Group inverses for some 2 × 2 block matrices over rings

Abstract We first consider the group inverses of the block matrices %$\left( {\begin{array}{*{20}{c}} A&B \\ 0&C \end{array}} \right)%$ over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the bloc...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Cao, Chongguang [verfasserIn] Wang, Yingchun [verfasserIn] Sheng, Yuqiu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	Group inverse block matrix right Ore domain associative ring

Übergeordnetes Werk:	Enthalten in: Frontiers of mathematics in China - Berlin : Heidelberg : Springer, 2006, 11(2016), 3 vom: 01. März, Seite 521-538
Übergeordnetes Werk:	volume:11 ; year:2016 ; number:3 ; day:01 ; month:03 ; pages:521-538

Links:	Volltext

DOI / URN:	10.1007/s11464-016-0490-6

Katalog-ID:	SPR01986146X

Internformat


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520			\|a Abstract We first consider the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ 0&C \end{array}} \right)%$ over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ C&D \end{array}} \right)%$ over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B# and (BπA)# both exist; (ii) B is invertible and m = n; (iii) A# and (D − CA#B)# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively.
650		4	\|a Group inverse \|7 (dpeaa)DE-He213
650		4	\|a block matrix \|7 (dpeaa)DE-He213
650		4	\|a right Ore domain \|7 (dpeaa)DE-He213
650		4	\|a associative ring \|7 (dpeaa)DE-He213
700	1		\|a Wang, Yingchun \|e verfasserin \|4 aut
700	1		\|a Sheng, Yuqiu \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Frontiers of mathematics in China \|d Berlin : Heidelberg : Springer, 2006 \|g 11(2016), 3 vom: 01. März, Seite 521-538 \|w (DE-627)509757677 \|w (DE-600)2228282-8 \|x 1673-3576 \|7 nnns
773	1	8	\|g volume:11 \|g year:2016 \|g number:3 \|g day:01 \|g month:03 \|g pages:521-538
856	4	0	\|u https://dx.doi.org/10.1007/s11464-016-0490-6 \|z lizenzpflichtig \|3 Volltext
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912			\|a GBV_ILN_20
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912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
951			\|a AR
952			\|d 11 \|j 2016 \|e 3 \|b 01 \|c 03 \|h 521-538

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author_variant	c c cc y w yw y s ys
matchkey_str	article:16733576:2016----::ruivrefroe2lcmti
hierarchy_sort_str	2016
publishDate	2016
allfields	10.1007/s11464-016-0490-6 doi (DE-627)SPR01986146X (SPR)s11464-016-0490-6-e DE-627 ger DE-627 rakwb eng 510 ASE Cao, Chongguang verfasserin aut Group inverses for some 2 × 2 block matrices over rings 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We first consider the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ 0&C \end{array}} \right)%$ over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ C&D \end{array}} \right)%$ over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B# and (BπA)# both exist; (ii) B is invertible and m = n; (iii) A# and (D − CA#B)# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively. Group inverse (dpeaa)DE-He213 block matrix (dpeaa)DE-He213 right Ore domain (dpeaa)DE-He213 associative ring (dpeaa)DE-He213 Wang, Yingchun verfasserin aut Sheng, Yuqiu verfasserin aut Enthalten in Frontiers of mathematics in China Berlin : Heidelberg : Springer, 2006 11(2016), 3 vom: 01. März, Seite 521-538 (DE-627)509757677 (DE-600)2228282-8 1673-3576 nnns volume:11 year:2016 number:3 day:01 month:03 pages:521-538 https://dx.doi.org/10.1007/s11464-016-0490-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 11 2016 3 01 03 521-538
spelling	10.1007/s11464-016-0490-6 doi (DE-627)SPR01986146X (SPR)s11464-016-0490-6-e DE-627 ger DE-627 rakwb eng 510 ASE Cao, Chongguang verfasserin aut Group inverses for some 2 × 2 block matrices over rings 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We first consider the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ 0&C \end{array}} \right)%$ over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ C&D \end{array}} \right)%$ over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B# and (BπA)# both exist; (ii) B is invertible and m = n; (iii) A# and (D − CA#B)# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively. Group inverse (dpeaa)DE-He213 block matrix (dpeaa)DE-He213 right Ore domain (dpeaa)DE-He213 associative ring (dpeaa)DE-He213 Wang, Yingchun verfasserin aut Sheng, Yuqiu verfasserin aut Enthalten in Frontiers of mathematics in China Berlin : Heidelberg : Springer, 2006 11(2016), 3 vom: 01. März, Seite 521-538 (DE-627)509757677 (DE-600)2228282-8 1673-3576 nnns volume:11 year:2016 number:3 day:01 month:03 pages:521-538 https://dx.doi.org/10.1007/s11464-016-0490-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 11 2016 3 01 03 521-538
allfields_unstemmed	10.1007/s11464-016-0490-6 doi (DE-627)SPR01986146X (SPR)s11464-016-0490-6-e DE-627 ger DE-627 rakwb eng 510 ASE Cao, Chongguang verfasserin aut Group inverses for some 2 × 2 block matrices over rings 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We first consider the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ 0&C \end{array}} \right)%$ over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ C&D \end{array}} \right)%$ over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B# and (BπA)# both exist; (ii) B is invertible and m = n; (iii) A# and (D − CA#B)# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively. Group inverse (dpeaa)DE-He213 block matrix (dpeaa)DE-He213 right Ore domain (dpeaa)DE-He213 associative ring (dpeaa)DE-He213 Wang, Yingchun verfasserin aut Sheng, Yuqiu verfasserin aut Enthalten in Frontiers of mathematics in China Berlin : Heidelberg : Springer, 2006 11(2016), 3 vom: 01. März, Seite 521-538 (DE-627)509757677 (DE-600)2228282-8 1673-3576 nnns volume:11 year:2016 number:3 day:01 month:03 pages:521-538 https://dx.doi.org/10.1007/s11464-016-0490-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 11 2016 3 01 03 521-538
allfieldsGer	10.1007/s11464-016-0490-6 doi (DE-627)SPR01986146X (SPR)s11464-016-0490-6-e DE-627 ger DE-627 rakwb eng 510 ASE Cao, Chongguang verfasserin aut Group inverses for some 2 × 2 block matrices over rings 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We first consider the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ 0&C \end{array}} \right)%$ over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ C&D \end{array}} \right)%$ over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B# and (BπA)# both exist; (ii) B is invertible and m = n; (iii) A# and (D − CA#B)# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively. Group inverse (dpeaa)DE-He213 block matrix (dpeaa)DE-He213 right Ore domain (dpeaa)DE-He213 associative ring (dpeaa)DE-He213 Wang, Yingchun verfasserin aut Sheng, Yuqiu verfasserin aut Enthalten in Frontiers of mathematics in China Berlin : Heidelberg : Springer, 2006 11(2016), 3 vom: 01. März, Seite 521-538 (DE-627)509757677 (DE-600)2228282-8 1673-3576 nnns volume:11 year:2016 number:3 day:01 month:03 pages:521-538 https://dx.doi.org/10.1007/s11464-016-0490-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 11 2016 3 01 03 521-538
allfieldsSound	10.1007/s11464-016-0490-6 doi (DE-627)SPR01986146X (SPR)s11464-016-0490-6-e DE-627 ger DE-627 rakwb eng 510 ASE Cao, Chongguang verfasserin aut Group inverses for some 2 × 2 block matrices over rings 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We first consider the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ 0&C \end{array}} \right)%$ over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ C&D \end{array}} \right)%$ over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B# and (BπA)# both exist; (ii) B is invertible and m = n; (iii) A# and (D − CA#B)# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively. Group inverse (dpeaa)DE-He213 block matrix (dpeaa)DE-He213 right Ore domain (dpeaa)DE-He213 associative ring (dpeaa)DE-He213 Wang, Yingchun verfasserin aut Sheng, Yuqiu verfasserin aut Enthalten in Frontiers of mathematics in China Berlin : Heidelberg : Springer, 2006 11(2016), 3 vom: 01. März, Seite 521-538 (DE-627)509757677 (DE-600)2228282-8 1673-3576 nnns volume:11 year:2016 number:3 day:01 month:03 pages:521-538 https://dx.doi.org/10.1007/s11464-016-0490-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 11 2016 3 01 03 521-538
language	English
source	Enthalten in Frontiers of mathematics in China 11(2016), 3 vom: 01. März, Seite 521-538 volume:11 year:2016 number:3 day:01 month:03 pages:521-538
sourceStr	Enthalten in Frontiers of mathematics in China 11(2016), 3 vom: 01. März, Seite 521-538 volume:11 year:2016 number:3 day:01 month:03 pages:521-538
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Group inverse block matrix right Ore domain associative ring
dewey-raw	510
isfreeaccess_bool	false
container_title	Frontiers of mathematics in China
authorswithroles_txt_mv	Cao, Chongguang @@aut@@ Wang, Yingchun @@aut@@ Sheng, Yuqiu @@aut@@
publishDateDaySort_date	2016-03-01T00:00:00Z
hierarchy_top_id	509757677
dewey-sort	3510
id	SPR01986146X
language_de	englisch
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author	Cao, Chongguang
spellingShingle	Cao, Chongguang ddc 510 misc Group inverse misc block matrix misc right Ore domain misc associative ring Group inverses for some 2 × 2 block matrices over rings
authorStr	Cao, Chongguang
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issn	1673-3576
topic_title	510 ASE Group inverses for some 2 × 2 block matrices over rings Group inverse (dpeaa)DE-He213 block matrix (dpeaa)DE-He213 right Ore domain (dpeaa)DE-He213 associative ring (dpeaa)DE-He213
topic	ddc 510 misc Group inverse misc block matrix misc right Ore domain misc associative ring
topic_unstemmed	ddc 510 misc Group inverse misc block matrix misc right Ore domain misc associative ring
topic_browse	ddc 510 misc Group inverse misc block matrix misc right Ore domain misc associative ring
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	Group inverses for some 2 × 2 block matrices over rings
ctrlnum	(DE-627)SPR01986146X (SPR)s11464-016-0490-6-e
title_full	Group inverses for some 2 × 2 block matrices over rings
author_sort	Cao, Chongguang
journal	Frontiers of mathematics in China
journalStr	Frontiers of mathematics in China
lang_code	eng
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container_start_page	521
author_browse	Cao, Chongguang Wang, Yingchun Sheng, Yuqiu
container_volume	11
class	510 ASE
format_se	Elektronische Aufsätze
author-letter	Cao, Chongguang
doi_str_mv	10.1007/s11464-016-0490-6
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title_sort	group inverses for some 2 × 2 block matrices over rings
title_auth	Group inverses for some 2 × 2 block matrices over rings
abstract	Abstract We first consider the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ 0&C \end{array}} \right)%$ over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ C&D \end{array}} \right)%$ over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B# and (BπA)# both exist; (ii) B is invertible and m = n; (iii) A# and (D − CA#B)# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively.
abstractGer	Abstract We first consider the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ 0&C \end{array}} \right)%$ over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ C&D \end{array}} \right)%$ over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B# and (BπA)# both exist; (ii) B is invertible and m = n; (iii) A# and (D − CA#B)# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively.
abstract_unstemmed	Abstract We first consider the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ 0&C \end{array}} \right)%$ over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices %$\left( {\begin{array}{{20}{c}} A&B \\ C&D \end{array}} \right)%$ over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B# and (BπA)# both exist; (ii) B is invertible and m = n; (iii) A# and (D − CA#B)# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively.
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container_issue	3
title_short	Group inverses for some 2 × 2 block matrices over rings
url	https://dx.doi.org/10.1007/s11464-016-0490-6
remote_bool	true
author2	Wang, Yingchun Sheng, Yuqiu
author2Str	Wang, Yingchun Sheng, Yuqiu
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doi_str	10.1007/s11464-016-0490-6
up_date	2024-07-04T03:09:05.817Z
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