Further results on the group inverse of some anti-triangular block matrices

Abstract Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the follo...
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Gespeichert in:

Autor*in:	Cao, Chongguang [verfasserIn] Zhang, Hanyu Ge, Yanling

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Schlagwörter:	Right Ore domain Block matrix Group inverse Ring

Anmerkung:	© The Author(s) 2013

Übergeordnetes Werk:	Enthalten in: Journal of applied mathematics and computing - Berlin : Springer, 2006, 46(2013), 1-2 vom: 30. Nov., Seite 169-179
Übergeordnetes Werk:	volume:46 ; year:2013 ; number:1-2 ; day:30 ; month:11 ; pages:169-179

Links:	Volltext

DOI / URN:	10.1007/s12190-013-0744-3

Katalog-ID:	SPR025153935

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520			\|a Abstract Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA=C; (ii) , where B♯ exists and BA=BAB♯B. The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010). Some results in special cases are also generalized to any ring.
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700	1		\|a Ge, Yanling \|4 aut
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912			\|a GBV_ILN_161
912			\|a GBV_ILN_165
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912			\|a GBV_ILN_293
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912			\|a GBV_ILN_2037
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912			\|a GBV_ILN_2039
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Indexfelder

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publishDate	2013
allfields	10.1007/s12190-013-0744-3 doi (DE-627)SPR025153935 (SPR)s12190-013-0744-3-e DE-627 ger DE-627 rakwb eng Cao, Chongguang verfasserin aut Further results on the group inverse of some anti-triangular block matrices 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2013 Abstract Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA=C; (ii) , where B♯ exists and BA=BAB♯B. The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010). Some results in special cases are also generalized to any ring. Right Ore domain (dpeaa)DE-He213 Block matrix (dpeaa)DE-He213 Group inverse (dpeaa)DE-He213 Ring (dpeaa)DE-He213 Zhang, Hanyu aut Ge, Yanling aut Enthalten in Journal of applied mathematics and computing Berlin : Springer, 2006 46(2013), 1-2 vom: 30. Nov., Seite 169-179 (DE-627)565516833 (DE-600)2424171-4 1865-2085 nnns volume:46 year:2013 number:1-2 day:30 month:11 pages:169-179 https://dx.doi.org/10.1007/s12190-013-0744-3 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_165 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_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_2190 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 46 2013 1-2 30 11 169-179
spelling	10.1007/s12190-013-0744-3 doi (DE-627)SPR025153935 (SPR)s12190-013-0744-3-e DE-627 ger DE-627 rakwb eng Cao, Chongguang verfasserin aut Further results on the group inverse of some anti-triangular block matrices 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2013 Abstract Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA=C; (ii) , where B♯ exists and BA=BAB♯B. The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010). Some results in special cases are also generalized to any ring. Right Ore domain (dpeaa)DE-He213 Block matrix (dpeaa)DE-He213 Group inverse (dpeaa)DE-He213 Ring (dpeaa)DE-He213 Zhang, Hanyu aut Ge, Yanling aut Enthalten in Journal of applied mathematics and computing Berlin : Springer, 2006 46(2013), 1-2 vom: 30. Nov., Seite 169-179 (DE-627)565516833 (DE-600)2424171-4 1865-2085 nnns volume:46 year:2013 number:1-2 day:30 month:11 pages:169-179 https://dx.doi.org/10.1007/s12190-013-0744-3 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_165 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_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_2190 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 46 2013 1-2 30 11 169-179
allfields_unstemmed	10.1007/s12190-013-0744-3 doi (DE-627)SPR025153935 (SPR)s12190-013-0744-3-e DE-627 ger DE-627 rakwb eng Cao, Chongguang verfasserin aut Further results on the group inverse of some anti-triangular block matrices 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2013 Abstract Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA=C; (ii) , where B♯ exists and BA=BAB♯B. The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010). Some results in special cases are also generalized to any ring. Right Ore domain (dpeaa)DE-He213 Block matrix (dpeaa)DE-He213 Group inverse (dpeaa)DE-He213 Ring (dpeaa)DE-He213 Zhang, Hanyu aut Ge, Yanling aut Enthalten in Journal of applied mathematics and computing Berlin : Springer, 2006 46(2013), 1-2 vom: 30. Nov., Seite 169-179 (DE-627)565516833 (DE-600)2424171-4 1865-2085 nnns volume:46 year:2013 number:1-2 day:30 month:11 pages:169-179 https://dx.doi.org/10.1007/s12190-013-0744-3 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_165 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_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_2190 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 46 2013 1-2 30 11 169-179
allfieldsGer	10.1007/s12190-013-0744-3 doi (DE-627)SPR025153935 (SPR)s12190-013-0744-3-e DE-627 ger DE-627 rakwb eng Cao, Chongguang verfasserin aut Further results on the group inverse of some anti-triangular block matrices 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2013 Abstract Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA=C; (ii) , where B♯ exists and BA=BAB♯B. The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010). Some results in special cases are also generalized to any ring. Right Ore domain (dpeaa)DE-He213 Block matrix (dpeaa)DE-He213 Group inverse (dpeaa)DE-He213 Ring (dpeaa)DE-He213 Zhang, Hanyu aut Ge, Yanling aut Enthalten in Journal of applied mathematics and computing Berlin : Springer, 2006 46(2013), 1-2 vom: 30. Nov., Seite 169-179 (DE-627)565516833 (DE-600)2424171-4 1865-2085 nnns volume:46 year:2013 number:1-2 day:30 month:11 pages:169-179 https://dx.doi.org/10.1007/s12190-013-0744-3 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_165 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_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_2190 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 46 2013 1-2 30 11 169-179
allfieldsSound	10.1007/s12190-013-0744-3 doi (DE-627)SPR025153935 (SPR)s12190-013-0744-3-e DE-627 ger DE-627 rakwb eng Cao, Chongguang verfasserin aut Further results on the group inverse of some anti-triangular block matrices 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2013 Abstract Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA=C; (ii) , where B♯ exists and BA=BAB♯B. The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010). Some results in special cases are also generalized to any ring. Right Ore domain (dpeaa)DE-He213 Block matrix (dpeaa)DE-He213 Group inverse (dpeaa)DE-He213 Ring (dpeaa)DE-He213 Zhang, Hanyu aut Ge, Yanling aut Enthalten in Journal of applied mathematics and computing Berlin : Springer, 2006 46(2013), 1-2 vom: 30. Nov., Seite 169-179 (DE-627)565516833 (DE-600)2424171-4 1865-2085 nnns volume:46 year:2013 number:1-2 day:30 month:11 pages:169-179 https://dx.doi.org/10.1007/s12190-013-0744-3 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_165 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_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_2190 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 46 2013 1-2 30 11 169-179
language	English
source	Enthalten in Journal of applied mathematics and computing 46(2013), 1-2 vom: 30. Nov., Seite 169-179 volume:46 year:2013 number:1-2 day:30 month:11 pages:169-179
sourceStr	Enthalten in Journal of applied mathematics and computing 46(2013), 1-2 vom: 30. Nov., Seite 169-179 volume:46 year:2013 number:1-2 day:30 month:11 pages:169-179
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Right Ore domain Block matrix Group inverse Ring
isfreeaccess_bool	true
container_title	Journal of applied mathematics and computing
authorswithroles_txt_mv	Cao, Chongguang @@aut@@ Zhang, Hanyu @@aut@@ Ge, Yanling @@aut@@
publishDateDaySort_date	2013-11-30T00:00:00Z
hierarchy_top_id	565516833
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author	Cao, Chongguang
spellingShingle	Cao, Chongguang misc Right Ore domain misc Block matrix misc Group inverse misc Ring Further results on the group inverse of some anti-triangular block matrices
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topic_title	Further results on the group inverse of some anti-triangular block matrices Right Ore domain (dpeaa)DE-He213 Block matrix (dpeaa)DE-He213 Group inverse (dpeaa)DE-He213 Ring (dpeaa)DE-He213
topic	misc Right Ore domain misc Block matrix misc Group inverse misc Ring
topic_unstemmed	misc Right Ore domain misc Block matrix misc Group inverse misc Ring
topic_browse	misc Right Ore domain misc Block matrix misc Group inverse misc Ring
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title	Further results on the group inverse of some anti-triangular block matrices
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title_full	Further results on the group inverse of some anti-triangular block matrices
author_sort	Cao, Chongguang
journal	Journal of applied mathematics and computing
journalStr	Journal of applied mathematics and computing
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author_browse	Cao, Chongguang Zhang, Hanyu Ge, Yanling
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author-letter	Cao, Chongguang
doi_str_mv	10.1007/s12190-013-0744-3
title_sort	further results on the group inverse of some anti-triangular block matrices
title_auth	Further results on the group inverse of some anti-triangular block matrices
abstract	Abstract Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA=C; (ii) , where B♯ exists and BA=BAB♯B. The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010). Some results in special cases are also generalized to any ring. © The Author(s) 2013
abstractGer	Abstract Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA=C; (ii) , where B♯ exists and BA=BAB♯B. The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010). Some results in special cases are also generalized to any ring. © The Author(s) 2013
abstract_unstemmed	Abstract Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA=C; (ii) , where B♯ exists and BA=BAB♯B. The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010). Some results in special cases are also generalized to any ring. © The Author(s) 2013
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title_short	Further results on the group inverse of some anti-triangular block matrices
url	https://dx.doi.org/10.1007/s12190-013-0744-3
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author2	Zhang, Hanyu Ge, Yanling
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doi_str	10.1007/s12190-013-0744-3
up_date	2024-07-03T14:12:00.204Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR025153935</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230403063740.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2013 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s12190-013-0744-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR025153935</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s12190-013-0744-3-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cao, Chongguang</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Further results on the group inverse of some anti-triangular block matrices</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA=C; (ii) , where B♯ exists and BA=BAB♯B. The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010). 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Further results on the group inverse of some anti-triangular block matrices

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