624	145	6	decomposition	decomposition	NOUN
ejpam-1624	145	7	of	of	ADP
ejpam-1624	145	8	h	h	NOUN
ejpam-1624	145	9	=	=	SYM
ejpam-1624	145	10	r(q1)⊕r(q1	r(q1)⊕r(q1	PROPN
ejpam-1624	145	11	)	)	PUNCT
ejpam-1624	145	12	⊥	⊥	PROPN
ejpam-1624	145	13	⊕r(q2)⊕r(q32)⊕r(q32	⊕r(q2)⊕r(q32)⊕r(q32	PROPN
ejpam-1624	145	14	)	)	PUNCT
ejpam-1624	145	15	⊥	⊥	NOUN
ejpam-1624	145	16	,	,	PUNCT
ejpam-1624	145	17	the	the	DET
ejpam-1624	145	18	operators	operator	NOUN
ejpam-1624	145	19	p	p	NOUN
ejpam-1624	145	20	and	and	CCONJ
ejpam-1624	145	21	q	q	NOUN
ejpam-1624	145	22	can	can	AUX
ejpam-1624	145	23	then	then	ADV
ejpam-1624	145	24	be	be	AUX
ejpam-1624	145	25	further	far	ADV
ejpam-1624	145	26	written	write	VERB
ejpam-1624	145	27	as	as	ADP
ejpam-1624	145	28	p	p	NOUN
ejpam-1624	145	29	=	=	PUNCT
ejpam-1624	145	30			PROPN
ejpam-1624	145	31			NOUN
ejpam-1624	145	32			NOUN
ejpam-1624	145	33			NOUN
ejpam-1624	145	34			NOUN
ejpam-1624	145	35			NOUN
ejpam-1624	145	36			NOUN
ejpam-1624	145	37	i	i	PRON
ejpam-1624	145	38	0	0	NUM
ejpam-1624	145	39	0	0	NUM
ejpam-1624	145	40	0	0	NUM
ejpam-1624	145	41	0	0	NUM
ejpam-1624	145	42	0	0	NUM
ejpam-1624	146	1	i	i	NOUN
ejpam-1624	146	2	0	0	NUM
ejpam-1624	146	3	0	0	NUM
ejpam-1624	146	4	0	0	NUM
ejpam-1624	146	5	0	0	NUM
ejpam-1624	146	6	0	0	NUM
ejpam-1624	146	7	0	0	NUM
ejpam-1624	146	8	0	0	NUM
ejpam-1624	146	9	0	0	NUM
ejpam-1624	146	10	0	0	NUM
ejpam-1624	146	11	0	0	NUM
ejpam-1624	146	12	0	0	NUM
ejpam-1624	146	13	0	0	NUM
ejpam-1624	146	14	0	0	NUM
ejpam-1624	146	15	0	0	NUM
ejpam-1624	146	16	0	0	NUM
ejpam-1624	146	17	0	0	NUM
ejpam-1624	146	18	0	0	NUM
ejpam-1624	146	19	0	0	NUM
ejpam-1624	146	20			NOUN
ejpam-1624	146	21			NOUN
ejpam-1624	146	22			VERB
ejpam-1624	146	23			NOUN
ejpam-1624	146	24			NOUN
ejpam-1624	146	25			NOUN
ejpam-1624	146	26			PUNCT
ejpam-1624	146	27	,	,	PUNCT
ejpam-1624	146	28	q	q	NOUN
ejpam-1624	146	29	=	=	SYM
ejpam-1624	146	30			PROPN
ejpam-1624	146	31			NOUN
ejpam-1624	146	32			NOUN
ejpam-1624	146	33			NOUN
ejpam-1624	146	34			NOUN
ejpam-1624	146	35			NOUN
ejpam-1624	146	36			NOUN
ejpam-1624	146	37	i	i	PRON
ejpam-1624	146	38	0	0	NUM
ejpam-1624	146	39	0	0	NUM
ejpam-1624	146	40	0	0	NUM
ejpam-1624	147	1	q′′11	q′′11	NOUN
ejpam-1624	147	2	0	0	PUNCT
ejpam-1624	148	1	i	i	NOUN
ejpam-1624	148	2	0	0	NUM
ejpam-1624	148	3	0	0	NUM
ejpam-1624	148	4	0	0	NUM
ejpam-1624	148	5	q21	q21	NOUN
ejpam-1624	148	6	q22	q22	NOUN
ejpam-1624	148	7	0	0	NUM
ejpam-1624	149	1	q′31	q′31	NOUN
ejpam-1624	150	1	q′′31	q′′31	ADP
ejpam-1624	150	2	0	0	NUM
ejpam-1624	150	3	0	0	NUM
ejpam-1624	150	4	0	0	NUM
ejpam-1624	151	1	i	i	PRON
ejpam-1624	151	2	q′′32	q′′32	NOUN
ejpam-1624	151	3	0	0	NUM
ejpam-1624	151	4	0	0	NUM
ejpam-1624	151	5	0	0	NUM
ejpam-1624	151	6	0	0	NUM
ejpam-1624	151	7	0	0	NUM
ejpam-1624	151	8			NOUN
ejpam-1624	151	9			NOUN
ejpam-1624	151	10			VERB
ejpam-1624	151	11			NOUN
ejpam-1624	151	12			NOUN
ejpam-1624	151	13			NOUN
ejpam-1624	151	14			PUNCT
ejpam-1624	151	15	,	,	PUNCT
ejpam-1624	152	1	where	where	SCONJ
ejpam-1624	152	2	q21q′′11	q21q′′11	PROPN
ejpam-1624	152	3	+	+	NOUN
ejpam-1624	152	4	q′31q′′32	q′31q′′32	NOUN
ejpam-1624	152	5	=	=	SYM
ejpam-1624	152	6	q′′31	q′′31	PROPN
ejpam-1624	152	7	.	.	PUNCT
ejpam-1624	152	8	(	(	PUNCT
ejpam-1624	152	9	i	i	NOUN
ejpam-1624	152	10	)	)	PUNCT
ejpam-1624	152	11	if	if	SCONJ
ejpam-1624	152	12	a+	a+	X
ejpam-1624	152	13	b+	b+	X
ejpam-1624	152	14	c	c	X
ejpam-1624	152	15	+	+	SYM
ejpam-1624	152	16	d	d	X
ejpam-1624	152	17	6=	6=	NUM
ejpam-1624	152	18	0	0	NUM
ejpam-1624	152	19	,	,	PUNCT
ejpam-1624	152	20	then	then	ADV
ejpam-1624	152	21	ap+bq+cpq+dqp	ap+bq+cpq+dqp	NOUN
ejpam-1624	152	22	=	=	SYM
ejpam-1624	152	23			PROPN
ejpam-1624	152	24			NOUN
ejpam-1624	152	25			NOUN
ejpam-1624	152	26			NOUN
ejpam-1624	152	27			NOUN
ejpam-1624	152	28			NOUN
ejpam-1624	152	29			NOUN
ejpam-1624	152	30	(	(	PUNCT
ejpam-1624	152	31	a+	a+	X
ejpam-1624	152	32	b+	b+	X
ejpam-1624	152	33	c	c	NOUN
ejpam-1624	152	34	+	+	PUNCT
ejpam-1624	152	35	d)i	d)i	X
ejpam-1624	152	36	0	0	NUM
ejpam-1624	152	37	0	0	NUM
ejpam-1624	152	38	0	0	NUM
ejpam-1624	152	39	(	(	PUNCT
ejpam-1624	152	40	b+	b+	ADP
ejpam-1624	152	41	c)q′′11	c)q′′11	PROPN
ejpam-1624	152	42	0	0	NUM
ejpam-1624	152	43	(	(	PUNCT
ejpam-1624	152	44	a+	a+	X
ejpam-1624	152	45	b+	b+	X
ejpam-1624	152	46	c	c	NOUN
ejpam-1624	152	47	+	+	PUNCT
ejpam-1624	152	48	d)i	d)i	X
ejpam-1624	152	49	0	0	NUM
ejpam-1624	152	50	0	0	NUM
ejpam-1624	152	51	0	0	NUM
ejpam-1624	152	52	(	(	PUNCT
ejpam-1624	152	53	b+	b+	X
ejpam-1624	152	54	d)q21	d)q21	PROPN
ejpam-1624	152	55	(	(	PUNCT
ejpam-1624	152	56	b+	b+	X
ejpam-1624	152	57	d)q22	d)q22	PROPN
ejpam-1624	152	58	0	0	PUNCT
ejpam-1624	153	1	bq′31	bq′31	PRON
ejpam-1624	153	2	bq′′31	bq′′31	VERB
ejpam-1624	153	3	0	0	NUM
ejpam-1624	153	4	0	0	NUM
ejpam-1624	153	5	0	0	NUM
ejpam-1624	153	6	bi	bi	NOUN
ejpam-1624	153	7	bq′′32	bq′′32	NOUN
ejpam-1624	153	8	0	0	NOUN
ejpam-1624	153	9	0	0	NUM
ejpam-1624	153	10	0	0	NUM
ejpam-1624	153	11	0	0	NUM
ejpam-1624	153	12	0	0	NUM
ejpam-1624	153	13			NOUN
ejpam-1624	153	14			NOUN
ejpam-1624	153	15			VERB
ejpam-1624	153	16			NOUN
ejpam-1624	153	17			NOUN
ejpam-1624	153	18			NOUN
ejpam-1624	153	19			PUNCT
ejpam-1624	153	20	.	.	PUNCT
ejpam-1624	154	1	t.	t.	PROPN
ejpam-1624	154	2	xie	xie	PROPN
ejpam-1624	154	3	,	,	PUNCT
ejpam-1624	154	4	k.	k.	PROPN
ejpam-1624	154	5	zuo	zuo	PROPN
ejpam-1624	154	6	/	/	SYM
ejpam-1624	154	7	eur	eur	PROPN
ejpam-1624	154	8	.	.	PUNCT
ejpam-1624	155	1	j.	j.	PROPN
ejpam-1624	155	2	pure	pure	PROPN
ejpam-1624	155	3	appl	appl	PROPN
ejpam-1624	155	4	.	.	PROPN
ejpam-1624	155	5	math	math	PROPN
ejpam-1624	155	6	,	,	PUNCT
ejpam-1624	155	7	5	5	NUM
ejpam-1624	155	8	(	(	PUNCT
ejpam-1624	155	9	2012	2012	NUM
ejpam-1624	155	10	)	)	PUNCT
ejpam-1624	155	11	,	,	PUNCT
ejpam-1624	155	12	480	480	NUM
ejpam-1624	155	13	-	-	SYM
ejpam-1624	155	14	491	491	NUM
ejpam-1624	155	15	486	486	NUM
ejpam-1624	155	16	since	since	SCONJ
ejpam-1624	155	17	b	b	PROPN
ejpam-1624	155	18	6=	6=	PROPN
ejpam-1624	155	19	0	0	NUM
ejpam-1624	155	20	,	,	PUNCT
ejpam-1624	155	21	let	let	VERB
ejpam-1624	155	22	a′	a′	NOUN
ejpam-1624	155	23	=	=	PUNCT
ejpam-1624	155	24	a	a	DET
ejpam-1624	155	25	b	b	PROPN
ejpam-1624	155	26	,	,	PUNCT
ejpam-1624	155	27	c′	c′	NOUN
ejpam-1624	155	28	=	=	PUNCT
ejpam-1624	155	29	c	c	PROPN
ejpam-1624	155	30	b	b	PROPN
ejpam-1624	155	31	,	,	PUNCT
ejpam-1624	155	32	d	d	NOUN
ejpam-1624	155	33	′	′	NOUN
ejpam-1624	156	1	=	=	PUNCT
ejpam-1624	156	2	d	d	SYM
ejpam-1624	156	3	b	b	PROPN
ejpam-1624	156	4	,	,	PUNCT
ejpam-1624	156	5	then	then	ADV
ejpam-1624	156	6	we	we	PRON
ejpam-1624	156	7	consider	consider	VERB
ejpam-1624	156	8	the	the	DET
ejpam-1624	156	9	following	follow	VERB
ejpam-1624	156	10	combination	combination	NOUN
ejpam-1624	156	11	a′p+q+c′pq+d	a′p+q+c′pq+d	PUNCT
ejpam-1624	156	12	′qp	′qp	NOUN
ejpam-1624	156	13	=	=	SYM
ejpam-1624	156	14			PROPN
ejpam-1624	156	15			NOUN
ejpam-1624	156	16			NOUN
ejpam-1624	156	17			NOUN
ejpam-1624	156	18			NOUN
ejpam-1624	156	19			NOUN
ejpam-1624	156	20			NOUN
ejpam-1624	156	21	(	(	PUNCT
ejpam-1624	156	22	a′	a′	ADJ
ejpam-1624	156	23	+	+	SYM
ejpam-1624	156	24	1	1	NUM
ejpam-1624	156	25	+	+	NUM
ejpam-1624	156	26	c′	c′	NOUN
ejpam-1624	157	1	+	+	CCONJ
ejpam-1624	157	2	d	d	NOUN
ejpam-1624	157	3	′)i	′)i	PROPN
ejpam-1624	157	4	0	0	NUM
ejpam-1624	157	5	0	0	NUM
ejpam-1624	157	6	0	0	NUM
ejpam-1624	157	7	(	(	PUNCT
ejpam-1624	157	8	1	1	NUM
ejpam-1624	157	9	+	+	NUM
ejpam-1624	157	10	c′)q′′11	c′)q′′11	NOUN
ejpam-1624	157	11	0	0	NUM
ejpam-1624	157	12	(	(	PUNCT
ejpam-1624	157	13	a′	a′	ADJ
ejpam-1624	157	14	+	+	SYM
ejpam-1624	157	15	1	1	NUM
ejpam-1624	157	16	+	+	NUM
ejpam-1624	157	17	c′	c′	NOUN
ejpam-1624	157	18	+	+	CCONJ
ejpam-1624	157	19	d	d	NOUN
ejpam-1624	157	20	′)i	′)i	PROPN
ejpam-1624	157	21	0	0	NUM
ejpam-1624	157	22	0	0	NUM
ejpam-1624	157	23	0	0	NUM
ejpam-1624	157	24	(	(	PUNCT
ejpam-1624	157	25	1	1	NUM
ejpam-1624	157	26	+	+	NUM
ejpam-1624	157	27	d	d	NOUN
ejpam-1624	157	28	′)q21	′)q21	NOUN
ejpam-1624	157	29	(	(	PUNCT
ejpam-1624	157	30	1	1	NUM
ejpam-1624	157	31	+	+	NUM
ejpam-1624	157	32	d	d	NOUN
ejpam-1624	157	33	′)q22	′)q22	NOUN
ejpam-1624	157	34	0	0	NUM
ejpam-1624	157	35	q′31	q′31	NOUN
ejpam-1624	158	1	q′′31	q′′31	ADP
ejpam-1624	158	2	0	0	NUM
ejpam-1624	158	3	0	0	NUM
ejpam-1624	158	4	0	0	NUM
ejpam-1624	159	1	i	i	PRON
ejpam-1624	159	2	q′′32	q′′32	NOUN
ejpam-1624	159	3	0	0	NUM
ejpam-1624	159	4	0	0	NUM
ejpam-1624	159	5	0	0	NUM
ejpam-1624	159	6	0	0	NUM
ejpam-1624	159	7	0	0	NUM
ejpam-1624	159	8			NOUN
ejpam-1624	159	9			NOUN
ejpam-1624	159	10			VERB
ejpam-1624	159	11			NOUN
ejpam-1624	159	12			NOUN
ejpam-1624	159	13			NOUN
ejpam-1624	159	14			PUNCT
ejpam-1624	159	15	.	.	PUNCT
ejpam-1624	160	1	let	let	VERB
ejpam-1624	160	2	s	s	PRON
ejpam-1624	160	3	=	=	NOUN
ejpam-1624	160	4			PROPN
ejpam-1624	160	5			NOUN
ejpam-1624	160	6			NOUN
ejpam-1624	160	7			NOUN
ejpam-1624	160	8			NOUN
ejpam-1624	160	9			NOUN
ejpam-1624	160	10			NOUN
ejpam-1624	161	1	i	i	PRON
ejpam-1624	161	2	0	0	NUM
ejpam-1624	161	3	0	0	NUM
ejpam-1624	161	4	0	0	NUM
ejpam-1624	161	5	1+c′	1+c′	NUM
ejpam-1624	161	6	(	(	PUNCT
ejpam-1624	161	7	a′+1+c′+d′	a′+1+c′+d′	PROPN
ejpam-1624	161	8	)	)	PUNCT
ejpam-1624	161	9	q′′11	q′′11	PROPN
ejpam-1624	161	10	0	0	PUNCT
ejpam-1624	162	1	i	i	NOUN
ejpam-1624	162	2	0	0	NUM
ejpam-1624	162	3	0	0	NUM
ejpam-1624	162	4	0	0	NUM
ejpam-1624	162	5	0	0	NUM
ejpam-1624	162	6	0	0	NUM
ejpam-1624	162	7	0	0	NUM
ejpam-1624	163	1	i	i	PRON
ejpam-1624	163	2	q′′32	q′′32	NOUN
ejpam-1624	163	3	0	0	PUNCT
ejpam-1624	163	4	0	0	PUNCT
ejpam-1624	164	1	i	i	PRON
ejpam-1624	164	2	0	0	PUNCT
ejpam-1624	165	1	q′′32	q′′32	NOUN
ejpam-1624	165	2	0	0	NUM
ejpam-1624	165	3	0	0	NUM
ejpam-1624	165	4	0	0	NUM
ejpam-1624	165	5	0	0	NUM
ejpam-1624	166	1	i	i	PRON
ejpam-1624	166	2			PROPN
ejpam-1624	166	3			NOUN
ejpam-1624	166	4			VERB
ejpam-1624	166	5			NOUN
ejpam-1624	166	6			NOUN
ejpam-1624	166	7			NOUN
ejpam-1624	166	8			PUNCT
ejpam-1624	167	1	,	,	PUNCT
ejpam-1624	167	2	then	then	ADV
ejpam-1624	167	3	s−1	s−1	PROPN
ejpam-1624	167	4	=	=	SYM
ejpam-1624	167	5			PROPN
ejpam-1624	167	6			NOUN
ejpam-1624	167	7			NOUN
ejpam-1624	167	8			NOUN
ejpam-1624	167	9			NOUN
ejpam-1624	167	10			NOUN
ejpam-1624	167	11			NOUN
ejpam-1624	167	12	i	i	PRON
ejpam-1624	167	13	0	0	NUM
ejpam-1624	167	14	0	0	NUM
ejpam-1624	167	15	0	0	NUM
ejpam-1624	168	1	−	−	PROPN
ejpam-1624	168	2	1+c′	1+c′	NUM
ejpam-1624	168	3	(	(	PUNCT
ejpam-1624	168	4	a′+1+c′+d′	a′+1+c′+d′	PROPN
ejpam-1624	168	5	)	)	PUNCT
ejpam-1624	168	6	q′′11	q′′11	PROPN
ejpam-1624	168	7	0	0	PUNCT
ejpam-1624	169	1	i	i	NOUN
ejpam-1624	169	2	0	0	NUM
ejpam-1624	169	3	0	0	NUM
ejpam-1624	169	4	0	0	NUM
ejpam-1624	169	5	0	0	NUM
ejpam-1624	169	6	0	0	NUM
ejpam-1624	169	7	0	0	NUM
ejpam-1624	170	1	i	i	PRON
ejpam-1624	170	2	−q′′32	−q′′32	NOUN
ejpam-1624	170	3	0	0	NUM
ejpam-1624	170	4	0	0	PUNCT
ejpam-1624	171	1	i	i	PRON
ejpam-1624	171	2	0	0	NUM
ejpam-1624	172	1	−q′′32	−q′′32	NOUN
ejpam-1624	172	2	0	0	NUM
ejpam-1624	172	3	0	0	NUM
ejpam-1624	172	4	0	0	NUM
ejpam-1624	172	5	0	0	NUM
ejpam-1624	173	1	i	i	PRON
ejpam-1624	173	2			PROPN
ejpam-1624	173	3			NOUN
ejpam-1624	173	4			VERB
ejpam-1624	173	5			NOUN
ejpam-1624	173	6			NOUN
ejpam-1624	173	7			NOUN
ejpam-1624	173	8			PUNCT
ejpam-1624	173	9	.	.	PUNCT
ejpam-1624	174	1	direct	direct	ADJ
ejpam-1624	174	2	calculation	calculation	NOUN
ejpam-1624	174	3	shows	show	VERB
ejpam-1624	174	4	that	that	SCONJ
ejpam-1624	174	5	s(a′p	s(a′p	PROPN
ejpam-1624	175	1	+	+	PROPN
ejpam-1624	175	2	q+	q+	PROPN
ejpam-1624	175	3	c′pq+	c′pq+	PROPN
ejpam-1624	176	1	d	d	NOUN
ejpam-1624	176	2	′qp)s−1	′qp)s−1	NOUN
ejpam-1624	176	3	=	=	SYM
ejpam-1624	176	4			PROPN
ejpam-1624	176	5			NOUN
ejpam-1624	176	6			NOUN
ejpam-1624	176	7			NOUN
ejpam-1624	176	8			NOUN
ejpam-1624	176	9			NOUN
ejpam-1624	176	10			NOUN
ejpam-1624	176	11	(	(	PUNCT
ejpam-1624	176	12	a′+	a′+	NOUN
ejpam-1624	176	13	1	1	NUM
ejpam-1624	176	14	+	+	NUM
ejpam-1624	176	15	c′	c′	NOUN
ejpam-1624	177	1	+	+	CCONJ
ejpam-1624	177	2	d	d	NOUN
ejpam-1624	177	3	′)i	′)i	NOUN
ejpam-1624	177	4	0	0	NUM
ejpam-1624	177	5	0	0	NUM
ejpam-1624	177	6	0	0	NUM
ejpam-1624	177	7	0	0	NUM
ejpam-1624	177	8	0	0	NUM
ejpam-1624	177	9	(	(	PUNCT
ejpam-1624	177	10	a′+	a′+	NOUN
ejpam-1624	177	11	1	1	NUM
ejpam-1624	177	12	+	+	NUM
ejpam-1624	177	13	c′	c′	NOUN
ejpam-1624	178	1	+	+	CCONJ
ejpam-1624	178	2	d	d	NOUN
ejpam-1624	178	3	′)i	′)i	NOUN
ejpam-1624	178	4	0	0	NUM
ejpam-1624	178	5	0	0	NUM
ejpam-1624	178	6	0	0	NUM
ejpam-1624	178	7	0	0	NUM
ejpam-1624	178	8	0	0	NUM
ejpam-1624	179	1	i	i	NOUN
ejpam-1624	179	2	0	0	NUM
ejpam-1624	179	3	0	0	NUM
ejpam-1624	180	1	(	(	PUNCT
ejpam-1624	180	2	1	1	NUM
ejpam-1624	180	3	+	+	NUM
ejpam-1624	180	4	d	d	NOUN
ejpam-1624	180	5	′)q21	′)q21	NOUN
ejpam-1624	180	6	(	(	PUNCT
ejpam-1624	180	7	1	1	NUM
ejpam-1624	180	8	+	+	NUM
ejpam-1624	180	9	d	d	NOUN
ejpam-1624	180	10	′)q22	′)q22	ADJ
ejpam-1624	180	11	q′31	q′31	NOUN
ejpam-1624	180	12	0	0	NUM
ejpam-1624	180	13	a′−c′d′	a′−c′d′	NOUN
ejpam-1624	180	14	(	(	PUNCT
ejpam-1624	180	15	a′+1+c′+d′	a′+1+c′+d′	NOUN
ejpam-1624	180	16	)	)	PUNCT
ejpam-1624	180	17	q21q′′11	q21q′′11	PROPN
ejpam-1624	180	18	0	0	NUM
ejpam-1624	180	19	0	0	NUM
ejpam-1624	180	20	0	0	NUM
ejpam-1624	180	21	0	0	NUM
ejpam-1624	180	22	0	0	NUM
ejpam-1624	180	23			NOUN
ejpam-1624	180	24			NOUN
ejpam-1624	180	25			VERB
ejpam-1624	180	26			NOUN
ejpam-1624	180	27			NOUN
ejpam-1624	180	28			NOUN
ejpam-1624	180	29			PUNCT
ejpam-1624	180	30	.	.	PUNCT
ejpam-1624	181	1	it	it	PRON
ejpam-1624	181	2	follows	follow	VERB
ejpam-1624	181	3	that	that	SCONJ
ejpam-1624	181	4	(	(	PUNCT
ejpam-1624	181	5	a′p	a′p	PRON
ejpam-1624	181	6	+	+	ADJ
ejpam-1624	181	7	q+	q+	NOUN
ejpam-1624	181	8	c′pq)d	c′pq)d	NOUN
ejpam-1624	181	9	=	=	PUNCT
ejpam-1624	181	10	s−1(s(a′p	s−1(s(a′p	PROPN
ejpam-1624	182	1	+	+	PROPN
ejpam-1624	182	2	q+	q+	ADP
ejpam-1624	182	3	c′pq)s−1)ds	c′pq)s−1)d	VERB
ejpam-1624	182	4	=	=	SYM
ejpam-1624	182	5			PROPN
ejpam-1624	182	6			NOUN
ejpam-1624	182	7			NOUN
ejpam-1624	182	8			NOUN
ejpam-1624	182	9			NOUN
ejpam-1624	182	10			NOUN
ejpam-1624	182	11			NOUN
ejpam-1624	182	12			NOUN
ejpam-1624	182	13	1	1	NUM
ejpam-1624	182	14	(	(	PUNCT
ejpam-1624	182	15	a′+1+c′+d′	a′+1+c′+d′	NOUN
ejpam-1624	182	16	)	)	PUNCT
ejpam-1624	182	17	i	i	NOUN
ejpam-1624	182	18	0	0	NUM
ejpam-1624	182	19	0	0	NUM
ejpam-1624	182	20	0	0	NUM
ejpam-1624	182	21	1+c′	1+c′	NUM
ejpam-1624	182	22	(	(	PUNCT
ejpam-1624	182	23	a′+1+c′+d′)2	a′+1+c′+d′)2	NOUN
ejpam-1624	182	24	q′′11	q′′11	PROPN
ejpam-1624	182	25	0	0	NUM
ejpam-1624	182	26	1	1	NUM
ejpam-1624	182	27	(	(	PUNCT
ejpam-1624	182	28	a′+1+c′+d′	a′+1+c′+d′	PROPN
ejpam-1624	182	29	)	)	PUNCT
ejpam-1624	182	30	i	i	NOUN
ejpam-1624	182	31	0	0	NUM
ejpam-1624	182	32	0	0	NUM
ejpam-1624	182	33	0	0	NUM
ejpam-1624	182	34	1+d′	1+d′	NUM
ejpam-1624	182	35	(	(	PUNCT
ejpam-1624	182	36	a′+1+c′+d′)2	a′+1+c′+d′)2	NOUN
ejpam-1624	182	37	q21	q21	PROPN
ejpam-1624	182	38	1+d′	1+d′	PROPN
ejpam-1624	182	39	(	(	PUNCT
ejpam-1624	182	40	a′+1+c′+d′)2	a′+1+c′+d′)2	NOUN
ejpam-1624	182	41	q22	q22	NOUN
ejpam-1624	182	42	0	0	NUM
ejpam-1624	182	43	q′31	q′31	NOUN
ejpam-1624	182	44	(	(	PUNCT
ejpam-1624	182	45	1+c′)(1+d′	1+c′)(1+d′	NUM
ejpam-1624	182	46	)	)	PUNCT
ejpam-1624	182	47	(	(	PUNCT
ejpam-1624	182	48	a′+1+c′+d′)3	a′+1+c′+d′)3	PROPN
ejpam-1624	182	49	q21q′′11	q21q′′11	PROPN
ejpam-1624	182	50	+	+	PROPN
ejpam-1624	182	51	q′31q′′32	q′31q′′32	NOUN
ejpam-1624	182	52	0	0	NUM
ejpam-1624	182	53	0	0	NUM
ejpam-1624	182	54	0	0	NUM
ejpam-1624	183	1	i	i	PRON
ejpam-1624	183	2	q′′32	q′′32	NOUN
ejpam-1624	183	3	0	0	NUM
ejpam-1624	183	4	0	0	NUM
ejpam-1624	183	5	0	0	NUM
ejpam-1624	183	6	0	0	NUM
ejpam-1624	183	7	0	0	NUM
ejpam-1624	183	8			NOUN
ejpam-1624	183	9			NOUN
ejpam-1624	183	10			VERB
ejpam-1624	183	11			NOUN
ejpam-1624	183	12			NOUN
ejpam-1624	183	13			NOUN
ejpam-1624	183	14			NOUN
ejpam-1624	183	15			PUNCT
ejpam-1624	184	1	=	=	PUNCT
ejpam-1624	184	2	(	(	PUNCT
ejpam-1624	184	3	a′	a′	PROPN
ejpam-1624	184	4	+	+	CCONJ
ejpam-1624	184	5	c′)(a′+	c′)(a′+	NUM
ejpam-1624	184	6	d	d	NOUN
ejpam-1624	184	7	′	′	NOUN
ejpam-1624	184	8	)	)	PUNCT
ejpam-1624	184	9	(	(	PUNCT
ejpam-1624	184	10	a′	a′	PROPN
ejpam-1624	184	11	+	+	SYM
ejpam-1624	184	12	1	1	NUM
ejpam-1624	184	13	+	+	NUM
ejpam-1624	184	14	c′	c′	NOUN
ejpam-1624	184	15	+	+	CCONJ
ejpam-1624	184	16	d	d	PROPN
ejpam-1624	184	17	′)3	′)3	PROPN
ejpam-1624	184	18	p	p	PROPN
ejpam-1624	184	19	+	+	PROPN
ejpam-1624	184	20	q+	q+	PUNCT
ejpam-1624	184	21	(	(	PUNCT
ejpam-1624	184	22	1	1	NUM
ejpam-1624	184	23	+	+	NUM
ejpam-1624	184	24	c′)(a′+	c′)(a′+	NUM
ejpam-1624	184	25	c′	c′	NOUN
ejpam-1624	184	26	)	)	PUNCT
ejpam-1624	184	27	(	(	PUNCT
ejpam-1624	184	28	a′	a′	PROPN
ejpam-1624	184	29	+	+	SYM
ejpam-1624	184	30	1	1	NUM
ejpam-1624	184	31	+	+	NUM
ejpam-1624	184	32	c′	c′	NOUN
ejpam-1624	184	33	+	+	CCONJ
ejpam-1624	184	34	d	d	PROPN
ejpam-1624	184	35	′)3	′)3	PROPN
ejpam-1624	184	36	pq+	pq+	PROPN
ejpam-1624	184	37	(	(	PUNCT
ejpam-1624	184	38	1	1	NUM
ejpam-1624	184	39	+	+	NUM
ejpam-1624	184	40	d	d	X
ejpam-1624	184	41	′)(a′+	′)(a′+	PROPN
ejpam-1624	184	42	d	d	PROPN
ejpam-1624	184	43	′	′	NOUN
ejpam-1624	184	44	)	)	PUNCT
ejpam-1624	184	45	(	(	PUNCT
ejpam-1624	184	46	a′+	a′+	NOUN
ejpam-1624	184	47	1	1	NUM
ejpam-1624	184	48	+	+	NUM
ejpam-1624	184	49	c′	c′	NOUN
ejpam-1624	184	50	+	+	CCONJ
ejpam-1624	184	51	d	d	PROPN
ejpam-1624	184	52	′)3	′)3	PROPN
ejpam-1624	184	53	qp	qp	ADP
ejpam-1624	184	54	+	+	PROPN
ejpam-1624	184	55	[	[	PUNCT
ejpam-1624	184	56	(	(	PUNCT
ejpam-1624	184	57	1	1	NUM
ejpam-1624	184	58	+	+	NUM
ejpam-1624	184	59	c′)(1	c′)(1	NOUN
ejpam-1624	184	60	+	+	NOUN
ejpam-1624	184	61	d	d	NOUN
ejpam-1624	184	62	′	′	NUM
ejpam-1624	184	63	)	)	PUNCT
ejpam-1624	184	64	(	(	PUNCT
ejpam-1624	184	65	a′	a′	PROPN
ejpam-1624	184	66	+	+	SYM
ejpam-1624	184	67	1	1	NUM
ejpam-1624	184	68	+	+	NUM
ejpam-1624	184	69	c′	c′	NOUN
ejpam-1624	184	70	+	+	CCONJ
ejpam-1624	184	71	d	d	PROPN
ejpam-1624	184	72	′)3	′)3	PROPN
ejpam-1624	184	73	−	−	PROPN
ejpam-1624	184	74	1]qpq	1]qpq	PROPN
ejpam-1624	184	75	.	.	PUNCT
ejpam-1624	185	1	t.	t.	PROPN
ejpam-1624	185	2	xie	xie	PROPN
ejpam-1624	185	3	,	,	PUNCT
ejpam-1624	185	4	k.	k.	PROPN
ejpam-1624	185	5	zuo	zuo	PROPN
ejpam-1624	185	6	/	/	SYM
ejpam-1624	185	7	eur	eur	PROPN
ejpam-1624	185	8	.	.	PUNCT
ejpam-1624	186	1	j.	j.	PROPN
ejpam-1624	186	2	pure	pure	PROPN
ejpam-1624	186	3	appl	appl	PROPN
ejpam-1624	186	4	.	.	PROPN
ejpam-1624	186	5	math	math	PROPN
ejpam-1624	186	6	,	,	PUNCT
ejpam-1624	186	7	5	5	NUM
ejpam-1624	186	8	(	(	PUNCT
ejpam-1624	186	9	2012	2012	NUM
ejpam-1624	186	10	)	)	PUNCT
ejpam-1624	186	11	,	,	PUNCT
ejpam-1624	186	12	480	480	NUM
ejpam-1624	186	13	-	-	SYM
ejpam-1624	186	14	491	491	NUM
ejpam-1624	186	15	487	487	NUM
ejpam-1624	186	16	moreover	moreover	ADV
ejpam-1624	186	17	,	,	PUNCT
ejpam-1624	186	18	since	since	SCONJ
ejpam-1624	186	19	(	(	PUNCT
ejpam-1624	186	20	ct	ct	NOUN
ejpam-1624	186	21	)	)	PUNCT
ejpam-1624	186	22	d	d	NOUN
ejpam-1624	186	23	=	=	SYM
ejpam-1624	186	24	1	1	NUM
ejpam-1624	186	25	c	c	NOUN
ejpam-1624	186	26	t	t	PROPN
ejpam-1624	186	27	d	d	NOUN
ejpam-1624	186	28	holds	hold	VERB
ejpam-1624	186	29	for	for	ADP
ejpam-1624	186	30	any	any	DET
ejpam-1624	186	31	c	c	NOUN
ejpam-1624	186	32	6=	6=	ADP
ejpam-1624	186	33	0	0	NUM
ejpam-1624	186	34	and	and	CCONJ
ejpam-1624	186	35	any	any	DET
ejpam-1624	186	36	drazin	drazin	PROPN
ejpam-1624	186	37	invertible	invertible	ADJ
ejpam-1624	186	38	operator	operator	NOUN
ejpam-1624	186	39	t	t	PROPN
ejpam-1624	186	40	∈	∈	PROPN
ejpam-1624	186	41	b(h	b(h	PROPN
ejpam-1624	186	42	)	)	PUNCT
ejpam-1624	186	43	.	.	PUNCT
ejpam-1624	187	1	hence	hence	ADV
ejpam-1624	187	2	(	(	PUNCT
ejpam-1624	187	3	ap	ap	PROPN
ejpam-1624	187	4	+	+	NUM
ejpam-1624	187	5	bq+	bq+	NOUN
ejpam-1624	187	6	cpq+	cpq+	ADP
ejpam-1624	187	7	dqp)d	dqp)d	PROPN
ejpam-1624	187	8	=	=	PUNCT
ejpam-1624	188	1	[	[	X
ejpam-1624	188	2	b(a′p	b(a′p	NOUN
ejpam-1624	188	3	+	+	PUNCT
ejpam-1624	188	4	q+	q+	PROPN
ejpam-1624	188	5	c′pq+	c′pq+	PROPN
ejpam-1624	188	6	d	d	ADP
ejpam-1624	188	7	′qp)]d	′qp)]d	PUNCT
ejpam-1624	188	8	=	=	SYM
ejpam-1624	188	9	1	1	NUM
ejpam-1624	188	10	b	b	X
ejpam-1624	188	11	(	(	PUNCT
ejpam-1624	188	12	a′p	a′p	NOUN
ejpam-1624	188	13	+	+	PROPN
ejpam-1624	188	14	q+	q+	NOUN
ejpam-1624	188	15	c′pq+	c′pq+	PROPN
ejpam-1624	189	1	d	d	NOUN
ejpam-1624	189	2	′qp)d	′qp)d	NOUN
ejpam-1624	189	3	=	=	SYM
ejpam-1624	189	4	(	(	PUNCT
ejpam-1624	189	5	a+	a+	X
ejpam-1624	189	6	c)(a+	c)(a+	NOUN
ejpam-1624	189	7	d	d	PROPN
ejpam-1624	189	8	)	)	PUNCT
ejpam-1624	189	9	(	(	PUNCT
ejpam-1624	189	10	a+	a+	X
ejpam-1624	189	11	b+	b+	X
ejpam-1624	189	12	c	c	X
ejpam-1624	189	13	+	+	PUNCT
ejpam-1624	189	14	d)3	d)3	NOUN
ejpam-1624	189	15	p	p	NOUN
ejpam-1624	189	16	+	+	NOUN
ejpam-1624	189	17	1	1	NUM
ejpam-1624	189	18	b	b	NOUN
ejpam-1624	189	19	q+	q+	X
ejpam-1624	189	20	(	(	PUNCT
ejpam-1624	189	21	b+	b+	X
ejpam-1624	189	22	c)(a+	c)(a+	NOUN
ejpam-1624	189	23	c	c	NOUN
ejpam-1624	189	24	)	)	PUNCT
ejpam-1624	189	25	(	(	PUNCT
ejpam-1624	189	26	a+	a+	X
ejpam-1624	189	27	b+	b+	X
ejpam-1624	189	28	c	c	X
ejpam-1624	189	29	+	+	PUNCT
ejpam-1624	189	30	d)3	d)3	PROPN
ejpam-1624	189	31	pq	pq	NOUN
ejpam-1624	189	32	+	+	CCONJ
ejpam-1624	189	33	(	(	PUNCT
ejpam-1624	189	34	a+	a+	X
ejpam-1624	189	35	d)(b+	d)(b+	NOUN
ejpam-1624	189	36	d	d	NOUN
ejpam-1624	189	37	)	)	PUNCT
ejpam-1624	189	38	(	(	PUNCT
ejpam-1624	189	39	a+	a+	X
ejpam-1624	189	40	b+	b+	X
ejpam-1624	189	41	c	c	X
ejpam-1624	189	42	+	+	PUNCT
ejpam-1624	189	43	d)3	d)3	NOUN
ejpam-1624	189	44	qp	qp	ADP
ejpam-1624	190	1	+	+	NOUN
ejpam-1624	190	2	[	[	PUNCT
ejpam-1624	190	3	(	(	PUNCT
ejpam-1624	190	4	b+	b+	X
ejpam-1624	190	5	c)(b+	c)(b+	X
ejpam-1624	190	6	d	d	X
ejpam-1624	190	7	)	)	PUNCT
ejpam-1624	190	8	(	(	PUNCT
ejpam-1624	190	9	a+	a+	X
ejpam-1624	190	10	b+	b+	X
ejpam-1624	190	11	c	c	X
ejpam-1624	190	12	+	+	PUNCT
ejpam-1624	190	13	d)3	d)3	VERB
ejpam-1624	190	14	−	−	PROPN
ejpam-1624	190	15	1	1	NUM
ejpam-1624	190	16	b	b	NOUN
ejpam-1624	190	17	]	]	X
ejpam-1624	190	18	qpq	qpq	NOUN
ejpam-1624	190	19	.	.	PUNCT
ejpam-1624	191	1	(	(	PUNCT
ejpam-1624	191	2	ii	ii	NOUN
ejpam-1624	191	3	)	)	PUNCT
ejpam-1624	191	4	if	if	SCONJ
ejpam-1624	191	5	a+	a+	X
ejpam-1624	191	6	b+	b+	X
ejpam-1624	191	7	c	c	X
ejpam-1624	192	1	+	+	SYM
ejpam-1624	192	2	d	d	X
ejpam-1624	192	3	=	=	SYM
ejpam-1624	192	4	0	0	NUM
ejpam-1624	192	5	,	,	PUNCT
ejpam-1624	192	6	then	then	ADV
ejpam-1624	192	7	(	(	PUNCT
ejpam-1624	192	8	ap	ap	PROPN
ejpam-1624	192	9	+	+	NUM
ejpam-1624	192	10	bq+	bq+	NOUN
ejpam-1624	192	11	cpq+	cpq+	ADP
ejpam-1624	192	12	dqp)d	dqp)d	PROPN
ejpam-1624	192	13	=	=	SYM
ejpam-1624	192	14			PROPN
ejpam-1624	192	15			NOUN
ejpam-1624	192	16			NOUN
ejpam-1624	192	17			NOUN
ejpam-1624	192	18			NOUN
ejpam-1624	192	19			NOUN
ejpam-1624	192	20			NOUN
ejpam-1624	192	21	0	0	NUM
ejpam-1624	192	22	0	0	NUM
ejpam-1624	192	23	0	0	NUM
ejpam-1624	192	24	0	0	NUM
ejpam-1624	192	25	(	(	PUNCT
ejpam-1624	192	26	b+	b+	ADP
ejpam-1624	192	27	c)q′′11	c)q′′11	PROPN
ejpam-1624	192	28	0	0	NUM
ejpam-1624	192	29	0	0	NUM
ejpam-1624	192	30	0	0	NUM
ejpam-1624	192	31	0	0	NUM
ejpam-1624	192	32	0	0	NUM
ejpam-1624	192	33	(	(	PUNCT
ejpam-1624	192	34	b+	b+	X
ejpam-1624	192	35	d)q21	d)q21	PROPN
ejpam-1624	192	36	(	(	PUNCT
ejpam-1624	192	37	b+	b+	X
ejpam-1624	192	38	d)q22	d)q22	PROPN
ejpam-1624	192	39	0	0	PUNCT
ejpam-1624	193	1	bq′31	bq′31	PRON
ejpam-1624	193	2	bq′′31	bq′′31	VERB
ejpam-1624	193	3	0	0	NUM
ejpam-1624	193	4	0	0	NUM
ejpam-1624	193	5	0	0	NUM
ejpam-1624	193	6	bi	bi	NOUN
ejpam-1624	193	7	bq′′32	bq′′32	NOUN
ejpam-1624	193	8	0	0	NOUN
ejpam-1624	193	9	0	0	NUM
ejpam-1624	193	10	0	0	NUM
ejpam-1624	193	11	0	0	NUM
ejpam-1624	193	12	0	0	NUM
ejpam-1624	193	13			NOUN
ejpam-1624	193	14			NOUN
ejpam-1624	193	15			VERB
ejpam-1624	193	16			NOUN
ejpam-1624	193	17			NOUN
ejpam-1624	193	18			NOUN
ejpam-1624	193	19			PUNCT
ejpam-1624	194	1	d	d	NOUN
ejpam-1624	194	2	=	=	SYM
ejpam-1624	194	3	1	1	NUM
ejpam-1624	194	4	b	b	PROPN
ejpam-1624	194	5			PROPN
ejpam-1624	194	6			NOUN
ejpam-1624	194	7			NOUN
ejpam-1624	194	8			NOUN
ejpam-1624	194	9			NOUN
ejpam-1624	194	10			NOUN
ejpam-1624	194	11			NOUN
ejpam-1624	194	12	0	0	NUM
ejpam-1624	194	13	0	0	NUM
ejpam-1624	194	14	0	0	NUM
ejpam-1624	194	15	0	0	NUM
ejpam-1624	194	16	0	0	NUM
ejpam-1624	194	17	0	0	NUM
ejpam-1624	194	18	0	0	NUM
ejpam-1624	194	19	0	0	NUM
ejpam-1624	194	20	0	0	NUM
ejpam-1624	194	21	0	0	NUM
ejpam-1624	194	22	0	0	NUM
ejpam-1624	194	23	0	0	NUM
ejpam-1624	194	24	0	0	NUM
ejpam-1624	195	1	q′31	q′31	NOUN
ejpam-1624	195	2	q′31q′′32	q′31q′′32	NOUN
ejpam-1624	195	3	0	0	NUM
ejpam-1624	195	4	0	0	NUM
ejpam-1624	195	5	0	0	NUM
ejpam-1624	196	1	i	i	PRON
ejpam-1624	196	2	q′′32	q′′32	NOUN
ejpam-1624	196	3	0	0	NUM
ejpam-1624	196	4	0	0	NUM
ejpam-1624	196	5	0	0	NUM
ejpam-1624	196	6	0	0	NUM
ejpam-1624	196	7	0	0	NUM
ejpam-1624	196	8			NOUN
ejpam-1624	196	9			NOUN
ejpam-1624	196	10			VERB
ejpam-1624	196	11			NOUN
ejpam-1624	196	12			NOUN
ejpam-1624	196	13			NOUN
ejpam-1624	196	14			PUNCT
ejpam-1624	197	1	=	=	SYM
ejpam-1624	197	2	1	1	NUM
ejpam-1624	197	3	b	b	X
ejpam-1624	197	4	(	(	PUNCT
ejpam-1624	197	5	q−qpq	q−qpq	PROPN
ejpam-1624	197	6	)	)	PUNCT
ejpam-1624	197	7	.	.	PUNCT
ejpam-1624	198	1	now	now	ADV
ejpam-1624	198	2	we	we	PRON
ejpam-1624	198	3	can	can	AUX
ejpam-1624	198	4	derive	derive	VERB
ejpam-1624	198	5	some	some	DET
ejpam-1624	198	6	special	special	ADJ
ejpam-1624	198	7	cases	case	NOUN
ejpam-1624	198	8	from	from	ADP
ejpam-1624	198	9	theorem	theorem	ADJ
ejpam-1624	198	10	2	2	NUM
ejpam-1624	198	11	.	.	PUNCT
ejpam-1624	199	1	these	these	DET
ejpam-1624	199	2	results	result	NOUN
ejpam-1624	199	3	are	be	AUX
ejpam-1624	199	4	the	the	DET
ejpam-1624	199	5	special	special	ADJ
ejpam-1624	199	6	cases	case	NOUN
ejpam-1624	199	7	of	of	ADP
ejpam-1624	199	8	theorem	theorem	NOUN
ejpam-1624	199	9	2.3	2.3	NUM
ejpam-1624	199	10	in	in	ADP
ejpam-1624	199	11	[	[	X
ejpam-1624	199	12	4	4	NUM
ejpam-1624	199	13	]	]	PUNCT
ejpam-1624	199	14	.	.	PUNCT
ejpam-1624	200	1	corollary	corollary	ADJ
ejpam-1624	200	2	3	3	X
ejpam-1624	200	3	.	.	PUNCT
ejpam-1624	201	1	let	let	VERB
ejpam-1624	201	2	p	p	NOUN
ejpam-1624	201	3	and	and	CCONJ
ejpam-1624	201	4	q	q	NOUN
ejpam-1624	201	5	be	be	AUX
ejpam-1624	201	6	two	two	NUM
ejpam-1624	201	7	idempotents	idempotent	NOUN
ejpam-1624	201	8	in	in	ADP
ejpam-1624	201	9	b(h	b(h	PROPN
ejpam-1624	201	10	)	)	PUNCT
ejpam-1624	201	11	.	.	PUNCT
ejpam-1624	202	1	assume	assume	VERB
ejpam-1624	202	2	that	that	SCONJ
ejpam-1624	202	3	pqp	pqp	NOUN
ejpam-1624	203	1	=	=	NOUN
ejpam-1624	203	2	p	p	X
ejpam-1624	203	3	,	,	PUNCT
ejpam-1624	203	4	then	then	ADV
ejpam-1624	203	5	the	the	DET
ejpam-1624	203	6	following	follow	VERB
ejpam-1624	203	7	statements	statement	NOUN
ejpam-1624	203	8	hold	hold	VERB
ejpam-1624	203	9	.	.	PUNCT
ejpam-1624	204	1	(	(	PUNCT
ejpam-1624	204	2	i	i	NOUN
ejpam-1624	204	3	)	)	PUNCT
ejpam-1624	204	4	(	(	PUNCT
ejpam-1624	204	5	p	p	NOUN
ejpam-1624	204	6	+	+	NOUN
ejpam-1624	204	7	q)d	q)d	NOUN
ejpam-1624	204	8	=	=	SYM
ejpam-1624	204	9	1	1	NUM
ejpam-1624	204	10	8	8	NUM
ejpam-1624	204	11	p	p	NOUN
ejpam-1624	204	12	+	+	ADJ
ejpam-1624	204	13	q+	q+	ADP
ejpam-1624	204	14	1	1	NUM
ejpam-1624	204	15	8	8	NUM
ejpam-1624	204	16	(	(	PUNCT
ejpam-1624	204	17	pq+qp)−	pq+qp)−	NOUN
ejpam-1624	204	18	7	7	NUM
ejpam-1624	204	19	8	8	NUM
ejpam-1624	204	20	qpq	qpq	ADJ
ejpam-1624	204	21	.	.	PUNCT
ejpam-1624	205	1	(	(	PUNCT
ejpam-1624	205	2	ii	ii	NOUN
ejpam-1624	205	3	)	)	PUNCT
ejpam-1624	205	4	(	(	PUNCT
ejpam-1624	205	5	p	p	NOUN
ejpam-1624	205	6	−q)d	−q)d	VERB
ejpam-1624	205	7	=	=	SYM
ejpam-1624	205	8	qpq−q	qpq−q	PROPN
ejpam-1624	205	9	.	.	PUNCT
ejpam-1624	206	1	if	if	SCONJ
ejpam-1624	206	2	the	the	DET
ejpam-1624	206	3	stronger	strong	ADJ
ejpam-1624	206	4	condition	condition	NOUN
ejpam-1624	206	5	qp	qp	ADP
ejpam-1624	206	6	=	=	PUNCT
ejpam-1624	206	7	p	p	NOUN
ejpam-1624	206	8	is	be	AUX
ejpam-1624	206	9	satisfied	satisfied	ADJ
ejpam-1624	206	10	,	,	PUNCT
ejpam-1624	206	11	then	then	ADV
ejpam-1624	206	12	by	by	ADP
ejpam-1624	206	13	theorem	theorem	NOUN
ejpam-1624	206	14	2	2	NUM
ejpam-1624	206	15	,	,	PUNCT
ejpam-1624	206	16	we	we	PRON
ejpam-1624	206	17	can	can	AUX
ejpam-1624	206	18	also	also	ADV
ejpam-1624	206	19	derive	derive	VERB
ejpam-1624	206	20	the	the	DET
ejpam-1624	206	21	formulaes	formulaes	NOUN
ejpam-1624	206	22	of	of	ADP
ejpam-1624	206	23	drazin	drazin	PROPN
ejpam-1624	206	24	inverses	inverses	PROPN
ejpam-1624	206	25	of	of	ADP
ejpam-1624	206	26	linear	linear	PROPN
ejpam-1624	206	27	combinations	combination	NOUN
ejpam-1624	206	28	of	of	ADP
ejpam-1624	206	29	p	p	NOUN
ejpam-1624	206	30	and	and	CCONJ
ejpam-1624	206	31	q.	q.	PROPN
ejpam-1624	206	32	corollary	corollary	NOUN
ejpam-1624	206	33	4	4	NUM
ejpam-1624	206	34	.	.	PUNCT
ejpam-1624	207	1	let	let	VERB
ejpam-1624	207	2	p	p	NOUN
ejpam-1624	207	3	and	and	CCONJ
ejpam-1624	207	4	q	q	NOUN
ejpam-1624	207	5	be	be	AUX
ejpam-1624	207	6	two	two	NUM
ejpam-1624	207	7	idempotents	idempotent	NOUN
ejpam-1624	207	8	in	in	ADP
ejpam-1624	207	9	b(h	b(h	PROPN
ejpam-1624	207	10	)	)	PUNCT
ejpam-1624	207	11	,	,	PUNCT
ejpam-1624	207	12	and	and	CCONJ
ejpam-1624	207	13	a	a	DET
ejpam-1624	207	14	,	,	PUNCT
ejpam-1624	207	15	b	b	X
ejpam-1624	207	16	∈	∈	PROPN
ejpam-1624	207	17	c	c	X
ejpam-1624	207	18	,	,	PUNCT
ejpam-1624	207	19	ab	ab	PROPN
ejpam-1624	207	20	6=	6=	ADP
ejpam-1624	207	21	0	0	NUM
ejpam-1624	207	22	.	.	PUNCT
ejpam-1624	208	1	if	if	SCONJ
ejpam-1624	208	2	qp	qp	ADV
ejpam-1624	208	3	=	=	SYM
ejpam-1624	208	4	p	p	NOUN
ejpam-1624	208	5	,	,	PUNCT
ejpam-1624	208	6	then	then	ADV
ejpam-1624	208	7	(	(	PUNCT
ejpam-1624	208	8	ap	ap	PROPN
ejpam-1624	208	9	+	+	CCONJ
ejpam-1624	208	10	bq)d	bq)d	PROPN
ejpam-1624	208	11	=	=	SYM
ejpam-1624	208	12	(	(	PUNCT
ejpam-1624	208	13	a	a	PRON
ejpam-1624	208	14	(	(	PUNCT
ejpam-1624	208	15	a+b)2	a+b)2	NOUN
ejpam-1624	208	16	p	p	X
ejpam-1624	209	1	+	+	NOUN
ejpam-1624	209	2	1	1	NUM
ejpam-1624	209	3	b	b	X
ejpam-1624	209	4	q+	q+	ADP
ejpam-1624	209	5	[	[	PUNCT
ejpam-1624	209	6	b	b	X
ejpam-1624	209	7	(	(	PUNCT
ejpam-1624	209	8	a+b)2	a+b)2	NOUN
ejpam-1624	209	9	−	−	PROPN
ejpam-1624	209	10	1	1	NUM
ejpam-1624	209	11	b	b	PROPN
ejpam-1624	209	12	]	]	X
ejpam-1624	209	13	pq	pq	NOUN
ejpam-1624	209	14	,	,	PUNCT
ejpam-1624	209	15	when	when	SCONJ
ejpam-1624	209	16	a+	a+	PRON
ejpam-1624	209	17	b	b	X
ejpam-1624	209	18	6=	6=	SYM
ejpam-1624	209	19	0	0	NUM
ejpam-1624	209	20	1	1	NUM
ejpam-1624	209	21	b	b	X
ejpam-1624	209	22	(	(	PUNCT
ejpam-1624	209	23	q−	q−	PROPN
ejpam-1624	209	24	pq	pq	PROPN
ejpam-1624	209	25	)	)	PUNCT
ejpam-1624	209	26	,	,	PUNCT
ejpam-1624	209	27	when	when	SCONJ
ejpam-1624	209	28	a+	a+	PRON
ejpam-1624	209	29	b	b	X
ejpam-1624	209	30	=	=	SYM
ejpam-1624	209	31	0	0	PROPN
ejpam-1624	209	32	.	.	PUNCT
ejpam-1624	210	1	t.	t.	PROPN
ejpam-1624	210	2	xie	xie	PROPN
ejpam-1624	210	3	,	,	PUNCT
ejpam-1624	210	4	k.	k.	PROPN
ejpam-1624	210	5	zuo	zuo	PROPN
ejpam-1624	210	6	/	/	SYM
ejpam-1624	210	7	eur	eur	PROPN
ejpam-1624	210	8	.	.	PUNCT
ejpam-1624	211	1	j.	j.	PROPN
ejpam-1624	211	2	pure	pure	PROPN
ejpam-1624	211	3	appl	appl	PROPN
ejpam-1624	211	4	.	.	PROPN
ejpam-1624	211	5	math	math	PROPN
ejpam-1624	211	6	,	,	PUNCT
ejpam-1624	211	7	5	5	NUM
ejpam-1624	211	8	(	(	PUNCT
ejpam-1624	211	9	2012	2012	NUM
ejpam-1624	211	10	)	)	PUNCT
ejpam-1624	211	11	,	,	PUNCT
ejpam-1624	211	12	480	480	NUM
ejpam-1624	211	13	-	-	SYM
ejpam-1624	211	14	491	491	NUM
ejpam-1624	211	15	488	488	NUM
ejpam-1624	211	16	next	next	ADV
ejpam-1624	211	17	we	we	PRON
ejpam-1624	211	18	discuss	discuss	VERB
ejpam-1624	211	19	the	the	DET
ejpam-1624	211	20	drazin	drazin	PROPN
ejpam-1624	211	21	inverse	inverse	NOUN
ejpam-1624	211	22	of	of	ADP
ejpam-1624	211	23	ap	ap	PROPN
ejpam-1624	211	24	+	+	CCONJ
ejpam-1624	211	25	bq+	bq+	PROPN
ejpam-1624	211	26	cpq	cpq	PROPN
ejpam-1624	211	27	+	+	CCONJ
ejpam-1624	211	28	dqp	dqp	NOUN
ejpam-1624	211	29	under	under	ADP
ejpam-1624	211	30	the	the	DET
ejpam-1624	211	31	assumption	assumption	NOUN
ejpam-1624	211	32	that	that	SCONJ
ejpam-1624	211	33	pqp	pqp	NOUN
ejpam-1624	211	34	=	=	SYM
ejpam-1624	211	35	pq	pq	PROPN
ejpam-1624	211	36	.	.	PUNCT
ejpam-1624	211	37	theorem	theorem	PROPN
ejpam-1624	211	38	3	3	X
ejpam-1624	211	39	.	.	PUNCT
ejpam-1624	212	1	let	let	VERB
ejpam-1624	212	2	p	p	NOUN
ejpam-1624	212	3	and	and	CCONJ
ejpam-1624	212	4	q	q	NOUN
ejpam-1624	212	5	be	be	AUX
ejpam-1624	212	6	two	two	NUM
ejpam-1624	212	7	idempotents	idempotent	NOUN
ejpam-1624	212	8	in	in	ADP
ejpam-1624	212	9	b(h	b(h	PROPN
ejpam-1624	212	10	)	)	PUNCT
ejpam-1624	213	1	,	,	PUNCT
ejpam-1624	213	2	then	then	ADV
ejpam-1624	213	3	for	for	ADP
ejpam-1624	213	4	any	any	DET
ejpam-1624	213	5	a	a	DET
ejpam-1624	213	6	,	,	PUNCT
ejpam-1624	213	7	b	b	NOUN
ejpam-1624	213	8	,	,	PUNCT
ejpam-1624	213	9	c	c	NOUN
ejpam-1624	213	10	,	,	PUNCT
ejpam-1624	213	11	d	d	PROPN
ejpam-1624	213	12	∈	∈	PROPN
ejpam-1624	213	13	c	c	X
ejpam-1624	213	14	,	,	PUNCT
ejpam-1624	213	15	ab	ab	PROPN
ejpam-1624	213	16	6=	6=	PROPN
ejpam-1624	213	17	0	0	NUM
ejpam-1624	213	18	,	,	PUNCT
ejpam-1624	213	19	the	the	DET
ejpam-1624	213	20	combinations	combination	NOUN
ejpam-1624	213	21	ap	ap	PROPN
ejpam-1624	213	22	+	+	CCONJ
ejpam-1624	213	23	bq+	bq+	PROPN
ejpam-1624	213	24	cpq+	cpq+	PROPN
ejpam-1624	213	25	dqp	dqp	NOUN
ejpam-1624	213	26	are	be	AUX
ejpam-1624	213	27	drazin	drazin	PROPN
ejpam-1624	213	28	invertible	invertible	ADJ
ejpam-1624	213	29	under	under	ADP
ejpam-1624	213	30	the	the	DET
ejpam-1624	213	31	condition	condition	NOUN
ejpam-1624	213	32	pqp	pqp	NOUN
ejpam-1624	214	1	=	=	SYM
ejpam-1624	214	2	pq	pq	PROPN
ejpam-1624	214	3	.	.	PUNCT
ejpam-1624	215	1	the	the	DET
ejpam-1624	215	2	drazin	drazin	PROPN
ejpam-1624	215	3	inverses	inverses	PROPN
ejpam-1624	215	4	of	of	ADP
ejpam-1624	215	5	ap	ap	PROPN
ejpam-1624	215	6	+	+	CCONJ
ejpam-1624	215	7	bq+	bq+	PROPN
ejpam-1624	215	8	cpq+	cpq+	PROPN
ejpam-1624	215	9	dqp	dqp	NOUN
ejpam-1624	215	10	can	can	AUX
ejpam-1624	215	11	be	be	AUX
ejpam-1624	215	12	represented	represent	VERB
ejpam-1624	215	13	as	as	ADP
ejpam-1624	215	14	following	follow	VERB
ejpam-1624	215	15	:	:	PUNCT
ejpam-1624	215	16	(	(	PUNCT
ejpam-1624	215	17	i	i	NOUN
ejpam-1624	215	18	)	)	PUNCT
ejpam-1624	215	19	if	if	SCONJ
ejpam-1624	215	20	a+	a+	X
ejpam-1624	215	21	b+	b+	X
ejpam-1624	215	22	c	c	X
ejpam-1624	216	1	+	+	SYM
ejpam-1624	216	2	d	d	X
ejpam-1624	216	3	6=	6=	NUM
ejpam-1624	216	4	0	0	NUM
ejpam-1624	216	5	,	,	PUNCT
ejpam-1624	216	6	then	then	ADV
ejpam-1624	216	7	(	(	PUNCT
ejpam-1624	216	8	ap	ap	PROPN
ejpam-1624	216	9	+	+	NUM
ejpam-1624	216	10	bq+	bq+	NOUN
ejpam-1624	216	11	cpq+	cpq+	ADP
ejpam-1624	216	12	dqp)d	dqp)d	PROPN
ejpam-1624	216	13	=	=	PUNCT
ejpam-1624	216	14	1	1	NUM
ejpam-1624	216	15	a	a	DET
ejpam-1624	216	16	p	p	X
ejpam-1624	216	17	+	+	NOUN
ejpam-1624	216	18	1	1	NUM
ejpam-1624	216	19	b	b	X
ejpam-1624	216	20	q+	q+	ADP
ejpam-1624	216	21	[	[	PUNCT
ejpam-1624	216	22	1	1	NUM
ejpam-1624	216	23	(	(	PUNCT
ejpam-1624	216	24	a+	a+	X
ejpam-1624	216	25	b+	b+	X
ejpam-1624	216	26	c	c	X
ejpam-1624	216	27	+	+	SYM
ejpam-1624	216	28	d	d	NOUN
ejpam-1624	216	29	)	)	PUNCT
ejpam-1624	216	30	−	−	NOUN
ejpam-1624	216	31	b+	b+	ADP
ejpam-1624	216	32	d	d	X
ejpam-1624	216	33	(	(	PUNCT
ejpam-1624	216	34	a+	a+	X
ejpam-1624	216	35	b+	b+	X
ejpam-1624	216	36	c	c	NOUN
ejpam-1624	216	37	+	+	PUNCT
ejpam-1624	216	38	d)2	d)2	NOUN
ejpam-1624	216	39	−	−	PROPN
ejpam-1624	216	40	1	1	NUM
ejpam-1624	216	41	a	a	DET
ejpam-1624	216	42	]	]	X
ejpam-1624	216	43	pq	pq	NOUN
ejpam-1624	216	44	−	−	PROPN
ejpam-1624	216	45	(	(	PUNCT
ejpam-1624	216	46	a+	a+	X
ejpam-1624	216	47	b+	b+	X
ejpam-1624	216	48	d	d	PROPN
ejpam-1624	216	49	ab	ab	PROPN
ejpam-1624	216	50	)	)	PUNCT
ejpam-1624	216	51	qp	qp	VERB
ejpam-1624	217	1	+	+	NOUN
ejpam-1624	217	2	[	[	PUNCT
ejpam-1624	217	3	b+	b+	X
ejpam-1624	217	4	d	d	X
ejpam-1624	217	5	(	(	PUNCT
ejpam-1624	217	6	a+	a+	X
ejpam-1624	217	7	b+	b+	X
ejpam-1624	217	8	c	c	NOUN
ejpam-1624	217	9	+	+	PUNCT
ejpam-1624	217	10	d)2	d)2	PROPN
ejpam-1624	217	11	+	+	CCONJ
ejpam-1624	217	12	b+	b+	NOUN
ejpam-1624	217	13	d	d	PROPN
ejpam-1624	217	14	ab	ab	X
ejpam-1624	217	15	]	]	X
ejpam-1624	217	16	qpq	qpq	X
ejpam-1624	217	17	.	.	PUNCT
ejpam-1624	218	1	(	(	PUNCT
ejpam-1624	218	2	ii	ii	NOUN
ejpam-1624	218	3	)	)	PUNCT
ejpam-1624	218	4	if	if	SCONJ
ejpam-1624	218	5	a+	a+	X
ejpam-1624	218	6	b+	b+	X
ejpam-1624	218	7	c	c	X
ejpam-1624	219	1	+	+	SYM
ejpam-1624	219	2	d	d	X
ejpam-1624	219	3	=	=	SYM
ejpam-1624	219	4	0	0	NUM
ejpam-1624	219	5	,	,	PUNCT
ejpam-1624	219	6	then	then	ADV
ejpam-1624	219	7	(	(	PUNCT
ejpam-1624	219	8	ap	ap	PROPN
ejpam-1624	219	9	+	+	NUM
ejpam-1624	219	10	bq+	bq+	NOUN
ejpam-1624	219	11	cpq+	cpq+	ADP
ejpam-1624	219	12	dqp)d	dqp)d	PROPN
ejpam-1624	219	13	=	=	PUNCT
ejpam-1624	219	14	1	1	NUM
ejpam-1624	219	15	a	a	DET
ejpam-1624	219	16	p	p	X
ejpam-1624	220	1	+	+	NOUN
ejpam-1624	220	2	1	1	NUM
ejpam-1624	220	3	b	b	X
ejpam-1624	220	4	q−	q−	PROPN
ejpam-1624	220	5	1	1	NUM
ejpam-1624	220	6	a	a	DET
ejpam-1624	220	7	pq	pq	NOUN
ejpam-1624	220	8	−	−	NOUN
ejpam-1624	220	9	(	(	PUNCT
ejpam-1624	220	10	1	1	NUM
ejpam-1624	220	11	a	a	DET
ejpam-1624	220	12	+	+	NUM
ejpam-1624	220	13	1	1	NUM
ejpam-1624	220	14	b	b	NOUN
ejpam-1624	220	15	+	+	CCONJ
ejpam-1624	220	16	d	d	PROPN
ejpam-1624	220	17	ab	ab	PROPN
ejpam-1624	220	18	)	)	PUNCT
ejpam-1624	220	19	qp	qp	VERB
ejpam-1624	221	1	+	+	SYM
ejpam-1624	221	2	b+	b+	NOUN
ejpam-1624	221	3	d	d	X
ejpam-1624	221	4	ab	ab	PROPN
ejpam-1624	221	5	qpq	qpq	PROPN
ejpam-1624	221	6	.	.	PUNCT
ejpam-1624	222	1	proof	proof	NOUN
ejpam-1624	222	2	.	.	PUNCT
ejpam-1624	223	1	if	if	SCONJ
ejpam-1624	223	2	pqp	pqp	NOUN
ejpam-1624	223	3	=	=	SYM
ejpam-1624	223	4	pq	pq	PROPN
ejpam-1624	223	5	,	,	PUNCT
ejpam-1624	223	6	then	then	ADV
ejpam-1624	223	7	p	p	NOUN
ejpam-1624	223	8	and	and	CCONJ
ejpam-1624	223	9	q	q	NOUN
ejpam-1624	223	10	can	can	AUX
ejpam-1624	223	11	be	be	AUX
ejpam-1624	223	12	written	write	VERB
ejpam-1624	223	13	as	as	ADP
ejpam-1624	223	14	p	p	PROPN
ejpam-1624	223	15	=	=	PROPN
ejpam-1624	223	16	�	�	PROPN
ejpam-1624	223	17	i	i	NOUN
ejpam-1624	223	18	0	0	NUM
ejpam-1624	223	19	0	0	SYM
ejpam-1624	223	20	0	0	NUM
ejpam-1624	223	21	�	�	PROPN
ejpam-1624	223	22	,	,	PUNCT
ejpam-1624	223	23	q	q	NOUN
ejpam-1624	223	24	=	=	SYM
ejpam-1624	223	25	�	�	PROPN
ejpam-1624	223	26	q1	q1	PROPN
ejpam-1624	223	27	0	0	NUM
ejpam-1624	223	28	q2	q2	PROPN
ejpam-1624	223	29	q3	q3	PROPN
ejpam-1624	223	30	�	�	PROPN
ejpam-1624	223	31	under	under	ADP
ejpam-1624	223	32	the	the	DET
ejpam-1624	223	33	space	space	NOUN
ejpam-1624	223	34	decomposition	decomposition	NOUN
ejpam-1624	223	35	of	of	ADP
ejpam-1624	223	36	h	h	NOUN
ejpam-1624	223	37	=	=	PUNCT
ejpam-1624	223	38	r(p)⊕r(p)⊥.	r(p)⊕r(p)⊥.	ADP
ejpam-1624	223	39	the	the	DET
ejpam-1624	223	40	idempotency	idempotency	NOUN
ejpam-1624	223	41	of	of	ADP
ejpam-1624	223	42	q	q	NOUN
ejpam-1624	223	43	yields	yield	NOUN
ejpam-1624	223	44	that	that	PRON
ejpam-1624	223	45	q2	q2	NOUN
ejpam-1624	223	46	1	1	NUM
ejpam-1624	223	47	=	=	SYM
ejpam-1624	223	48	q1	q1	PROPN
ejpam-1624	223	49	,	,	PUNCT
ejpam-1624	223	50	q2	q2	NOUN
ejpam-1624	223	51	3	3	NUM
ejpam-1624	223	52	=	=	SYM
ejpam-1624	223	53	q3	q3	NOUN
ejpam-1624	223	54	,	,	PUNCT
ejpam-1624	223	55	q3q2	q3q2	NOUN
ejpam-1624	223	56	=	=	SYM
ejpam-1624	223	57	0	0	PUNCT
ejpam-1624	223	58	and	and	CCONJ
ejpam-1624	223	59	q2q1	q2q1	PROPN
ejpam-1624	223	60	+	+	NOUN
ejpam-1624	223	61	q2	q2	NOUN
ejpam-1624	223	62	3	3	NUM
ejpam-1624	223	63	=	=	SYM
ejpam-1624	223	64	q2	q2	NOUN
ejpam-1624	223	65	.	.	PUNCT
ejpam-1624	224	1	with	with	ADP
ejpam-1624	224	2	respect	respect	NOUN
ejpam-1624	224	3	to	to	ADP
ejpam-1624	224	4	the	the	DET
ejpam-1624	224	5	space	space	NOUN
ejpam-1624	224	6	decomposition	decomposition	NOUN
ejpam-1624	224	7	h	h	NOUN
ejpam-1624	225	1	=	=	NOUN
ejpam-1624	225	2	r(q1	r(q1	NOUN
ejpam-1624	225	3	)	)	PUNCT
ejpam-1624	226	1	⊥	⊥	NOUN
ejpam-1624	226	2	⊕r(q1)⊕r(q	⊕r(q1)⊕r(q	NUM
ejpam-1624	226	3	∗	∗	NOUN
ejpam-1624	226	4	3)⊕r(q	3)⊕r(q	NUM
ejpam-1624	226	5	∗	∗	NOUN
ejpam-1624	226	6	3	3	NUM
ejpam-1624	226	7	)	)	PUNCT
ejpam-1624	226	8	,	,	PUNCT
ejpam-1624	226	9	p	p	NOUN
ejpam-1624	226	10	and	and	CCONJ
ejpam-1624	226	11	q	q	NOUN
ejpam-1624	226	12	can	can	AUX
ejpam-1624	226	13	be	be	AUX
ejpam-1624	226	14	further	far	ADV
ejpam-1624	226	15	represented	represent	VERB
ejpam-1624	226	16	as	as	ADP
ejpam-1624	226	17	p	p	NOUN
ejpam-1624	226	18	=	=	PUNCT
ejpam-1624	226	19			PROPN
ejpam-1624	226	20			NOUN
ejpam-1624	226	21			NOUN
ejpam-1624	226	22			NOUN
ejpam-1624	226	23			NOUN
ejpam-1624	226	24	i	i	PRON
ejpam-1624	226	25	0	0	NUM
ejpam-1624	226	26	0	0	NUM
ejpam-1624	226	27	0	0	NUM
ejpam-1624	226	28	0	0	NUM
ejpam-1624	227	1	i	i	NOUN
ejpam-1624	227	2	0	0	NUM
ejpam-1624	227	3	0	0	NUM
ejpam-1624	227	4	0	0	NUM
ejpam-1624	227	5	0	0	NUM
ejpam-1624	227	6	0	0	NUM
ejpam-1624	227	7	0	0	NUM
ejpam-1624	227	8	0	0	NUM
ejpam-1624	227	9	0	0	NUM
ejpam-1624	227	10	0	0	NUM
ejpam-1624	227	11	0	0	NUM
ejpam-1624	227	12			NOUN
ejpam-1624	227	13			NOUN
ejpam-1624	227	14			VERB
ejpam-1624	227	15			NOUN
ejpam-1624	227	16			PUNCT
ejpam-1624	227	17	,	,	PUNCT
ejpam-1624	227	18	q	q	NOUN
ejpam-1624	227	19	=	=	SYM
ejpam-1624	227	20			PROPN
ejpam-1624	227	21			NOUN
ejpam-1624	227	22			NOUN
ejpam-1624	227	23			NOUN
ejpam-1624	227	24			NOUN
ejpam-1624	227	25	0	0	NUM
ejpam-1624	227	26	0	0	NUM
ejpam-1624	227	27	0	0	NUM
ejpam-1624	227	28	0	0	NUM
ejpam-1624	227	29	q11	q11	NOUN
ejpam-1624	228	1	i	i	NOUN
ejpam-1624	228	2	0	0	NUM
ejpam-1624	228	3	0	0	NUM
ejpam-1624	228	4	q21	q21	NOUN
ejpam-1624	228	5	0	0	NUM
ejpam-1624	229	1	i	i	NOUN
ejpam-1624	229	2	0	0	NUM
ejpam-1624	230	1	q23	q23	PRON
ejpam-1624	230	2	q24	q24	NOUN
ejpam-1624	230	3	q31	q31	PROPN
ejpam-1624	230	4	0	0	NUM
ejpam-1624	230	5			NOUN
ejpam-1624	230	6			NOUN
ejpam-1624	230	7			VERB
ejpam-1624	230	8			NOUN
ejpam-1624	230	9			PUNCT
ejpam-1624	230	10	,	,	PUNCT
ejpam-1624	230	11	where	where	SCONJ
ejpam-1624	230	12	q24q11	q24q11	NOUN
ejpam-1624	230	13	+	+	NOUN
ejpam-1624	230	14	q31q21	q31q21	NOUN
ejpam-1624	230	15	=	=	X
ejpam-1624	230	16	q23	q23	PROPN
ejpam-1624	230	17	.	.	PUNCT
ejpam-1624	231	1	(	(	PUNCT
ejpam-1624	231	2	i	i	NOUN
ejpam-1624	231	3	)	)	PUNCT
ejpam-1624	231	4	if	if	SCONJ
ejpam-1624	231	5	a+	a+	X
ejpam-1624	231	6	b+	b+	X
ejpam-1624	231	7	c	c	X
ejpam-1624	232	1	+	+	SYM
ejpam-1624	232	2	d	d	X
ejpam-1624	232	3	6=	6=	NUM
ejpam-1624	232	4	0	0	NUM
ejpam-1624	232	5	,	,	PUNCT
ejpam-1624	232	6	then	then	ADV
ejpam-1624	232	7	ap	ap	PROPN
ejpam-1624	232	8	+	+	CCONJ
ejpam-1624	232	9	bq+	bq+	NOUN
ejpam-1624	232	10	cpq+	cpq+	ADP
ejpam-1624	232	11	dqp	dqp	NOUN
ejpam-1624	232	12	=	=	SYM
ejpam-1624	232	13			PROPN
ejpam-1624	232	14			NOUN
ejpam-1624	232	15			NOUN
ejpam-1624	232	16			NOUN
ejpam-1624	232	17			NOUN
ejpam-1624	232	18	ai	ai	VERB
ejpam-1624	232	19	0	0	NUM
ejpam-1624	232	20	0	0	NUM
ejpam-1624	232	21	0	0	NUM
ejpam-1624	232	22	(	(	PUNCT
ejpam-1624	232	23	b+	b+	X
ejpam-1624	232	24	c	c	X
ejpam-1624	232	25	+	+	CCONJ
ejpam-1624	232	26	d)q11	d)q11	X
ejpam-1624	232	27	(	(	PUNCT
ejpam-1624	232	28	a+	a+	X
ejpam-1624	232	29	b+	b+	X
ejpam-1624	232	30	c	c	NOUN
ejpam-1624	232	31	+	+	PUNCT
ejpam-1624	232	32	d)i	d)i	X
ejpam-1624	232	33	0	0	SYM
ejpam-1624	232	34	0	0	NUM
ejpam-1624	232	35	(	(	PUNCT
ejpam-1624	232	36	b+	b+	X
ejpam-1624	232	37	d)q21	d)q21	PROPN
ejpam-1624	232	38	0	0	NUM
ejpam-1624	232	39	bi	bi	NOUN
ejpam-1624	232	40	0	0	NUM
ejpam-1624	232	41	(	(	PUNCT
ejpam-1624	232	42	b+	b+	X
ejpam-1624	232	43	d)q23	d)q23	X
ejpam-1624	232	44	(	(	PUNCT
ejpam-1624	232	45	b+	b+	NOUN
ejpam-1624	232	46	d)q24	d)q24	VERB
ejpam-1624	232	47	bq31	bq31	PROPN
ejpam-1624	232	48	0	0	NUM
ejpam-1624	232	49			NOUN
ejpam-1624	232	50			NOUN
ejpam-1624	232	51			VERB
ejpam-1624	232	52			NOUN
ejpam-1624	232	53			PUNCT
ejpam-1624	232	54	.	.	PUNCT
ejpam-1624	233	1	since	since	SCONJ
ejpam-1624	233	2	ab	ab	PROPN
ejpam-1624	233	3	6=	6=	ADP
ejpam-1624	233	4	0	0	NUM
ejpam-1624	233	5	and	and	CCONJ
ejpam-1624	233	6	a+	a+	X
ejpam-1624	233	7	b+	b+	X
ejpam-1624	233	8	c	c	X
ejpam-1624	233	9	+	+	CCONJ
ejpam-1624	233	10	d	d	X
ejpam-1624	233	11	6=	6=	ADP
ejpam-1624	233	12	0	0	NUM
ejpam-1624	233	13	then	then	ADV
ejpam-1624	233	14	the	the	DET
ejpam-1624	233	15	submatrix	submatrix	NOUN
ejpam-1624	233	16			NOUN
ejpam-1624	233	17			NOUN
ejpam-1624	233	18			NOUN
ejpam-1624	233	19	ai	ai	VERB
ejpam-1624	233	20	0	0	NUM
ejpam-1624	233	21	0	0	NUM
ejpam-1624	233	22	(	(	PUNCT
ejpam-1624	233	23	b+	b+	X
ejpam-1624	233	24	c	c	X
ejpam-1624	233	25	+	+	CCONJ
ejpam-1624	233	26	d)q11	d)q11	X
ejpam-1624	233	27	(	(	PUNCT
ejpam-1624	233	28	a+	a+	X
ejpam-1624	233	29	b+	b+	X
ejpam-1624	233	30	c	c	NOUN
ejpam-1624	233	31	+	+	PUNCT
ejpam-1624	233	32	d)i	d)i	X
ejpam-1624	233	33	0	0	PUNCT
ejpam-1624	233	34	(	(	PUNCT
ejpam-1624	233	35	b+	b+	X
ejpam-1624	233	36	d)q21	d)q21	PROPN
ejpam-1624	233	37	0	0	NUM
ejpam-1624	233	38	bi	bi	NOUN
ejpam-1624	233	39			PROPN
ejpam-1624	233	40			NOUN
ejpam-1624	233	41			PUNCT
ejpam-1624	234	1	t.	t.	PROPN
ejpam-1624	234	2	xie	xie	PROPN
ejpam-1624	234	3	,	,	PUNCT
ejpam-1624	234	4	k.	k.	PROPN
ejpam-1624	234	5	zuo	zuo	PROPN
ejpam-1624	234	6	/	/	SYM
ejpam-1624	234	7	eur	eur	PROPN
ejpam-1624	234	8	.	.	PUNCT
ejpam-1624	235	1	j.	j.	PROPN
ejpam-1624	235	2	pure	pure	PROPN
ejpam-1624	235	3	appl	appl	PROPN
ejpam-1624	235	4	.	.	PROPN
ejpam-1624	235	5	math	math	PROPN
ejpam-1624	235	6	,	,	PUNCT
ejpam-1624	235	7	5	5	NUM
ejpam-1624	235	8	(	(	PUNCT
ejpam-1624	235	9	2012	2012	NUM
ejpam-1624	235	10	)	)	PUNCT
ejpam-1624	235	11	,	,	PUNCT
ejpam-1624	235	12	480	480	NUM
ejpam-1624	235	13	-	-	SYM
ejpam-1624	235	14	491	491	NUM
ejpam-1624	235	15	489	489	NUM
ejpam-1624	235	16	of	of	ADP
ejpam-1624	235	17	ap	ap	PROPN
ejpam-1624	235	18	+	+	CCONJ
ejpam-1624	235	19	bq+	bq+	PROPN
ejpam-1624	235	20	cpq+	cpq+	PROPN
ejpam-1624	235	21	dqp	dqp	NOUN
ejpam-1624	235	22	is	be	AUX
ejpam-1624	235	23	invertible	invertible	ADJ
ejpam-1624	235	24	and	and	CCONJ
ejpam-1624	235	25	it	it	PRON
ejpam-1624	235	26	’s	’	VERB
ejpam-1624	235	27	inverse	inverse	NOUN
ejpam-1624	235	28	is	be	AUX
ejpam-1624	235	29			NOUN
ejpam-1624	235	30			NOUN
ejpam-1624	235	31			NOUN
ejpam-1624	235	32			NOUN
ejpam-1624	235	33	1	1	NUM
ejpam-1624	235	34	a	a	PRON
ejpam-1624	236	1	i	i	NOUN
ejpam-1624	236	2	0	0	NUM
ejpam-1624	236	3	0	0	NUM
ejpam-1624	237	1	−	−	NOUN
ejpam-1624	237	2	b+c+d	b+c+d	NOUN
ejpam-1624	237	3	a(a+b+c+d	a(a+b+c+d	PROPN
ejpam-1624	237	4	)	)	PUNCT
ejpam-1624	237	5	q11	q11	NOUN
ejpam-1624	237	6	1	1	NUM
ejpam-1624	237	7	a+b+c+d	a+b+c+d	PROPN
ejpam-1624	238	1	i	i	INTJ
ejpam-1624	238	2	0	0	NUM
ejpam-1624	239	1	−	−	NOUN
ejpam-1624	239	2	b+d	b+d	NUM
ejpam-1624	239	3	ab	ab	PROPN
ejpam-1624	239	4	q21	q21	PROPN
ejpam-1624	239	5	0	0	NUM
ejpam-1624	239	6	1	1	NUM
ejpam-1624	239	7	b	b	NOUN
ejpam-1624	240	1	i	i	PRON
ejpam-1624	240	2			PROPN
ejpam-1624	240	3			NOUN
ejpam-1624	240	4			NOUN
ejpam-1624	240	5			PUNCT
ejpam-1624	240	6	by	by	ADP
ejpam-1624	240	7	using	use	VERB
ejpam-1624	240	8	the	the	DET
ejpam-1624	240	9	results	result	NOUN
ejpam-1624	240	10	of	of	ADP
ejpam-1624	240	11	lemma	lemma	PROPN
ejpam-1624	240	12	2	2	NUM
ejpam-1624	240	13	we	we	PRON
ejpam-1624	240	14	have	have	VERB
ejpam-1624	240	15	(	(	PUNCT
ejpam-1624	240	16	ap	ap	NOUN
ejpam-1624	240	17	+	+	NUM
ejpam-1624	240	18	bq+	bq+	NOUN
ejpam-1624	240	19	cpq+	cpq+	ADP
ejpam-1624	240	20	dqp)d	dqp)d	PROPN
ejpam-1624	240	21	=	=	SYM
ejpam-1624	240	22			PROPN
ejpam-1624	240	23			NOUN
ejpam-1624	240	24			NOUN
ejpam-1624	240	25			NOUN
ejpam-1624	240	26			NOUN
ejpam-1624	240	27			NOUN
ejpam-1624	240	28	1	1	NUM
ejpam-1624	240	29	a	a	PRON
ejpam-1624	241	1	i	i	NOUN
ejpam-1624	241	2	0	0	NUM
ejpam-1624	241	3	0	0	NUM
ejpam-1624	241	4	0	0	NUM
ejpam-1624	242	1	−	−	NOUN
ejpam-1624	242	2	b+c+d	b+c+d	NOUN
ejpam-1624	242	3	a(a+b+c+d	a(a+b+c+d	PROPN
ejpam-1624	242	4	)	)	PUNCT
ejpam-1624	242	5	q11	q11	NOUN
ejpam-1624	242	6	1	1	NUM
ejpam-1624	242	7	a+b+c+d	a+b+c+d	PROPN
ejpam-1624	242	8	i	i	PRON
ejpam-1624	242	9	0	0	NUM
ejpam-1624	242	10	0	0	NUM
ejpam-1624	243	1	−	−	PROPN
ejpam-1624	243	2	b+d	b+d	NUM
ejpam-1624	243	3	ab	ab	PROPN
ejpam-1624	243	4	q21	q21	PROPN
ejpam-1624	243	5	0	0	NUM
ejpam-1624	244	1	1	1	NUM
ejpam-1624	244	2	b	b	X
ejpam-1624	244	3	i	i	NOUN
ejpam-1624	244	4	0	0	NUM
ejpam-1624	244	5	x	x	SYM
ejpam-1624	244	6	b+d	b+d	X
ejpam-1624	244	7	(	(	PUNCT
ejpam-1624	244	8	a+b+c+d)2	a+b+c+d)2	PROPN
ejpam-1624	244	9	q24	q24	NOUN
ejpam-1624	244	10	1	1	NUM
ejpam-1624	244	11	b	b	PROPN
ejpam-1624	244	12	q31	q31	PROPN
ejpam-1624	244	13	0	0	NUM
ejpam-1624	244	14			NOUN
ejpam-1624	244	15			NOUN
ejpam-1624	244	16			VERB
ejpam-1624	244	17			NOUN
ejpam-1624	244	18			NOUN
ejpam-1624	244	19			PUNCT
ejpam-1624	244	20	,	,	PUNCT
ejpam-1624	244	21	where	where	SCONJ
ejpam-1624	244	22	x	x	ADP
ejpam-1624	244	23	=	=	SYM
ejpam-1624	244	24	−	−	PROPN
ejpam-1624	244	25	b+d	b+d	X
ejpam-1624	245	1	ab	ab	PROPN
ejpam-1624	245	2	q23	q23	PROPN
ejpam-1624	245	3	+	+	CCONJ
ejpam-1624	245	4	[	[	PUNCT
ejpam-1624	245	5	b+d	b+d	X
ejpam-1624	245	6	ab	ab	PROPN
ejpam-1624	245	7	+	+	CCONJ
ejpam-1624	245	8	b+d	b+d	PROPN
ejpam-1624	245	9	a2	a2	PROPN
ejpam-1624	245	10	−	−	PROPN
ejpam-1624	245	11	(	(	PUNCT
ejpam-1624	245	12	b+d)(b+c+d	b+d)(b+c+d	PROPN
ejpam-1624	245	13	)	)	PUNCT
ejpam-1624	245	14	(	(	PUNCT
ejpam-1624	245	15	a+b+c+d	a+b+c+d	PROPN
ejpam-1624	245	16	)	)	PUNCT
ejpam-1624	245	17	(	(	PUNCT
ejpam-1624	245	18	1	1	NUM
ejpam-1624	245	19	a2	a2	PROPN
ejpam-1624	245	20	+	+	X
ejpam-1624	245	21	1)]q24q11	1)]q24q11	NOUN
ejpam-1624	245	22	.	.	PUNCT
ejpam-1624	246	1	the	the	DET
ejpam-1624	246	2	coefficients	coefficient	NOUN
ejpam-1624	246	3	of	of	ADP
ejpam-1624	246	4	p	p	X
ejpam-1624	246	5	,	,	PUNCT
ejpam-1624	246	6	q	q	ADJ
ejpam-1624	246	7	,	,	PUNCT
ejpam-1624	246	8	pq	pq	PROPN
ejpam-1624	246	9	,	,	PUNCT
ejpam-1624	246	10	qp	qp	PROPN
ejpam-1624	246	11	,	,	PUNCT
ejpam-1624	246	12	qpq	qpq	ADJ
ejpam-1624	246	13	in	in	ADP
ejpam-1624	246	14	the	the	DET
ejpam-1624	246	15	expression	expression	NOUN
ejpam-1624	246	16	of	of	ADP
ejpam-1624	246	17	(	(	PUNCT
ejpam-1624	246	18	ap	ap	PROPN
ejpam-1624	246	19	+	+	NUM
ejpam-1624	246	20	bq+	bq+	PROPN
ejpam-1624	246	21	cpq	cpq	PROPN
ejpam-1624	246	22	+	+	CCONJ
ejpam-1624	246	23	dqp)d	dqp)d	PROPN
ejpam-1624	246	24	can	can	AUX
ejpam-1624	246	25	be	be	AUX
ejpam-1624	246	26	obtained	obtain	VERB
ejpam-1624	246	27	by	by	ADP
ejpam-1624	246	28	solving	solve	VERB
ejpam-1624	246	29	some	some	DET
ejpam-1624	246	30	linear	linear	ADJ
ejpam-1624	246	31	equations	equation	NOUN
ejpam-1624	246	32	.	.	PUNCT
ejpam-1624	247	1	then	then	ADV
ejpam-1624	247	2	we	we	PRON
ejpam-1624	247	3	have	have	VERB
ejpam-1624	247	4	(	(	PUNCT
ejpam-1624	247	5	ap	ap	NOUN
ejpam-1624	247	6	+	+	NUM
ejpam-1624	247	7	bq+	bq+	NOUN
ejpam-1624	247	8	cpq+	cpq+	ADP
ejpam-1624	247	9	dqp)d	dqp)d	PROPN
ejpam-1624	247	10	=	=	PUNCT
ejpam-1624	247	11	1	1	NUM
ejpam-1624	247	12	a	a	DET
ejpam-1624	247	13	p	p	X
ejpam-1624	248	1	+	+	NOUN
ejpam-1624	248	2	1	1	NUM
ejpam-1624	248	3	b	b	X
ejpam-1624	248	4	q+	q+	ADP
ejpam-1624	248	5	[	[	PUNCT
ejpam-1624	248	6	1	1	NUM
ejpam-1624	248	7	(	(	PUNCT
ejpam-1624	248	8	a+	a+	X
ejpam-1624	248	9	b+	b+	X
ejpam-1624	248	10	c	c	X
ejpam-1624	248	11	+	+	SYM
ejpam-1624	248	12	d	d	NOUN
ejpam-1624	248	13	)	)	PUNCT
ejpam-1624	248	14	−	−	NOUN
ejpam-1624	248	15	b+	b+	ADP
ejpam-1624	248	16	d	d	X
ejpam-1624	248	17	(	(	PUNCT
ejpam-1624	248	18	a+	a+	X
ejpam-1624	248	19	b+	b+	X
ejpam-1624	248	20	c	c	NOUN
ejpam-1624	248	21	+	+	PUNCT
ejpam-1624	248	22	d)2	d)2	NOUN
ejpam-1624	248	23	−	−	PROPN
ejpam-1624	248	24	1	1	NUM
ejpam-1624	248	25	a	a	DET
ejpam-1624	248	26	]	]	X
ejpam-1624	248	27	pq	pq	NOUN
ejpam-1624	248	28	−	−	PROPN
ejpam-1624	248	29	(	(	PUNCT
ejpam-1624	248	30	a+	a+	X
ejpam-1624	248	31	b+	b+	X
ejpam-1624	248	32	d	d	PROPN
ejpam-1624	248	33	ab	ab	PROPN
ejpam-1624	248	34	)	)	PUNCT
ejpam-1624	248	35	qp	qp	VERB
ejpam-1624	249	1	+	+	PUNCT
ejpam-1624	249	2	[	[	PUNCT
ejpam-1624	249	3	b+	b+	X
ejpam-1624	249	4	d	d	X
ejpam-1624	249	5	(	(	PUNCT
ejpam-1624	249	6	a+	a+	X
ejpam-1624	249	7	b+	b+	X
ejpam-1624	249	8	c	c	NOUN
ejpam-1624	249	9	+	+	PUNCT
ejpam-1624	249	10	d)2	d)2	PROPN
ejpam-1624	249	11	+	+	CCONJ
ejpam-1624	249	12	b+	b+	NOUN
ejpam-1624	249	13	d	d	PROPN
ejpam-1624	249	14	ab	ab	X
ejpam-1624	249	15	]	]	X
ejpam-1624	249	16	qpq	qpq	X
ejpam-1624	249	17	.	.	PUNCT
ejpam-1624	250	1	(	(	PUNCT
ejpam-1624	250	2	ii	ii	NOUN
ejpam-1624	250	3	)	)	PUNCT
ejpam-1624	250	4	if	if	SCONJ
ejpam-1624	250	5	a+	a+	X
ejpam-1624	250	6	b+	b+	X
ejpam-1624	250	7	c	c	X
ejpam-1624	251	1	+	+	SYM
ejpam-1624	251	2	d	d	X
ejpam-1624	251	3	=	=	SYM
ejpam-1624	251	4	0	0	NUM
ejpam-1624	251	5	,	,	PUNCT
ejpam-1624	251	6	then	then	ADV
ejpam-1624	251	7	ap	ap	PROPN
ejpam-1624	251	8	+	+	CCONJ
ejpam-1624	251	9	bq+	bq+	NOUN
ejpam-1624	251	10	cpq+	cpq+	ADP
ejpam-1624	251	11	dqp	dqp	NOUN
ejpam-1624	251	12	=	=	SYM
ejpam-1624	251	13			PROPN
ejpam-1624	251	14			NOUN
ejpam-1624	251	15			NOUN
ejpam-1624	251	16			NOUN
ejpam-1624	251	17			NOUN
ejpam-1624	251	18	ai	ai	VERB
ejpam-1624	251	19	0	0	NUM
ejpam-1624	251	20	0	0	NUM
ejpam-1624	251	21	0	0	NUM
ejpam-1624	252	1	−aq11	−aq11	NOUN
ejpam-1624	252	2	0	0	NUM
ejpam-1624	252	3	0	0	NUM
ejpam-1624	252	4	0	0	NUM
ejpam-1624	252	5	(	(	PUNCT
ejpam-1624	252	6	b+	b+	X
ejpam-1624	252	7	d)q21	d)q21	PROPN
ejpam-1624	252	8	0	0	NUM
ejpam-1624	252	9	bi	bi	NOUN
ejpam-1624	252	10	0	0	NUM
ejpam-1624	252	11	(	(	PUNCT
ejpam-1624	252	12	b+	b+	X
ejpam-1624	252	13	d)q23	d)q23	X
ejpam-1624	252	14	(	(	PUNCT
ejpam-1624	252	15	b+	b+	NOUN
ejpam-1624	252	16	d)q24	d)q24	VERB
ejpam-1624	252	17	bq31	bq31	PROPN
ejpam-1624	252	18	0	0	NUM
ejpam-1624	252	19			NOUN
ejpam-1624	252	20			NOUN
ejpam-1624	252	21			VERB
ejpam-1624	252	22			NOUN
ejpam-1624	252	23			PUNCT
ejpam-1624	252	24	.	.	PUNCT
ejpam-1624	253	1	let	let	VERB
ejpam-1624	253	2	s	s	PRON
ejpam-1624	253	3	=	=	NOUN
ejpam-1624	253	4			PROPN
ejpam-1624	253	5			NOUN
ejpam-1624	253	6			NOUN
ejpam-1624	253	7			NOUN
ejpam-1624	253	8			NOUN
ejpam-1624	253	9	i	i	PRON
ejpam-1624	253	10	0	0	NUM
ejpam-1624	253	11	0	0	NUM
ejpam-1624	253	12	0	0	NUM
ejpam-1624	253	13	0	0	NUM
ejpam-1624	253	14	0	0	NUM
ejpam-1624	254	1	i	i	NOUN
ejpam-1624	254	2	0	0	NUM
ejpam-1624	254	3	0	0	PUNCT
ejpam-1624	255	1	i	i	NOUN
ejpam-1624	255	2	0	0	NUM
ejpam-1624	255	3	0	0	NUM
ejpam-1624	255	4	0	0	NUM
ejpam-1624	255	5	0	0	NUM
ejpam-1624	255	6	0	0	NUM
ejpam-1624	256	1	i	i	PRON
ejpam-1624	256	2			PROPN
ejpam-1624	256	3			NOUN
ejpam-1624	256	4			VERB
ejpam-1624	256	5			NOUN
ejpam-1624	256	6			PUNCT
ejpam-1624	257	1	,	,	PUNCT
ejpam-1624	257	2	then	then	ADV
ejpam-1624	257	3	s(ap	s(ap	PROPN
ejpam-1624	257	4	+	+	CCONJ
ejpam-1624	257	5	bq+	bq+	NOUN
ejpam-1624	257	6	cpq+	cpq+	NOUN
ejpam-1624	257	7	dqp)s−1	dqp)s−1	ADJ
ejpam-1624	257	8	=	=	SYM
ejpam-1624	257	9			PROPN
ejpam-1624	257	10			NOUN
ejpam-1624	257	11			NOUN
ejpam-1624	257	12			NOUN
ejpam-1624	257	13			NOUN
ejpam-1624	257	14	ai	ai	VERB
ejpam-1624	257	15	0	0	NUM
ejpam-1624	257	16	0	0	NUM
ejpam-1624	257	17	0	0	NUM
ejpam-1624	257	18	(	(	PUNCT
ejpam-1624	257	19	b+	b+	X
ejpam-1624	257	20	d)q21	d)q21	PROPN
ejpam-1624	257	21	bi	bi	NOUN
ejpam-1624	257	22	0	0	NUM
ejpam-1624	257	23	0	0	NUM
ejpam-1624	258	1	−aq11	−aq11	NOUN
ejpam-1624	258	2	0	0	NUM
ejpam-1624	258	3	0	0	NUM
ejpam-1624	258	4	0	0	NUM
ejpam-1624	258	5	(	(	PUNCT
ejpam-1624	258	6	b+	b+	X
ejpam-1624	258	7	d)q23	d)q23	X
ejpam-1624	258	8	bq31	bq31	PROPN
ejpam-1624	258	9	(	(	PUNCT
ejpam-1624	258	10	b+	b+	ADJ
ejpam-1624	258	11	d)q24	d)q24	NOUN
ejpam-1624	258	12	0	0	NUM
ejpam-1624	258	13			NOUN
ejpam-1624	258	14			NOUN
ejpam-1624	258	15			VERB
ejpam-1624	258	16			NOUN
ejpam-1624	258	17			PUNCT
ejpam-1624	258	18	.	.	PUNCT
ejpam-1624	259	1	(	(	PUNCT
ejpam-1624	259	2	ap	ap	NOUN
ejpam-1624	259	3	+	+	NUM
ejpam-1624	259	4	bq+	bq+	NOUN
ejpam-1624	259	5	cpq+	cpq+	ADP
ejpam-1624	259	6	dqp)d	dqp)d	PROPN
ejpam-1624	259	7	=	=	SYM
ejpam-1624	259	8	s−1[s(ap	s−1[s(ap	PROPN
ejpam-1624	259	9	+	+	CCONJ
ejpam-1624	259	10	bq+	bq+	NOUN
ejpam-1624	259	11	cpq)s−1]ds	cpq)s−1]ds	NOUN
ejpam-1624	259	12	references	reference	VERB
ejpam-1624	259	13	490	490	NUM
ejpam-1624	259	14	=	=	SYM
ejpam-1624	259	15			PROPN
ejpam-1624	259	16			NOUN
ejpam-1624	259	17			NOUN
ejpam-1624	259	18			NOUN
ejpam-1624	259	19			NOUN
ejpam-1624	259	20			NOUN
ejpam-1624	259	21	1	1	NUM
ejpam-1624	259	22	a	a	PRON
ejpam-1624	259	23	i	i	NOUN
ejpam-1624	259	24	0	0	NUM
ejpam-1624	259	25	0	0	NUM
ejpam-1624	259	26	0	0	NUM
ejpam-1624	260	1	−	−	NUM
ejpam-1624	260	2	1	1	NUM
ejpam-1624	260	3	a	a	DET
ejpam-1624	260	4	q11	q11	NOUN
ejpam-1624	260	5	0	0	NUM
ejpam-1624	260	6	0	0	NUM
ejpam-1624	260	7	0	0	NUM
ejpam-1624	261	1	−	−	NOUN
ejpam-1624	261	2	b+d	b+d	NUM
ejpam-1624	261	3	ab	ab	PROPN
ejpam-1624	261	4	q21	q21	PROPN
ejpam-1624	261	5	0	0	NUM
ejpam-1624	262	1	1	1	NUM
ejpam-1624	262	2	b	b	X
ejpam-1624	262	3	i	i	NOUN
ejpam-1624	262	4	0	0	NUM
ejpam-1624	262	5	−	−	NOUN
ejpam-1624	262	6	b+d	b+d	X
ejpam-1624	262	7	ab	ab	PROPN
ejpam-1624	262	8	q31q21	q31q21	NOUN
ejpam-1624	262	9	0	0	NUM
ejpam-1624	262	10	1	1	NUM
ejpam-1624	262	11	b	b	X
ejpam-1624	262	12	q31	q31	NUM
ejpam-1624	262	13	0	0	NUM
ejpam-1624	262	14			NOUN
ejpam-1624	262	15			NOUN
ejpam-1624	262	16			VERB
ejpam-1624	262	17			NOUN
ejpam-1624	262	18			NOUN
ejpam-1624	262	19			PUNCT
ejpam-1624	263	1	=	=	PUNCT
ejpam-1624	263	2	1	1	NUM
ejpam-1624	263	3	a	a	DET
ejpam-1624	263	4	p	p	X
ejpam-1624	263	5	+	+	NOUN
ejpam-1624	263	6	1	1	NUM
ejpam-1624	263	7	b	b	X
ejpam-1624	263	8	q−	q−	PROPN
ejpam-1624	263	9	1	1	NUM
ejpam-1624	263	10	a	a	DET
ejpam-1624	263	11	pq−	pq−	PROPN
ejpam-1624	263	12	(	(	PUNCT
ejpam-1624	263	13	1	1	NUM
ejpam-1624	263	14	a	a	DET
ejpam-1624	263	15	+	+	NUM
ejpam-1624	263	16	1	1	NUM
ejpam-1624	263	17	b	b	NOUN
ejpam-1624	263	18	+	+	CCONJ
ejpam-1624	263	19	d	d	PROPN
ejpam-1624	263	20	ab	ab	PROPN
ejpam-1624	263	21	)	)	PUNCT
ejpam-1624	263	22	qp	qp	VERB
ejpam-1624	264	1	+	+	SYM
ejpam-1624	264	2	b+	b+	NOUN
ejpam-1624	264	3	d	d	X
ejpam-1624	264	4	ab	ab	PROPN
ejpam-1624	264	5	qpq	qpq	PROPN
ejpam-1624	264	6	.	.	PUNCT
ejpam-1624	265	1	now	now	ADV
ejpam-1624	265	2	we	we	PRON
ejpam-1624	265	3	can	can	AUX
ejpam-1624	265	4	derive	derive	VERB
ejpam-1624	265	5	some	some	DET
ejpam-1624	265	6	special	special	ADJ
ejpam-1624	265	7	cases	case	NOUN
ejpam-1624	265	8	from	from	ADP
ejpam-1624	265	9	theorem	theorem	ADJ
ejpam-1624	265	10	3	3	NUM
ejpam-1624	265	11	.	.	PUNCT
ejpam-1624	266	1	these	these	DET
ejpam-1624	266	2	results	result	NOUN
ejpam-1624	266	3	are	be	AUX
ejpam-1624	266	4	also	also	ADV
ejpam-1624	266	5	special	special	ADJ
ejpam-1624	266	6	cases	case	NOUN
ejpam-1624	266	7	of	of	ADP
ejpam-1624	266	8	theorem	theorem	NOUN
ejpam-1624	266	9	2.6	2.6	NUM
ejpam-1624	266	10	in	in	ADP
ejpam-1624	266	11	[	[	X
ejpam-1624	266	12	4	4	NUM
ejpam-1624	266	13	]	]	PUNCT
ejpam-1624	266	14	.	.	PUNCT
ejpam-1624	267	1	corollary	corollary	ADJ
ejpam-1624	267	2	5	5	NUM
ejpam-1624	267	3	.	.	PUNCT
ejpam-1624	268	1	let	let	VERB
ejpam-1624	268	2	p	p	NOUN
ejpam-1624	268	3	and	and	CCONJ
ejpam-1624	268	4	q	q	NOUN
ejpam-1624	268	5	be	be	AUX
ejpam-1624	268	6	two	two	NUM
ejpam-1624	268	7	idempotents	idempotent	NOUN
ejpam-1624	268	8	in	in	ADP
ejpam-1624	268	9	b(h	b(h	PROPN
ejpam-1624	268	10	)	)	PUNCT
ejpam-1624	268	11	.	.	PUNCT
ejpam-1624	269	1	assume	assume	VERB
ejpam-1624	269	2	that	that	SCONJ
ejpam-1624	269	3	pqp	pqp	NOUN
ejpam-1624	269	4	=	=	SYM
ejpam-1624	269	5	pq	pq	PROPN
ejpam-1624	269	6	,	,	PUNCT
ejpam-1624	269	7	then	then	ADV
ejpam-1624	269	8	the	the	DET
ejpam-1624	269	9	following	follow	VERB
ejpam-1624	269	10	statements	statement	NOUN
ejpam-1624	269	11	hold	hold	VERB
ejpam-1624	269	12	.	.	PUNCT
ejpam-1624	270	1	(	(	PUNCT
ejpam-1624	270	2	i	i	NOUN
ejpam-1624	270	3	)	)	PUNCT
ejpam-1624	270	4	(	(	PUNCT
ejpam-1624	270	5	p	p	NOUN
ejpam-1624	270	6	+	+	NOUN
ejpam-1624	270	7	q)d	q)d	NOUN
ejpam-1624	270	8	=	=	NOUN
ejpam-1624	270	9	p	p	X
ejpam-1624	271	1	+	+	NOUN
ejpam-1624	271	2	q−	q−	PROPN
ejpam-1624	271	3	3	3	NUM
ejpam-1624	271	4	4	4	NUM
ejpam-1624	271	5	pq−	pq−	NOUN
ejpam-1624	271	6	2qp	2qp	NOUN
ejpam-1624	271	7	+	+	CCONJ
ejpam-1624	271	8	5	5	NUM
ejpam-1624	271	9	4	4	NUM
ejpam-1624	271	10	qpq	qpq	ADJ
ejpam-1624	271	11	.	.	PUNCT
ejpam-1624	272	1	(	(	PUNCT
ejpam-1624	272	2	ii	ii	NOUN
ejpam-1624	272	3	)	)	PUNCT
ejpam-1624	272	4	(	(	PUNCT
ejpam-1624	272	5	p	p	NOUN
ejpam-1624	272	6	−q)d	−q)d	VERB
ejpam-1624	272	7	=	=	SYM
ejpam-1624	272	8	p	p	NOUN
ejpam-1624	272	9	−q−	−q−	NOUN
ejpam-1624	272	10	pq+qpq	pq+qpq	X
ejpam-1624	272	11	.	.	PUNCT
ejpam-1624	273	1	we	we	PRON
ejpam-1624	273	2	can	can	AUX
ejpam-1624	273	3	also	also	ADV
ejpam-1624	273	4	derive	derive	VERB
ejpam-1624	273	5	the	the	DET
ejpam-1624	273	6	formulaes	formulaes	NOUN
ejpam-1624	273	7	of	of	ADP
ejpam-1624	273	8	drazin	drazin	PROPN
ejpam-1624	273	9	inverses	inverses	PROPN
ejpam-1624	273	10	of	of	ADP
ejpam-1624	273	11	linear	linear	PROPN
ejpam-1624	273	12	combinations	combination	NOUN
ejpam-1624	273	13	of	of	ADP
ejpam-1624	273	14	p	p	NOUN
ejpam-1624	273	15	and	and	CCONJ
ejpam-1624	273	16	q	q	NOUN
ejpam-1624	273	17	under	under	ADP
ejpam-1624	273	18	the	the	DET
ejpam-1624	273	19	condition	condition	NOUN
ejpam-1624	273	20	pqp	pqp	NOUN
ejpam-1624	273	21	=	=	SYM
ejpam-1624	273	22	pq	pq	PROPN
ejpam-1624	273	23	.	.	PUNCT
ejpam-1624	273	24	corollary	corollary	NOUN
ejpam-1624	273	25	6	6	NUM
ejpam-1624	273	26	.	.	PUNCT
ejpam-1624	274	1	let	let	VERB
ejpam-1624	274	2	p	p	NOUN
ejpam-1624	274	3	and	and	CCONJ
ejpam-1624	274	4	q	q	NOUN
ejpam-1624	274	5	be	be	AUX
ejpam-1624	274	6	two	two	NUM
ejpam-1624	274	7	idempotents	idempotent	NOUN
ejpam-1624	274	8	in	in	ADP
ejpam-1624	274	9	b(h	b(h	PROPN
ejpam-1624	274	10	)	)	PUNCT
ejpam-1624	274	11	.	.	PUNCT
ejpam-1624	275	1	assume	assume	VERB
ejpam-1624	275	2	that	that	SCONJ
ejpam-1624	275	3	pqp	pqp	NOUN
ejpam-1624	275	4	=	=	SYM
ejpam-1624	275	5	pq	pq	PROPN
ejpam-1624	275	6	,	,	PUNCT
ejpam-1624	275	7	then	then	ADV
ejpam-1624	275	8	the	the	DET
ejpam-1624	275	9	following	follow	VERB
ejpam-1624	275	10	statements	statement	NOUN
ejpam-1624	275	11	hold	hold	VERB
ejpam-1624	275	12	.	.	PUNCT
ejpam-1624	276	1	(	(	PUNCT
ejpam-1624	276	2	ap	ap	NOUN
ejpam-1624	277	1	+	+	CCONJ
ejpam-1624	277	2	bq)d	bq)d	PROPN
ejpam-1624	277	3	=	=	PUNCT
ejpam-1624	277	4			PROPN
ejpam-1624	277	5			ADP
ejpam-1624	277	6			NOUN
ejpam-1624	277	7	1	1	NUM
ejpam-1624	277	8	a	a	DET
ejpam-1624	277	9	p	p	X
ejpam-1624	277	10	+	+	NOUN
ejpam-1624	277	11	1	1	NUM
ejpam-1624	277	12	b	b	X
ejpam-1624	277	13	q+	q+	ADP
ejpam-1624	277	14	[	[	PUNCT
ejpam-1624	277	15	1	1	NUM
ejpam-1624	277	16	a+b	a+b	NUM
ejpam-1624	277	17	−	−	PROPN
ejpam-1624	277	18	b	b	NOUN
ejpam-1624	277	19	(	(	PUNCT
ejpam-1624	277	20	a+b)2	a+b)2	NOUN
ejpam-1624	277	21	−	−	PROPN
ejpam-1624	277	22	1	1	NUM
ejpam-1624	277	23	a	a	DET
ejpam-1624	277	24	]	]	X
ejpam-1624	277	25	pq	pq	NOUN
ejpam-1624	277	26	−	−	PROPN
ejpam-1624	277	27	a+b	a+b	NUM
ejpam-1624	277	28	ab	ab	NOUN
ejpam-1624	277	29	qp	qp	ADP
ejpam-1624	277	30	+	+	PUNCT
ejpam-1624	277	31	[	[	PUNCT
ejpam-1624	277	32	b	b	X
ejpam-1624	277	33	(	(	PUNCT
ejpam-1624	277	34	a+b)2	a+b)2	NOUN
ejpam-1624	277	35	+	+	CCONJ
ejpam-1624	277	36	1	1	NUM
ejpam-1624	277	37	a	a	DET
ejpam-1624	277	38	]	]	X
ejpam-1624	277	39	qpq	qpq	ADJ
ejpam-1624	277	40	,	,	PUNCT
ejpam-1624	277	41	whe	whe	NOUN
ejpam-1624	277	42	n	n	PROPN
ejpam-1624	277	43	a+	a+	PRON
ejpam-1624	277	44	b	b	PROPN
ejpam-1624	277	45	6=	6=	SYM
ejpam-1624	277	46	0	0	NUM
ejpam-1624	277	47	1	1	NUM
ejpam-1624	277	48	a	a	DET
ejpam-1624	277	49	(	(	PUNCT
ejpam-1624	277	50	p	p	NOUN
ejpam-1624	277	51	−q−	−q−	NOUN
ejpam-1624	277	52	pq+qpq	pq+qpq	PROPN
ejpam-1624	277	53	)	)	PUNCT
ejpam-1624	277	54	,	,	PUNCT
ejpam-1624	277	55	when	when	SCONJ
ejpam-1624	277	56	a+	a+	DET
ejpam-1624	277	57	b	b	X
ejpam-1624	277	58	=	=	SYM
ejpam-1624	277	59	0	0	PROPN
ejpam-1624	277	60	.	.	PUNCT
ejpam-1624	277	61	acknowledgements	acknowledgement	VERB
ejpam-1624	277	62	the	the	DET
ejpam-1624	277	63	paper	paper	NOUN
ejpam-1624	277	64	is	be	AUX
ejpam-1624	277	65	supported	support	VERB
ejpam-1624	277	66	by	by	ADP
ejpam-1624	277	67	the	the	DET
ejpam-1624	277	68	key	key	ADJ
ejpam-1624	277	69	research	research	NOUN
ejpam-1624	277	70	project	project	NOUN
ejpam-1624	277	71	and	and	CCONJ
ejpam-1624	277	72	youth	youth	NOUN
ejpam-1624	277	73	research	research	NOUN
ejpam-1624	277	74	project	project	NOUN
ejpam-1624	277	75	of	of	ADP
ejpam-1624	277	76	educational	educational	ADJ
ejpam-1624	277	77	department	department	PROPN
ejpam-1624	277	78	of	of	ADP
ejpam-1624	277	79	hubei	hubei	PROPN
ejpam-1624	277	80	province(d20122202	province(d20122202	PROPN
ejpam-1624	277	81	)	)	PUNCT
ejpam-1624	277	82	and	and	CCONJ
ejpam-1624	277	83	(	(	PUNCT
ejpam-1624	277	84	b20122203	b20122203	PROPN
ejpam-1624	277	85	)	)	PUNCT
ejpam-1624	277	86	of	of	ADP
ejpam-1624	277	87	china	china	PROPN
ejpam-1624	277	88	.	.	PUNCT
ejpam-1624	278	1	references	reference	NOUN
ejpam-1624	278	2	[	[	X
ejpam-1624	278	3	1	1	X
ejpam-1624	278	4	]	]	X
ejpam-1624	278	5	g.n	g.n	PROPN
ejpam-1624	278	6	.	.	PROPN
ejpam-1624	278	7	castro	castro	PROPN
ejpam-1624	278	8	,	,	PUNCT
ejpam-1624	278	9	j.j	j.j	PROPN
ejpam-1624	278	10	.	.	PROPN
ejpam-1624	278	11	koliha	koliha	PROPN
ejpam-1624	278	12	.	.	PUNCT
ejpam-1624	279	1	new	new	ADJ
ejpam-1624	279	2	additive	additive	ADJ
ejpam-1624	279	3	results	result	NOUN
ejpam-1624	279	4	for	for	ADP
ejpam-1624	279	5	the	the	DET
ejpam-1624	279	6	g	g	NOUN
ejpam-1624	279	7	-	-	PUNCT
ejpam-1624	279	8	drazin	drazin	NOUN
ejpam-1624	279	9	inverse	inverse	NOUN
ejpam-1624	279	10	.	.	PUNCT
ejpam-1624	280	1	preceedings	preceeding	NOUN
ejpam-1624	280	2	of	of	ADP
ejpam-1624	280	3	the	the	DET
ejpam-1624	280	4	royal	royal	ADJ
ejpam-1624	280	5	society	society	NOUN
ejpam-1624	280	6	of	of	ADP
ejpam-1624	280	7	edinburgh	edinburgh	PROPN
ejpam-1624	280	8	,	,	PUNCT
ejpam-1624	280	9	134(1):1085	134(1):1085	PROPN
ejpam-1624	280	10	-	-	SYM
ejpam-1624	280	11	1097	1097	NUM
ejpam-1624	280	12	,	,	PUNCT
ejpam-1624	280	13	2004	2004	NUM
ejpam-1624	280	14	.	.	PUNCT
ejpam-1624	281	1	[	[	X
ejpam-1624	281	2	2	2	NUM
ejpam-1624	281	3	]	]	X
ejpam-1624	281	4	s.l	s.l	PROPN
ejpam-1624	281	5	.	.	PROPN
ejpam-1624	281	6	campbell	campbell	PROPN
ejpam-1624	281	7	,	,	PUNCT
ejpam-1624	281	8	c.d	c.d	PROPN
ejpam-1624	281	9	.	.	PUNCT
ejpam-1624	281	10	meyer	meyer	PROPN
ejpam-1624	281	11	.	.	PROPN
ejpam-1624	281	12	generalized	generalized	ADJ
ejpam-1624	281	13	inverse	inverse	NOUN
ejpam-1624	281	14	of	of	ADP
ejpam-1624	281	15	linear	linear	ADJ
ejpam-1624	281	16	transformations	transformation	NOUN
ejpam-1624	281	17	.	.	PUNCT
ejpam-1624	282	1	london	london	PROPN
ejpam-1624	282	2	:	:	PUNCT
ejpam-1624	282	3	pitman	pitman	NOUN
ejpam-1624	282	4	press	press	PROPN
ejpam-1624	282	5	,	,	PUNCT
ejpam-1624	282	6	1979	1979	NUM
ejpam-1624	282	7	.	.	PUNCT
ejpam-1624	283	1	[	[	X
ejpam-1624	283	2	3	3	X
ejpam-1624	283	3	]	]	X
ejpam-1624	283	4	m.p	m.p	PROPN
ejpam-1624	283	5	.	.	PROPN
ejpam-1624	283	6	drazin	drazin	PROPN
ejpam-1624	283	7	.	.	PUNCT
ejpam-1624	284	1	pseudoinverse	pseudoinverse	NOUN
ejpam-1624	284	2	in	in	ADP
ejpam-1624	284	3	associative	associative	ADJ
ejpam-1624	284	4	rings	ring	NOUN
ejpam-1624	284	5	and	and	CCONJ
ejpam-1624	284	6	semigroups	semigroup	NOUN
ejpam-1624	284	7	.	.	PUNCT
ejpam-1624	285	1	american	american	PROPN
ejpam-1624	285	2	mathematical	mathematical	PROPN
ejpam-1624	285	3	monthly	monthly	ADV
ejpam-1624	285	4	,	,	PUNCT
ejpam-1624	285	5	65:506	65:506	NUM
ejpam-1624	285	6	-	-	SYM
ejpam-1624	285	7	514	514	NUM
ejpam-1624	285	8	,	,	PUNCT
ejpam-1624	285	9	1958	1958	NUM
ejpam-1624	285	10	.	.	PUNCT
ejpam-1624	286	1	[	[	X
ejpam-1624	286	2	4	4	NUM
ejpam-1624	286	3	]	]	X
ejpam-1624	286	4	chunyuan	chunyuan	PROPN
ejpam-1624	286	5	deng	deng	PROPN
ejpam-1624	286	6	.	.	PUNCT
ejpam-1624	287	1	the	the	DET
ejpam-1624	287	2	drazin	drazin	PROPN
ejpam-1624	287	3	inverses	inverse	VERB
ejpam-1624	287	4	of	of	ADP
ejpam-1624	287	5	sum	sum	NOUN
ejpam-1624	287	6	and	and	CCONJ
ejpam-1624	287	7	difference	difference	NOUN
ejpam-1624	287	8	of	of	ADP
ejpam-1624	287	9	idempotents	idempotent	NOUN
ejpam-1624	287	10	.	.	PUNCT
ejpam-1624	288	1	linear	linear	ADJ
ejpam-1624	288	2	algebra	algebra	NOUN
ejpam-1624	288	3	and	and	CCONJ
ejpam-1624	288	4	its	its	PRON
ejpam-1624	288	5	applications	application	NOUN
ejpam-1624	288	6	,	,	PUNCT
ejpam-1624	288	7	430	430	NUM
ejpam-1624	288	8	:	:	PUNCT
ejpam-1624	288	9	1282	1282	NUM
ejpam-1624	288	10	-	-	SYM
ejpam-1624	288	11	1291	1291	NUM
ejpam-1624	288	12	,	,	PUNCT
ejpam-1624	288	13	2009	2009	NUM
ejpam-1624	288	14	.	.	PUNCT
ejpam-1624	289	1	references	reference	NOUN
ejpam-1624	289	2	491	491	NUM
ejpam-1624	289	3	[	[	X
ejpam-1624	289	4	5	5	NUM
ejpam-1624	289	5	]	]	X
ejpam-1624	289	6	d.s	d.s	PROPN
ejpam-1624	289	7	.	.	PROPN
ejpam-1624	289	8	djordjrvic	djordjrvic	PROPN
ejpam-1624	289	9	,	,	PUNCT
ejpam-1624	289	10	p.s	p.s	PROPN
ejpam-1624	289	11	.	.	PROPN
ejpam-1624	289	12	stanimirovic	stanimirovic	PROPN
ejpam-1624	289	13	.	.	PUNCT
ejpam-1624	290	1	on	on	ADP
ejpam-1624	290	2	the	the	DET
ejpam-1624	290	3	generalized	generalized	ADJ
ejpam-1624	290	4	drazin	drazin	PROPN
ejpam-1624	290	5	inverse	inverse	NOUN
ejpam-1624	290	6	and	and	CCONJ
ejpam-1624	290	7	generalized	generalized	ADJ
ejpam-1624	290	8	resolvent	resolvent	NOUN
ejpam-1624	290	9	.	.	PUNCT
ejpam-1624	291	1	czechoslovak	czechoslovak	ADJ
ejpam-1624	291	2	mathematical	mathematical	PROPN
ejpam-1624	291	3	journal	journal	NOUN
ejpam-1624	291	4	,	,	PUNCT
ejpam-1624	291	5	126	126	NUM
ejpam-1624	291	6	:	:	PUNCT
ejpam-1624	291	7	671	671	NUM
ejpam-1624	291	8	-	-	SYM
ejpam-1624	291	9	634	634	NUM
ejpam-1624	291	10	,	,	PUNCT
ejpam-1624	291	11	2001	2001	NUM
ejpam-1624	291	12	.	.	PUNCT
ejpam-1624	292	1	[	[	X
ejpam-1624	292	2	6	6	NUM
ejpam-1624	292	3	]	]	SYM
ejpam-1624	292	4	r.g	r.g	PROPN
ejpam-1624	292	5	.	.	PROPN
ejpam-1624	292	6	douglas	douglas	PROPN
ejpam-1624	292	7	.	.	PUNCT
ejpam-1624	293	1	on	on	ADP
ejpam-1624	293	2	majorization	majorization	NOUN
ejpam-1624	293	3	factorization	factorization	NOUN
ejpam-1624	293	4	and	and	CCONJ
ejpam-1624	293	5	range	range	NOUN
ejpam-1624	293	6	inclusion	inclusion	NOUN
ejpam-1624	293	7	of	of	ADP
ejpam-1624	293	8	operators	operator	NOUN
ejpam-1624	293	9	in	in	ADP
ejpam-1624	293	10	hilbert	hilbert	NOUN
ejpam-1624	293	11	space	space	NOUN
ejpam-1624	293	12	.	.	PUNCT
ejpam-1624	294	1	proceedings	proceeding	NOUN
ejpam-1624	294	2	of	of	ADP
ejpam-1624	294	3	the	the	DET
ejpam-1624	294	4	american	american	PROPN
ejpam-1624	294	5	mathematical	mathematical	PROPN
ejpam-1624	294	6	society	society	NOUN
ejpam-1624	294	7	,	,	PUNCT
ejpam-1624	294	8	17	17	NUM
ejpam-1624	294	9	:	:	SYM
ejpam-1624	294	10	413	413	NUM
ejpam-1624	294	11	-	-	SYM
ejpam-1624	294	12	416	416	NUM
ejpam-1624	294	13	,	,	PUNCT
ejpam-1624	294	14	1966	1966	NUM
ejpam-1624	294	15	.	.	PUNCT
ejpam-1624	295	1	[	[	X
ejpam-1624	295	2	7	7	X
ejpam-1624	295	3	]	]	X
ejpam-1624	295	4	r.e	r.e	PROPN
ejpam-1624	295	5	.	.	PROPN
ejpam-1624	295	6	hartwig	hartwig	PROPN
ejpam-1624	295	7	,	,	PUNCT
ejpam-1624	295	8	j.	j.	PROPN
ejpam-1624	295	9	levine	levine	PROPN
ejpam-1624	295	10	.	.	PUNCT
ejpam-1624	296	1	applications	application	NOUN
ejpam-1624	296	2	of	of	ADP
ejpam-1624	296	3	the	the	DET
ejpam-1624	296	4	drazin	drazin	PROPN
ejpam-1624	296	5	inverse	inverse	NOUN
ejpam-1624	296	6	to	to	ADP
ejpam-1624	296	7	the	the	DET
ejpam-1624	296	8	hill	hill	NOUN
ejpam-1624	296	9	cryptographic	cryptographic	ADJ
ejpam-1624	296	10	system	system	NOUN
ejpam-1624	296	11	.	.	PUNCT
ejpam-1624	297	1	crytologia	crytologia	NOUN
ejpam-1624	297	2	,	,	PUNCT
ejpam-1624	297	3	5:67	5:67	NUM
ejpam-1624	297	4	-	-	PUNCT
ejpam-1624	297	5	77,1981	77,1981	NUM
ejpam-1624	297	6	.	.	PUNCT
ejpam-1624	298	1	[	[	X
ejpam-1624	298	2	8	8	NUM
ejpam-1624	298	3	]	]	X
ejpam-1624	298	4	r.e	r.e	PROPN
ejpam-1624	298	5	.	.	PROPN
ejpam-1624	298	6	hartwig	hartwig	PROPN
ejpam-1624	298	7	,	,	PUNCT
ejpam-1624	298	8	g.r	g.r	PROPN
ejpam-1624	298	9	.	.	PROPN
ejpam-1624	298	10	wang	wang	PROPN
ejpam-1624	298	11	,	,	PUNCT
ejpam-1624	298	12	y.	y.	PROPN
ejpam-1624	298	13	wei	wei	PROPN
ejpam-1624	298	14	.	.	PUNCT
ejpam-1624	299	1	some	some	DET
ejpam-1624	299	2	additive	additive	ADJ
ejpam-1624	299	3	results	result	NOUN
ejpam-1624	299	4	on	on	ADP
ejpam-1624	299	5	drazin	drazin	PROPN
ejpam-1624	299	6	inverse	inverse	NOUN
ejpam-1624	299	7	.	.	PUNCT
ejpam-1624	300	1	linear	linear	ADJ
ejpam-1624	300	2	algebra	algebra	NOUN
ejpam-1624	300	3	and	and	CCONJ
ejpam-1624	300	4	its	its	PRON
ejpam-1624	300	5	applications	application	NOUN
ejpam-1624	300	6	,	,	PUNCT
ejpam-1624	300	7	322:207	322:207	PROPN
ejpam-1624	300	8	-	-	SYM
ejpam-1624	300	9	217,2001	217,2001	NOUN
ejpam-1624	300	10	.	.	PUNCT
ejpam-1624	301	1	[	[	X
ejpam-1624	301	2	9	9	NUM
ejpam-1624	301	3	]	]	X
ejpam-1624	301	4	c.d	c.d	PROPN
ejpam-1624	301	5	.	.	PUNCT
ejpam-1624	301	6	meyer	meyer	PROPN
ejpam-1624	301	7	.	.	PUNCT
ejpam-1624	302	1	the	the	DET
ejpam-1624	302	2	condition	condition	NOUN
ejpam-1624	302	3	number	number	NOUN
ejpam-1624	302	4	of	of	ADP
ejpam-1624	302	5	a	a	DET
ejpam-1624	302	6	finite	finite	ADJ
ejpam-1624	302	7	markov	markov	NOUN
ejpam-1624	302	8	chains	chain	NOUN
ejpam-1624	302	9	and	and	CCONJ
ejpam-1624	302	10	perturbation	perturbation	NOUN
ejpam-1624	302	11	bounds	bound	NOUN
ejpam-1624	302	12	for	for	ADP
ejpam-1624	302	13	the	the	DET
ejpam-1624	302	14	limiting	limit	VERB
ejpam-1624	302	15	probabilities	probability	NOUN
ejpam-1624	302	16	.	.	PUNCT
ejpam-1624	303	1	sima	sima	PROPN
ejpam-1624	303	2	journal	journal	PROPN
ejpam-1624	303	3	on	on	ADP
ejpam-1624	303	4	algebraic	algebraic	ADJ
ejpam-1624	303	5	discrete	discrete	ADJ
ejpam-1624	303	6	methods	method	NOUN
ejpam-1624	303	7	,	,	PUNCT
ejpam-1624	303	8	1:273	1:273	NUM
ejpam-1624	303	9	-	-	SYM
ejpam-1624	303	10	283,1980	283,1980	NUM
ejpam-1624	303	11	.	.	PUNCT
ejpam-1624	304	1	[	[	X
ejpam-1624	304	2	10	10	NUM
ejpam-1624	304	3	]	]	X
ejpam-1624	304	4	b.	b.	PROPN
ejpam-1624	304	5	simeon	simeon	PROPN
ejpam-1624	304	6	,	,	PUNCT
ejpam-1624	304	7	c.	c.	PROPN
ejpam-1624	304	8	fuhrer	fuhrer	PROPN
ejpam-1624	304	9	,	,	PUNCT
ejpam-1624	304	10	p.	p.	NOUN
ejpam-1624	304	11	rentrop	rentrop	NOUN
ejpam-1624	304	12	.	.	PUNCT
ejpam-1624	305	1	the	the	DET
ejpam-1624	305	2	drazin	drazin	PROPN
ejpam-1624	305	3	inverse	inverse	NOUN
ejpam-1624	305	4	in	in	ADP
ejpam-1624	305	5	multibody	multibody	ADJ
ejpam-1624	305	6	system	system	NOUN
ejpam-1624	305	7	dynamics	dynamic	NOUN
ejpam-1624	305	8	.	.	PUNCT
ejpam-1624	306	1	numerische	numerische	PROPN
ejpam-1624	306	2	mathematik	mathematik	PROPN
ejpam-1624	306	3	,	,	PUNCT
ejpam-1624	306	4	64:521	64:521	NUM
ejpam-1624	306	5	-	-	SYM
ejpam-1624	306	6	536	536	NUM
ejpam-1624	306	7	,	,	PUNCT
ejpam-1624	306	8	1993	1993	NUM
ejpam-1624	306	9	.	.	PUNCT
ejpam-1624	307	1	[	[	X
ejpam-1624	307	2	11	11	NUM
ejpam-1624	307	3	]	]	X
ejpam-1624	307	4	xiaoji	xiaoji	PROPN
ejpam-1624	307	5	liu	liu	PROPN
ejpam-1624	307	6	,	,	PUNCT
ejpam-1624	307	7	lingling	lingling	PROPN
ejpam-1624	307	8	wu	wu	PROPN
ejpam-1624	307	9	,	,	PUNCT
ejpam-1624	307	10	yaoming	yaoming	PROPN
ejpam-1624	307	11	yu	yu	PROPN
ejpam-1624	307	12	.	.	PUNCT
ejpam-1624	308	1	the	the	DET
ejpam-1624	308	2	group	group	NOUN
ejpam-1624	308	3	inverse	inverse	NOUN
ejpam-1624	308	4	of	of	ADP
ejpam-1624	308	5	the	the	DET
ejpam-1624	308	6	combinations	combination	NOUN
ejpam-1624	308	7	of	of	ADP
ejpam-1624	308	8	two	two	NUM
ejpam-1624	308	9	idempotent	idempotent	ADJ
ejpam-1624	308	10	matrices	matrix	NOUN
ejpam-1624	308	11	.	.	PUNCT
ejpam-1624	309	1	linear	linear	ADJ
ejpam-1624	309	2	and	and	CCONJ
ejpam-1624	309	3	multilinear	multilinear	PROPN
ejpam-1624	309	4	algebra	algebra	NOUN
ejpam-1624	309	5	,	,	PUNCT
ejpam-1624	309	6	59(1):101	59(1):101	NUM
ejpam-1624	309	7	-	-	PUNCT
ejpam-1624	309	8	115	115	NUM
ejpam-1624	309	9	,	,	PUNCT
ejpam-1624	309	10	2011	2011	NUM
ejpam-1624	309	11	.	.	PUNCT
ejpam-1624	310	1	[	[	X
ejpam-1624	310	2	12	12	NUM
ejpam-1624	310	3	]	]	PUNCT
ejpam-1624	310	4	t.	t.	PROPN
ejpam-1624	310	5	xie	xie	PROPN
ejpam-1624	310	6	,	,	PUNCT
ejpam-1624	310	7	k.	k.	PROPN
ejpam-1624	310	8	zuo	zuo	PROPN
ejpam-1624	310	9	.	.	PUNCT
ejpam-1624	311	1	fredholmness	fredholmness	PROPN
ejpam-1624	311	2	of	of	ADP
ejpam-1624	311	3	combinations	combination	NOUN
ejpam-1624	311	4	of	of	ADP
ejpam-1624	311	5	two	two	NUM
ejpam-1624	311	6	idempotents	idempotent	NOUN
ejpam-1624	311	7	.	.	PUNCT
ejpam-1624	312	1	european	european	ADJ
ejpam-1624	312	2	journal	journal	PROPN
ejpam-1624	312	3	of	of	ADP
ejpam-1624	312	4	pure	pure	ADJ
ejpam-1624	312	5	and	and	CCONJ
ejpam-1624	312	6	applied	applied	ADJ
ejpam-1624	312	7	mathematics	mathematic	NOUN
ejpam-1624	312	8	,	,	PUNCT
ejpam-1624	312	9	3(4):678	3(4):678	NUM
ejpam-1624	312	10	-	-	SYM
ejpam-1624	312	11	685	685	NUM
ejpam-1624	312	12	,	,	PUNCT
ejpam-1624	312	13	2010	2010	NUM
ejpam-1624	312	14	.	.	PUNCT
ejpam-1624	313	1	[	[	X
ejpam-1624	313	2	13	13	NUM
ejpam-1624	313	3	]	]	X
ejpam-1624	313	4	g.	g.	PROPN
ejpam-1624	313	5	wang	wang	PROPN
ejpam-1624	313	6	,	,	PUNCT
ejpam-1624	313	7	y.	y.	PROPN
ejpam-1624	313	8	wei	wei	PROPN
ejpam-1624	313	9	,	,	PUNCT
ejpam-1624	313	10	s.	s.	PROPN
ejpam-1624	313	11	qiao	qiao	PROPN
ejpam-1624	313	12	.	.	PUNCT
ejpam-1624	314	1	generalized	generalized	ADJ
ejpam-1624	314	2	inverse	inverse	NOUN
ejpam-1624	314	3	:	:	PUNCT
ejpam-1624	314	4	theory	theory	NOUN
ejpam-1624	314	5	and	and	CCONJ
ejpam-1624	314	6	computations	computation	NOUN
ejpam-1624	314	7	.	.	PUNCT
ejpam-1624	315	1	graduate	graduate	NOUN
ejpam-1624	315	2	series	series	NOUN
ejpam-1624	315	3	in	in	ADP
ejpam-1624	315	4	mathematics	mathematics	PROPN
ejpam-1624	315	5	,	,	PUNCT
ejpam-1624	315	6	beijing	beijing	PROPN
ejpam-1624	315	7	:	:	PUNCT
ejpam-1624	315	8	science	science	NOUN
ejpam-1624	315	9	press	press	PROPN
ejpam-1624	315	10	,	,	PUNCT
ejpam-1624	315	11	2004	2004	NUM
ejpam-1624	315	12	.	.	PUNCT
ejpam-1624	316	1	[	[	X
ejpam-1624	316	2	14	14	NUM
ejpam-1624	316	3	]	]	X
ejpam-1624	316	4	shifang	shifang	PROPN
ejpam-1624	316	5	zhang	zhang	PROPN
ejpam-1624	316	6	,	,	PUNCT
ejpam-1624	316	7	junde	junde	PROPN
ejpam-1624	316	8	wu	wu	PROPN
ejpam-1624	316	9	.	.	PUNCT
ejpam-1624	317	1	the	the	DET
ejpam-1624	317	2	drazin	drazin	PROPN
ejpam-1624	317	3	inverse	inverse	NOUN
ejpam-1624	317	4	of	of	ADP
ejpam-1624	317	5	the	the	DET
ejpam-1624	317	6	linear	linear	ADJ
ejpam-1624	317	7	combinations	combination	NOUN
ejpam-1624	317	8	of	of	ADP
ejpam-1624	317	9	two	two	NUM
ejpam-1624	317	10	idempotents	idempotent	NOUN
ejpam-1624	317	11	in	in	ADP
ejpam-1624	317	12	the	the	DET
ejpam-1624	317	13	banach	banach	NOUN
ejpam-1624	317	14	algebras	algebra	VERB
ejpam-1624	317	15	.	.	PUNCT
ejpam-1624	318	1	linear	linear	PROPN
ejpam-1624	318	2	algebra	algebra	PROPN
ejpam-1624	318	3	and	and	CCONJ
ejpam-1624	318	4	its	its	PRON
ejpam-1624	318	5	applications	application	NOUN
ejpam-1624	318	6	,	,	PUNCT
ejpam-1624	318	7	436:3132	436:3132	PROPN
ejpam-1624	318	8	-	-	NOUN
ejpam-1624	318	9	3138	3138	NUM
ejpam-1624	318	10	,	,	PUNCT
ejpam-1624	318	11	2012	2012	NUM
ejpam-1624	318	12	..	..	PUNCT
ejpam-1624	319	1	[	[	X
ejpam-1624	319	2	15	15	X
ejpam-1624	319	3	]	]	X
ejpam-1624	319	4	kezheng	kezheng	PROPN
ejpam-1624	319	5	zuo	zuo	PROPN
ejpam-1624	319	6	.	.	PROPN
ejpam-1624	319	7	nonsingularity	nonsingularity	NOUN
ejpam-1624	319	8	of	of	ADP
ejpam-1624	319	9	the	the	DET
ejpam-1624	319	10	difference	difference	NOUN
ejpam-1624	319	11	and	and	CCONJ
ejpam-1624	319	12	the	the	DET
ejpam-1624	319	13	sum	sum	NOUN
ejpam-1624	319	14	of	of	ADP
ejpam-1624	319	15	two	two	NUM
ejpam-1624	319	16	idempotents	idempotent	NOUN
ejpam-1624	319	17	matrices	matrix	NOUN
ejpam-1624	319	18	,	,	PUNCT
ejpam-1624	319	19	linear	linear	ADJ
ejpam-1624	319	20	algebra	algebra	NOUN
ejpam-1624	319	21	and	and	CCONJ
ejpam-1624	319	22	its	its	PRON
ejpam-1624	319	23	applications	application	NOUN
ejpam-1624	319	24	,	,	PUNCT
ejpam-1624	319	25	433:476	433:476	NOUN
ejpam-1624	319	26	-	-	PUNCT
ejpam-1624	319	27	482	482	NUM
ejpam-1624	319	28	,	,	PUNCT
ejpam-1624	319	29	2010	2010	NUM
ejpam-1624	319	30	.	.	PUNCT