id	sid	eid	entity	type
easat-9645	1	1	2576-8484	DATE
easat-9645	2	1	9	CARDINAL
easat-9645	2	2	8	CARDINAL
easat-9645	2	3	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	3	1	2025	CARDINAL
easat-9645	3	2	2025	CARDINAL
easat-9645	3	3	20 june 2025	DATE
easat-9645	3	4	8 august 2025	DATE
easat-9645	3	5	12	CARDINAL
easat-9645	4	1	25	CARDINAL
easat-9645	4	2	mannan.iu31@uttarauniversity.edu.bd hilbert	PERSON
easat-9645	6	1	abdul mannan1*	PERSON
easat-9645	6	2	mohammad alauddin2	PERSON
easat-9645	6	3	md nazmul hasan3	GPE
easat-9645	6	4	md.	GPE
easat-9645	6	5	hossain5	PERSON
easat-9645	6	6	md	GPE
easat-9645	6	7	shafikul islam6	PERSON
easat-9645	6	8	md.	GPE
easat-9645	7	1	alam chowdhury7	PERSON
easat-9645	7	2	akter8	DATE
easat-9645	7	3	sahib jada	PERSON
easat-9645	7	4	khan9 1department	PERSON
easat-9645	7	5	uttara university	ORG
easat-9645	7	6	dhaka	GPE
easat-9645	7	7	bangladesh	GPE
easat-9645	7	8	mannan.iu31@uttarauniversity.edu.bd (m.a.m.	PERSON
easat-9645	8	1	uttara university	ORG
easat-9645	8	2	dhaka	GPE
easat-9645	8	3	bangladesh	GPE
easat-9645	8	4	m.a.	ORG
easat-9645	11	1	m.s.a.c	GPE
easat-9645	12	1	3pompea	CARDINAL
easat-9645	12	2	university of new haven	ORG
easat-9645	12	3	west haven	GPE
easat-9645	12	4	ct, usa:	ORG
easat-9645	13	1	4pompea	CARDINAL
easat-9645	13	2	university of new haven	ORG
easat-9645	13	3	west haven	GPE
easat-9645	13	4	ct, usa: pghos1@unh.newhaven.edu	ORG
easat-9645	13	5	p.g.	GPE
easat-9645	14	1	5department	CARDINAL
easat-9645	14	2	uttara university	ORG
easat-9645	14	3	dhaka	GPE
easat-9645	16	1	titumir college	ORG
easat-9645	16	2	dhaka	GPE
easat-9645	16	3	b.a.	GPE
easat-9645	17	1	9biman	ORDINAL
easat-9645	17	2	bangladesh airlines	ORG
easat-9645	17	3	kurmitola	GPE
easat-9645	17	4	dhaka	GPE
easat-9645	18	1	hilbert spaces	ORG
easat-9645	20	1	hilbert spaces	ORG
easat-9645	20	2	normed	ORG
easat-9645	24	1	hilbert spaces	ORG
easat-9645	24	2	normed spaces	ORG
easat-9645	25	1	1	CARDINAL
easat-9645	25	2	hilbert spaces	ORG
easat-9645	27	1	hilbert spaces	ORG
easat-9645	27	2	1	CARDINAL
easat-9645	27	3	2	CARDINAL
easat-9645	32	1	1499	CARDINAL
easat-9645	32	2	2576-8484	DATE
easat-9645	33	1	9	CARDINAL
easat-9645	33	2	8	CARDINAL
easat-9645	33	3	1498-1523	CARDINAL
easat-9645	33	4	2025	CARDINAL
easat-9645	33	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	33	6	2025	CARDINAL
easat-9645	33	7	1.1	CARDINAL
easat-9645	34	1	hilbert spaces	ORG
easat-9645	37	1	hilbert spaces	ORG
easat-9645	37	2	normed spaces	ORG
easat-9645	38	1	kernel hilbert spaces	ORG
easat-9645	39	1	3	CARDINAL
easat-9645	39	2	4	CARDINAL
easat-9645	40	1	schmidt	PERSON
easat-9645	40	2	5	CARDINAL
easat-9645	41	1	6	CARDINAL
easat-9645	41	2	8	CARDINAL
easat-9645	43	1	hilbert spaces	ORG
easat-9645	43	2	9	CARDINAL
easat-9645	44	1	10	CARDINAL
easat-9645	46	1	hilbert spaces	ORG
easat-9645	46	2	11	CARDINAL
easat-9645	47	1	8	CARDINAL
easat-9645	47	2	14	CARDINAL
easat-9645	48	1	hilbert spaces	ORG
easat-9645	50	1	15	CARDINAL
easat-9645	50	2	16	CARDINAL
easat-9645	51	1	1.2	CARDINAL
easat-9645	51	2	normed	ORG
easat-9645	52	1	normed	ORG
easat-9645	55	1	normed	ORG
easat-9645	56	1	∈	ORG
easat-9645	56	2	∈ 𝐾. i. ‖𝑥‖	ORG
easat-9645	59	1	‖𝑥‖	ORG
easat-9645	59	2	𝑑(𝑥	PERSON
easat-9645	61	1	normed	ORG
easat-9645	64	1	∈	ORG
easat-9645	64	2	∈	ORG
easat-9645	64	3	1500	CARDINAL
easat-9645	64	4	2576-8484	DATE
easat-9645	65	1	9	CARDINAL
easat-9645	65	2	8	CARDINAL
easat-9645	65	3	1498-1523	CARDINAL
easat-9645	65	4	2025	CARDINAL
easat-9645	65	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	65	6	2025	CARDINAL
easat-9645	66	1	i. 〈𝑥	PERSON
easat-9645	66	2	0 ii	WORK_OF_ART
easat-9645	67	1	𝑦〉̅̅ ̅̅	ORG
easat-9645	68	1	𝛼〈𝑥	TIME
easat-9645	69	1	∈	ORG
easat-9645	72	1	𝑙(𝑝	ORG
easat-9645	72	2	s.t	PERSON
easat-9645	74	1	𝑙(𝑝	ORG
easat-9645	74	2	𝑙(𝑝	ORG
easat-9645	76	1	𝑑(𝑥	PERSON
easat-9645	76	2	1	CARDINAL
easat-9645	76	3	s.t. 1	PERSON
easat-9645	79	1	𝑑(𝑥	PERSON
easat-9645	79	2	1	CARDINAL
easat-9645	79	3	s.t	PERSON
easat-9645	81	1	𝑙(𝑝	ORG
easat-9645	83	1	𝑑(𝑥	PERSON
easat-9645	85	1	s.t. 1	PERSON
easat-9645	88	1	𝑑(𝑥	PERSON
easat-9645	90	1	s.t	PERSON
easat-9645	92	1	𝑙(𝑝	ORG
easat-9645	94	1	𝑑(𝑥	PERSON
easat-9645	96	1	s.t. 1	PERSON
easat-9645	99	1	𝑑(𝑥	PERSON
easat-9645	99	2	s.t	PERSON
easat-9645	101	1	𝑙(𝑝	ORG
easat-9645	103	1	𝑑(𝑥	PERSON
easat-9645	105	1	s.t. 1	PERSON
easat-9645	108	1	𝑑(𝑥	PERSON
easat-9645	108	2	1.3	CARDINAL
easat-9645	109	1	section 2	LAW
easat-9645	110	1	section 3	LAW
easat-9645	111	1	section 4 highlights	LAW
easat-9645	111	2	hilbert spaces	ORG
easat-9645	112	1	section 5	LAW
easat-9645	113	1	section 6 explores	LAW
easat-9645	113	2	section 7	LAW
easat-9645	114	1	section 8	LAW
easat-9645	115	1	section 9	LAW
easat-9645	116	1	section 10	LAW
easat-9645	117	1	2	CARDINAL
easat-9645	117	2	four	CARDINAL
easat-9645	119	1	normed vector spaces	ORG
easat-9645	124	1	1501	CARDINAL
easat-9645	124	2	2576-8484	DATE
easat-9645	125	1	9	CARDINAL
easat-9645	125	2	8	CARDINAL
easat-9645	125	3	1498-1523	CARDINAL
easat-9645	125	4	2025	CARDINAL
easat-9645	125	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	125	6	2025	CARDINAL
easat-9645	126	1	hilbert	PERSON
easat-9645	126	2	normed vector	ORG
easat-9645	127	1	2.1	CARDINAL
easat-9645	127	2	theorem	PERSON
easat-9645	127	3	two	CARDINAL
easat-9645	127	4	2‖𝑥‖2 + 2‖𝑦‖2	DATE
easat-9645	127	5	1	CARDINAL
easat-9645	128	1	1	CARDINAL
easat-9645	128	2	2d	DATE
easat-9645	129	1	two	CARDINAL
easat-9645	131	1	2‖𝑥‖2	CARDINAL
easat-9645	131	2	+ 2‖𝑦‖2,confirming	DATE
easat-9645	132	1	2.2	CARDINAL
easat-9645	132	2	2 2.2.1	CARDINAL
easat-9645	133	1	𝑝 ≠ 2	ORG
easat-9645	133	2	2	CARDINAL
easat-9645	134	1	1502	CARDINAL
easat-9645	134	2	2576-8484	DATE
easat-9645	135	1	9	CARDINAL
easat-9645	135	2	8	CARDINAL
easat-9645	135	3	1498-1523	CARDINAL
easat-9645	135	4	2025	CARDINAL
easat-9645	135	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	135	6	2025	CARDINAL
easat-9645	135	7	i. hilbert	PERSON
easat-9645	135	8	i. e. 𝑙2	PERSON
easat-9645	135	9	2d	DATE
easat-9645	138	1	r2	GPE
easat-9645	138	2	≠ 2	PRODUCT
easat-9645	139	1	one	CARDINAL
easat-9645	140	1	𝑝 ≠ 2	PERSON
easat-9645	141	1	𝑝 ≠ 2	FAC
easat-9645	142	1	1,1,0,0	CARDINAL
easat-9645	144	1	1, −1,0,0	DATE
easat-9645	145	1	∈	ORG
easat-9645	146	1	2,0,0	CARDINAL
easat-9645	148	1	0,2,0,0	CARDINAL
easat-9645	149	1	‖𝑥‖	ORG
easat-9645	152	1	1	CARDINAL
easat-9645	152	2	2	CARDINAL
easat-9645	152	3	‖𝑦‖	ORG
easat-9645	155	1	1	CARDINAL
easat-9645	155	2	2	CARDINAL
easat-9645	157	1	1	CARDINAL
easat-9645	157	2	2	CARDINAL
easat-9645	158	1	1	CARDINAL
easat-9645	159	1	22 + 22	CARDINAL
easat-9645	159	2	8	CARDINAL
easat-9645	159	3	2‖𝑥‖2 + 2‖𝑦‖2	DATE
easat-9645	159	4	2	CARDINAL
easat-9645	159	5	2 2	DATE
easat-9645	159	6	2‖𝑥‖2 + 2‖𝑦‖2	DATE
easat-9645	159	7	2(2	CARDINAL
easat-9645	159	8	+ 2	CARDINAL
easat-9645	159	9	8	CARDINAL
easat-9645	159	10	2‖𝑥‖2 + 2‖𝑦‖2	DATE
easat-9645	161	1	𝑝 ≠ 2	PERSON
easat-9645	162	1	𝑝 ≠ 2	PERSON
easat-9645	162	2	2d	DATE
easat-9645	164	1	4	CARDINAL
easat-9645	165	1	2	CARDINAL
easat-9645	165	2	𝐷(𝑝	ORG
easat-9645	165	3	4	CARDINAL
easat-9645	165	4	𝐷(𝑝	ORG
easat-9645	165	5	≠ 4.	PERSON
easat-9645	165	6	2576-8484	DATE
easat-9645	166	1	9	CARDINAL
easat-9645	166	2	8	CARDINAL
easat-9645	166	3	1498-1523	CARDINAL
easat-9645	166	4	2025	CARDINAL
easat-9645	166	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	166	6	2025	CARDINAL
easat-9645	166	7	2	CARDINAL
easat-9645	167	1	2	CARDINAL
easat-9645	167	2	2	CARDINAL
easat-9645	167	3	2	CARDINAL
easat-9645	167	4	2	CARDINAL
easat-9645	168	1	2.3	CARDINAL
easat-9645	168	2	schwartz	GPE
easat-9645	168	3	∈	ORG
easat-9645	169	1	two	CARDINAL
easat-9645	173	1	one	CARDINAL
easat-9645	174	1	two	CARDINAL
easat-9645	174	2	1	CARDINAL
easat-9645	175	1	2.3.2	CARDINAL
easat-9645	175	2	two	CARDINAL
easat-9645	176	1	1504	CARDINAL
easat-9645	176	2	2576-8484	DATE
easat-9645	177	1	9	CARDINAL
easat-9645	177	2	8	CARDINAL
easat-9645	177	3	1498-1523	CARDINAL
easat-9645	177	4	2025	CARDINAL
easat-9645	177	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	177	6	2025	CARDINAL
easat-9645	177	7	hilbert spaces	ORG
easat-9645	178	1	two	CARDINAL
easat-9645	179	1	3	CARDINAL
easat-9645	180	1	3	CARDINAL
easat-9645	180	2	2d	DATE
easat-9645	181	1	approximately (2.5	CARDINAL
easat-9645	181	2	2	CARDINAL
easat-9645	181	3	2	CARDINAL
easat-9645	183	1	≈ 8.00	CARDINAL
easat-9645	183	2	8.94	CARDINAL
easat-9645	191	1	i. geometry	PERSON
easat-9645	191	2	hilbert spaces	ORG
easat-9645	191	3	i. e. l2[a	PERSON
easat-9645	191	4	+ ‖𝑦‖2	GPE
easat-9645	192	1	1505	CARDINAL
easat-9645	192	2	2576-8484	DATE
easat-9645	193	1	9	CARDINAL
easat-9645	193	2	8	CARDINAL
easat-9645	193	3	1498-1523	CARDINAL
easat-9645	193	4	2025	CARDINAL
easat-9645	193	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	193	6	2025	CARDINAL
easat-9645	196	1	2d	DATE
easat-9645	196	2	normed	ORG
easat-9645	196	3	1	CARDINAL
easat-9645	197	1	2	CARDINAL
easat-9645	197	2	2	CARDINAL
easat-9645	203	1	4	CARDINAL
easat-9645	205	1	4	CARDINAL
easat-9645	206	1	𝑎𝑟𝑒	ORG
easat-9645	207	1	𝑥1(𝑏𝑙𝑢𝑒	ORG
easat-9645	207	2	𝑥10(𝑦𝑒𝑙𝑙𝑜𝑤	PRODUCT
easat-9645	207	3	𝑥50(𝑜𝑟𝑎𝑛𝑔𝑒	ORG
easat-9645	207	4	0	CARDINAL
easat-9645	207	5	0,1	CARDINAL
easat-9645	207	6	1	CARDINAL
easat-9645	207	7	1506	CARDINAL
easat-9645	207	8	2576-8484	DATE
easat-9645	208	1	9	CARDINAL
easat-9645	208	2	8	CARDINAL
easat-9645	208	3	1498-1523	CARDINAL
easat-9645	208	4	2025	CARDINAL
easat-9645	208	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	208	6	2025	CARDINAL
easat-9645	208	7	3	CARDINAL
easat-9645	208	8	hilbert	PERSON
easat-9645	209	1	kernel pca	ORG
easat-9645	209	2	kernel hilbert spaces	ORG
easat-9645	211	1	3	CARDINAL
easat-9645	211	2	1	CARDINAL
easat-9645	211	3	ℝ𝑛	PRODUCT
easat-9645	212	1	+ 𝑎2𝑏2 +	DATE
easat-9645	213	1	1	CARDINAL
easat-9645	214	1	𝑏1	NORP
easat-9645	214	2	𝑏2	GPE
easat-9645	216	1	1	CARDINAL
easat-9645	217	1	1 2	CARDINAL
easat-9645	217	2	2+	DATE
easat-9645	218	1	2⟩ 1 2	DATE
easat-9645	221	1	− 𝑏	PERSON
easat-9645	221	2	1 2	CARDINAL
easat-9645	221	3	− 𝑏1)2	PERSON
easat-9645	223	1	firstly	ORDINAL
easat-9645	223	2	ℝ𝑛	PRODUCT
easat-9645	224	1	ℝ𝑛 is 𝑑(𝑎	WORK_OF_ART
easat-9645	224	2	∑	PERSON
easat-9645	224	3	1 2	CARDINAL
easat-9645	225	1	𝑏2	GPE
easat-9645	225	2	∈	ORG
easat-9645	225	3	∈ ℕ s.t	ORG
easat-9645	225	4	𝑑(𝑎𝑚	NORP
easat-9645	226	1	∑	PERSON
easat-9645	226	2	2 𝑛	MONEY
easat-9645	226	3	1 2	CARDINAL
easat-9645	226	4	∈ ℕ	ORG
easat-9645	226	5	2	CARDINAL
easat-9645	227	1	2	CARDINAL
easat-9645	227	2	𝜖2	GPE
easat-9645	227	3	1,2,3	CARDINAL
easat-9645	228	1	1 ≤	MONEY
easat-9645	231	1	𝑑(𝑎𝑚	NORP
easat-9645	231	2	𝑚→∞	PRODUCT
easat-9645	231	3	ℝ𝑛	PRODUCT
easat-9645	232	1	1	CARDINAL
easat-9645	234	1	𝑏1	NORP
easat-9645	234	2	𝑏2	GPE
easat-9645	235	1	0	CARDINAL
easat-9645	235	2	two	CARDINAL
easat-9645	235	3	zero	CARDINAL
easat-9645	236	1	ℝ𝑛	PRODUCT
easat-9645	237	1	1507	CARDINAL
easat-9645	237	2	2576-8484	DATE
easat-9645	238	1	9	CARDINAL
easat-9645	238	2	8	CARDINAL
easat-9645	238	3	1498-1523	CARDINAL
easat-9645	238	4	2025	CARDINAL
easat-9645	238	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	238	6	2025	CARDINAL
easat-9645	238	7	5	CARDINAL
easat-9645	238	8	r2	GPE
easat-9645	239	1	5	CARDINAL
easat-9645	239	2	45∘.	CARDINAL
easat-9645	239	3	0	CARDINAL
easat-9645	239	4	0	DATE
easat-9645	239	5	approximately (3	CARDINAL
easat-9645	239	6	2	CARDINAL
easat-9645	239	7	2	CARDINAL
easat-9645	239	8	1.5	CARDINAL
easat-9645	239	9	1.5	CARDINAL
easat-9645	240	1	r2	GPE
easat-9645	240	2	1,0	CARDINAL
easat-9645	241	1	1	CARDINAL
easat-9645	241	2	0	CARDINAL
easat-9645	242	1	1	CARDINAL
easat-9645	242	2	0	CARDINAL
easat-9645	243	1	𝑅2	CARDINAL
easat-9645	243	2	1	CARDINAL
easat-9645	243	3	1	CARDINAL
easat-9645	244	1	2 +	DATE
easat-9645	244	2	2	CARDINAL
easat-9645	244	3	0	CARDINAL
easat-9645	245	1	1,0	CARDINAL
easat-9645	245	2	𝑅2	CARDINAL
easat-9645	246	1	3.2	CARDINAL
easat-9645	248	1	3	CARDINAL
easat-9645	250	1	𝑏1	NORP
easat-9645	250	2	𝑏2	GPE
easat-9645	252	1	3	CARDINAL
easat-9645	252	2	‖𝑎‖	PERSON
easat-9645	253	1	1 2	CARDINAL
easat-9645	254	1	1 2	CARDINAL
easat-9645	254	2	|𝑎|1 2 + |𝑎2|2+	ORG
easat-9645	255	1	1 2	CARDINAL
easat-9645	255	2	𝑑(𝑎	PERSON
easat-9645	258	1	− 𝑏	PERSON
easat-9645	258	2	1 2	CARDINAL
easat-9645	259	1	1 2	CARDINAL
easat-9645	259	2	2576-8484	DATE
easat-9645	260	1	9	CARDINAL
easat-9645	260	2	8	CARDINAL
easat-9645	260	3	1498-1523	CARDINAL
easat-9645	260	4	2025	CARDINAL
easat-9645	260	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	260	6	2025	CARDINAL
easat-9645	260	7	firstly	ORDINAL
easat-9645	261	1	1 2	CARDINAL
easat-9645	262	1	𝑏2	GPE
easat-9645	262	2	∈	ORG
easat-9645	262	3	s. t. 𝑑(𝑎𝑚	PERSON
easat-9645	263	1	∑	PERSON
easat-9645	263	2	2 𝑛	MONEY
easat-9645	263	3	1 2	CARDINAL
easat-9645	263	4	∈ ℕ	ORG
easat-9645	263	5	4	CARDINAL
easat-9645	264	1	2	CARDINAL
easat-9645	264	2	𝜖2	GPE
easat-9645	264	3	1,2,3	CARDINAL
easat-9645	264	4	1 ≤	MONEY
easat-9645	264	5	1	CARDINAL
easat-9645	264	6	2	CARDINAL
easat-9645	267	1	𝑑(𝑎𝑚	NORP
easat-9645	267	2	𝑚→∞	PRODUCT
easat-9645	267	3	3	CARDINAL
easat-9645	268	1	𝑏1	NORP
easat-9645	268	2	𝑏2	GPE
easat-9645	269	1	0	CARDINAL
easat-9645	270	1	two	CARDINAL
easat-9645	270	2	zero	CARDINAL
easat-9645	272	1	6	CARDINAL
easat-9645	273	1	2576-8484	DATE
easat-9645	274	1	9	CARDINAL
easat-9645	274	2	8	CARDINAL
easat-9645	274	3	1498-1523	CARDINAL
easat-9645	274	4	2025	CARDINAL
easat-9645	274	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	274	6	2025	CARDINAL
easat-9645	274	7	6	CARDINAL
easat-9645	274	8	68.180	CARDINAL
easat-9645	275	1	re(z	NORP
easat-9645	275	2	2d	DATE
easat-9645	276	1	𝐶2	GPE
easat-9645	276	2	1	CARDINAL
easat-9645	277	1	1 ·	CARDINAL
easat-9645	277	2	1	CARDINAL
easat-9645	277	3	0	CARDINAL
easat-9645	278	1	1	CARDINAL
easat-9645	279	1	3.3	CARDINAL
easat-9645	281	1	5	CARDINAL
easat-9645	283	1	𝑏1	NORP
easat-9645	283	2	𝑏2	GPE
easat-9645	285	1	3	CARDINAL
easat-9645	285	2	‖𝑎‖	PERSON
easat-9645	286	1	1 2	CARDINAL
easat-9645	287	1	1 2	CARDINAL
easat-9645	287	2	|𝑎|1 2 + |𝑎2|2+	ORG
easat-9645	288	1	1 2	CARDINAL
easat-9645	288	2	𝑑(𝑎	PERSON
easat-9645	291	1	− 𝑏	PERSON
easat-9645	291	2	1 2	CARDINAL
easat-9645	292	1	1 2	CARDINAL
easat-9645	292	2	firstly	ORDINAL
easat-9645	293	1	1 2	CARDINAL
easat-9645	294	1	𝑏2	GPE
easat-9645	295	1	∈	ORG
easat-9645	295	2	s. t. 𝑑(𝑎𝑚	PERSON
easat-9645	295	3	∑	PERSON
easat-9645	296	1	2 𝑛	MONEY
easat-9645	296	2	1 2	CARDINAL
easat-9645	296	3	∈ ℕ	ORG
easat-9645	296	4	6	CARDINAL
easat-9645	296	5	2	CARDINAL
easat-9645	296	6	𝜖2	GPE
easat-9645	296	7	1,2,3	CARDINAL
easat-9645	296	8	1 ≤	MONEY
easat-9645	296	9	1	CARDINAL
easat-9645	296	10	2	CARDINAL
easat-9645	298	1	∈	ORG
easat-9645	298	2	𝑑(𝑎𝑚	NORP
easat-9645	298	3	𝑚→∞	PRODUCT
easat-9645	298	4	3	CARDINAL
easat-9645	300	1	𝑏1	NORP
easat-9645	300	2	𝑏2	GPE
easat-9645	301	1	0	CARDINAL
easat-9645	302	1	two	CARDINAL
easat-9645	302	2	zero	CARDINAL
easat-9645	304	1	1510	CARDINAL
easat-9645	304	2	2576-8484	DATE
easat-9645	305	1	9	CARDINAL
easat-9645	305	2	8	CARDINAL
easat-9645	305	3	1498-1523	CARDINAL
easat-9645	305	4	2025	CARDINAL
easat-9645	305	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	305	6	2025	CARDINAL
easat-9645	305	7	7	CARDINAL
easat-9645	305	8	7	CARDINAL
easat-9645	305	9	2d	DATE
easat-9645	305	10	3d subspaces	QUANTITY
easat-9645	308	1	three	CARDINAL
easat-9645	308	2	r3	ORG
easat-9645	309	1	1	CARDINAL
easat-9645	309	2	0	DATE
easat-9645	309	3	0	DATE
easat-9645	310	1	0	CARDINAL
easat-9645	310	2	1	DATE
easat-9645	310	3	0	DATE
easat-9645	311	1	1	CARDINAL
easat-9645	312	1	1	CARDINAL
easat-9645	313	1	0	CARDINAL
easat-9645	313	2	1	CARDINAL
easat-9645	313	3	1	CARDINAL
easat-9645	315	1	1	CARDINAL
easat-9645	315	2	0	DATE
easat-9645	316	1	1 𝑘𝑛	QUANTITY
easat-9645	316	2	1	CARDINAL
easat-9645	316	3	𝑚𝑛|	ORG
easat-9645	316	4	2	CARDINAL
easat-9645	317	1	1	CARDINAL
easat-9645	317	2	0	CARDINAL
easat-9645	318	1	0	CARDINAL
easat-9645	318	2	0	DATE
easat-9645	319	1	∈	ORG
easat-9645	319	2	3.4	CARDINAL
easat-9645	322	1	𝐵 × 𝐵	ORG
easat-9645	322	2	4⟨𝑝	CARDINAL
easat-9645	327	1	1511	CARDINAL
easat-9645	327	2	2576-8484	DATE
easat-9645	328	1	9	CARDINAL
easat-9645	328	2	8	CARDINAL
easat-9645	328	3	1498-1523	CARDINAL
easat-9645	328	4	2025	CARDINAL
easat-9645	328	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	328	6	2025	CARDINAL
easat-9645	328	7	3.4.1	CARDINAL
easat-9645	329	1	4⟨𝑝	CARDINAL
easat-9645	332	1	2𝑝	CARDINAL
easat-9645	332	2	∥2− 0	EVENT
easat-9645	333	1	∥ 𝑝(1 − 𝑖	ORG
easat-9645	334	1	4 ∥ 𝑝 ∥2+	DATE
easat-9645	334	2	4 ∥ 𝑝 ∥2+ 2𝑖	DATE
easat-9645	336	1	=∥ 𝑝 ∥2≥ 0	PERSON
easat-9645	336	2	0	CARDINAL
easat-9645	336	3	0	CARDINAL
easat-9645	337	1	3.4.2	CARDINAL
easat-9645	337	2	4〈𝑝	CARDINAL
easat-9645	340	1	4〈𝑝	CARDINAL
easat-9645	340	2	4⟨𝑝	CARDINAL
easat-9645	341	1	3.4.3	CARDINAL
easat-9645	342	1	first	ORDINAL
easat-9645	342	2	∈	ORG
easat-9645	342	3	𝑟⟩.	CARDINAL
easat-9645	342	4	s.t. ∥ 𝑝	PERSON
easat-9645	345	1	3.4.4	CARDINAL
easat-9645	346	1	first	ORDINAL
easat-9645	346	2	∈ 𝐶	ORG
easat-9645	349	1	𝑆𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑒 − 𝑝 𝑖𝑛 𝑡ℎ𝑒	ORG
easat-9645	349	2	−⟨𝑝	PRODUCT
easat-9645	349	3	𝑊𝑟𝑖𝑡𝑒	PERSON
easat-9645	351	1	𝑖⟨𝑝	ORG
easat-9645	354	1	𝑎⟨𝑝	CARDINAL
easat-9645	359	1	𝐵	ORG
easat-9645	360	1	3.4.5	DATE
easat-9645	363	1	•	CARDINAL
easat-9645	364	1	1512	CARDINAL
easat-9645	364	2	2576-8484	DATE
easat-9645	365	1	9	CARDINAL
easat-9645	365	2	8	CARDINAL
easat-9645	365	3	1498-1523	CARDINAL
easat-9645	365	4	2025	CARDINAL
easat-9645	365	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	365	6	2025	CARDINAL
easat-9645	365	7	8	CARDINAL
easat-9645	367	1	8	CARDINAL
easat-9645	367	2	𝐶2showing	DATE
easat-9645	368	1	3d	CARDINAL
easat-9645	369	1	3.5	CARDINAL
easat-9645	369	2	ℝ𝑛	PRODUCT
easat-9645	370	1	two	CARDINAL
easat-9645	374	1	4	CARDINAL
easat-9645	374	2	4.1	CARDINAL
easat-9645	374	3	quantum	ORG
easat-9645	376	1	two	CARDINAL
easat-9645	376	2	1513	CARDINAL
easat-9645	376	3	2576-8484	DATE
easat-9645	377	1	9	CARDINAL
easat-9645	377	2	8	CARDINAL
easat-9645	377	3	1498-1523	CARDINAL
easat-9645	377	4	2025	CARDINAL
easat-9645	377	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	377	6	2025	CARDINAL
easat-9645	377	7	one	CARDINAL
easat-9645	379	1	4.2	CARDINAL
easat-9645	381	1	4.3	CARDINAL
easat-9645	381	2	kernel hilbert spaces	ORG
easat-9645	383	1	4.4	CARDINAL
easat-9645	384	1	hilbert spaces	ORG
easat-9645	386	1	5	CARDINAL
easat-9645	386	2	hilbert spaces	ORG
easat-9645	386	3	5.1	CARDINAL
easat-9645	387	1	kernel hilbert spaces	ORG
easat-9645	388	1	17	CARDINAL
easat-9645	388	2	18	CARDINAL
easat-9645	390	1	linear	ORG
easat-9645	392	1	k(x	PERSON
easat-9645	392	2	9	CARDINAL
easat-9645	393	1	1514	CARDINAL
easat-9645	393	2	2576-8484	DATE
easat-9645	394	1	9	CARDINAL
easat-9645	394	2	8	CARDINAL
easat-9645	394	3	1498-1523	CARDINAL
easat-9645	394	4	2025	CARDINAL
easat-9645	394	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	394	6	2025	CARDINAL
easat-9645	394	7	9	CARDINAL
easat-9645	395	1	3	CARDINAL
easat-9645	396	1	0.1	CARDINAL
easat-9645	396	2	1.0	CARDINAL
easat-9645	398	1	5.2	CARDINAL
easat-9645	404	1	10	CARDINAL
easat-9645	406	1	10	CARDINAL
easat-9645	407	1	two	CARDINAL
easat-9645	407	2	1	CARDINAL
easat-9645	409	1	5.3	CARDINAL
easat-9645	410	1	1515	CARDINAL
easat-9645	410	2	2576-8484	DATE
easat-9645	411	1	9	CARDINAL
easat-9645	411	2	8	CARDINAL
easat-9645	411	3	1498-1523	CARDINAL
easat-9645	411	4	2025	CARDINAL
easat-9645	411	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	411	6	2025	CARDINAL
easat-9645	413	1	first	ORDINAL
easat-9645	413	2	second	ORDINAL
easat-9645	414	1	11	CARDINAL
easat-9645	415	1	3d	CARDINAL
easat-9645	416	1	figure11	ORG
easat-9645	416	2	two	CARDINAL
easat-9645	417	1	75-100%	PERCENT
easat-9645	417	2	1 to 2.8	CARDINAL
easat-9645	419	1	3d	CARDINAL
easat-9645	420	1	1516	CARDINAL
easat-9645	420	2	2576-8484	DATE
easat-9645	421	1	9	CARDINAL
easat-9645	421	2	8	CARDINAL
easat-9645	421	3	1498-1523	CARDINAL
easat-9645	421	4	2025	CARDINAL
easat-9645	421	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	421	6	2025	CARDINAL
easat-9645	421	7	5.4	CARDINAL
easat-9645	422	1	𝐿2	CARDINAL
easat-9645	422	2	12	CARDINAL
easat-9645	423	1	𝐿2[0,2𝜋	NORP
easat-9645	424	1	12	CARDINAL
easat-9645	424	2	2𝜋]on	CARDINAL
easat-9645	424	3	three	CARDINAL
easat-9645	424	4	-1	ORG
easat-9645	424	5	1	CARDINAL
easat-9645	424	6	0	CARDINAL
easat-9645	425	1	sin(x	GPE
easat-9645	425	2	0	CARDINAL
easat-9645	425	3	-1	ORG
easat-9645	425	4	1	CARDINAL
easat-9645	425	5	6	CARDINAL
easat-9645	426	1	6.1	CARDINAL
easat-9645	426	2	quantum	ORG
easat-9645	429	1	6.2	CARDINAL
easat-9645	432	1	6.3	CARDINAL
easat-9645	433	1	3d	CARDINAL
easat-9645	435	1	1517	CARDINAL
easat-9645	435	2	2576-8484	DATE
easat-9645	436	1	9	CARDINAL
easat-9645	436	2	8	CARDINAL
easat-9645	436	3	1498-1523	CARDINAL
easat-9645	436	4	2025	CARDINAL
easat-9645	436	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	436	6	2025	CARDINAL
easat-9645	436	7	6.4	CARDINAL
easat-9645	437	1	pca	ORG
easat-9645	439	1	6.5	CARDINAL
easat-9645	440	1	ritz	ORG
easat-9645	442	1	6.6	CARDINAL
easat-9645	444	1	13	CARDINAL
easat-9645	446	1	13	CARDINAL
easat-9645	447	1	1	CARDINAL
easat-9645	448	1	7	CARDINAL
easat-9645	450	1	1518	CARDINAL
easat-9645	450	2	2576-8484	DATE
easat-9645	451	1	9	CARDINAL
easat-9645	451	2	8	CARDINAL
easat-9645	451	3	1498-1523	CARDINAL
easat-9645	451	4	2025	CARDINAL
easat-9645	451	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	451	6	2025	CARDINAL
easat-9645	451	7	7	CARDINAL
easat-9645	451	8	1	CARDINAL
easat-9645	455	1	7.2	CARDINAL
easat-9645	457	1	pca	ORG
easat-9645	458	1	7.3	CARDINAL
easat-9645	461	1	7.4	CARDINAL
easat-9645	464	1	19	CARDINAL
easat-9645	464	2	20	CARDINAL
easat-9645	465	1	8	CARDINAL
easat-9645	465	2	8.1	CARDINAL
easat-9645	468	1	pca & data	ORG
easat-9645	468	2	8.2	CARDINAL
easat-9645	469	1	hilbert spaces	ORG
easat-9645	470	1	hilbert spaces	ORG
easat-9645	470	2	linear	ORG
easat-9645	471	1	1519	CARDINAL
easat-9645	471	2	2576-8484	DATE
easat-9645	472	1	9	CARDINAL
easat-9645	472	2	8	CARDINAL
easat-9645	472	3	1498-1523	CARDINAL
easat-9645	472	4	2025	CARDINAL
easat-9645	472	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	472	6	2025	CARDINAL
easat-9645	472	7	1	CARDINAL
easat-9645	473	1	pca	GPE
easat-9645	473	2	rkhs	ORG
easat-9645	473	3	pca	GPE
easat-9645	474	1	14	CARDINAL
easat-9645	475	1	rkhs	PERSON
easat-9645	477	1	14	DATE
easat-9645	477	2	hilbert	PERSON
easat-9645	478	1	two	CARDINAL
easat-9645	479	1	approximately 7	CARDINAL
easat-9645	479	2	two	CARDINAL
easat-9645	480	1	1520	CARDINAL
easat-9645	480	2	2576-8484	DATE
easat-9645	481	1	9	CARDINAL
easat-9645	481	2	8	CARDINAL
easat-9645	481	3	1498-1523	CARDINAL
easat-9645	481	4	2025	CARDINAL
easat-9645	481	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	481	6	2025	CARDINAL
easat-9645	481	7	2	CARDINAL
easat-9645	482	1	hilbert spaces	ORG
easat-9645	483	1	linear svm	ORG
easat-9645	483	2	pca nonlinear classification	ORG
easat-9645	483	3	linear	ORG
easat-9645	483	4	gaussian kernel	PERSON
easat-9645	483	5	rbf'	ORG
easat-9645	483	6	15	CARDINAL
easat-9645	484	1	linear	ORG
easat-9645	484	2	kernel svm (	ORG
easat-9645	485	1	linear	ORG
easat-9645	486	1	15	CARDINAL
easat-9645	487	1	approximately 90-100%	CARDINAL
easat-9645	488	1	9	CARDINAL
easat-9645	489	1	1521	CARDINAL
easat-9645	489	2	2576-8484	DATE
easat-9645	490	1	9	CARDINAL
easat-9645	490	2	8	CARDINAL
easat-9645	490	3	1498-1523	CARDINAL
easat-9645	490	4	2025	CARDINAL
easat-9645	490	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	490	6	2025	CARDINAL
easat-9645	490	7	22	CARDINAL
easat-9645	491	1	16	CARDINAL
easat-9645	493	1	16	CARDINAL
easat-9645	493	2	•	CARDINAL
easat-9645	494	1	•	CARDINAL
easat-9645	495	1	10	CARDINAL
easat-9645	495	2	hilbert	PERSON
easat-9645	496	1	10.1	CARDINAL
easat-9645	497	1	bounded linear operators	ORG
easat-9645	500	1	1522	CARDINAL
easat-9645	500	2	2576-8484	DATE
easat-9645	501	1	9	CARDINAL
easat-9645	501	2	8	CARDINAL
easat-9645	501	3	1498-1523	CARDINAL
easat-9645	501	4	2025	CARDINAL
easat-9645	501	5	10.55214/2576-8484.v9i8.9645	CARDINAL
easat-9645	501	6	2025	CARDINAL
easat-9645	501	7	10.2	CARDINAL
easat-9645	505	1	11	CARDINAL
easat-9645	505	2	hilbert	PERSON
easat-9645	506	1	ℝ𝑛	PRODUCT
easat-9645	506	2	pca	GPE
easat-9645	506	3	hilbert spaces	ORG
easat-9645	507	1	hilbert schmidt operators	ORG
easat-9645	507	2	quantum	ORG
easat-9645	508	1	hilbert spaces emerge	ORG
easat-9645	512	1	dr.	PERSON
easat-9645	512	2	hossain	PERSON
easat-9645	513	1	2025	CARDINAL
easat-9645	514	1	https://creativecommons.org/licenses/by/4.0/	WORK_OF_ART
easat-9645	515	1	1	CARDINAL
easat-9645	515	2	e. brüning	PERSON
easat-9645	516	1	birkhäuser,	ORG
easat-9645	516	2	boston	GPE
easat-9645	516	3	2015	DATE
easat-9645	517	1	213-225	CARDINAL
easat-9645	518	1	2	CARDINAL
easat-9645	518	2	e. provenzi	PERSON
easat-9645	518	3	hilbert spaces:	ORG
easat-9645	519	1	london	GPE
easat-9645	519	2	uk: iste ltd	ORG
easat-9645	519	3	john wiley & sons	ORG
easat-9645	519	4	2021	CARDINAL
easat-9645	520	1	https://doi.org/10.1002/9781119851318	CARDINAL
easat-9645	520	2	3	CARDINAL
easat-9645	520	3	m. foroutan	PERSON
easat-9645	520	4	r. asadi	PERSON
easat-9645	520	5	kernel hilbert spaces via	ORG
easat-9645	520	6	31	DATE
easat-9645	520	7	3	CARDINAL
easat-9645	520	8	1805-1818	DATE
easat-9645	520	9	2023	CARDINAL
easat-9645	521	1	4	CARDINAL
easat-9645	521	2	j. e. gough	PERSON
easat-9645	521	3	n. h. amini	PERSON
easat-9645	521	4	h. ding	PERSON
easat-9645	521	5	kernel hilbert space approach	ORG
easat-9645	521	6	non-markovian	NORP
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easat-9645	523	2	4	CARDINAL
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easat-9645	528	6	4	CARDINAL
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easat-9645	528	8	2020	DATE
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easat-9645	542	7	2012	DATE
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easat-9645	550	1	2021	CARDINAL
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easat-9645	551	10	2021	CARDINAL
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easat-9645	561	1	21	CARDINAL
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easat-9645	563	2	5	CARDINAL
easat-9645	564	1	1299-1319	CARDINAL
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easat-9645	566	1	22	CARDINAL
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easat-9645	567	1	boston	GPE
easat-9645	567	2	ma, usa: academic press	ORG
easat-9645	567	3	2009	DATE
easat-9645	568	1	https://doi.org/10.1214/009053607000000677 https://doi.org/10.1214/12-aos1033	PERSON