Weak group inverse
In this paper, we introduce the weak group inverse (called as the WG inverse in the present paper) for square complex matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a pre-order and the other is a partial order, and...
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| Published in | Open mathematics (Warsaw, Poland) Vol. 16; no. 1; pp. 1218 - 1232 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Warsaw
De Gruyter
31.10.2018
De Gruyter Poland |
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| Abstract | In this paper, we introduce the weak group inverse (called as the WG inverse in the present paper) for square complex matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a pre-order and the other is a partial order, and derive several characterizations of the two orders. The paper ends with a characterization of the core EP order using WG inverses. |
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| AbstractList | In this paper, we introduce the weak group inverse (called as the WG inverse in the present paper) for square complex matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a pre-order and the other is a partial order, and derive several characterizations of the two orders. The paper ends with a characterization of the core EP order using WG inverses. |
| Author | Chen, Jianlong Wang, Hongxing |
| Author_xml | – sequence: 1 givenname: Hongxing surname: Wang fullname: Wang, Hongxing email: winghongxing0902@163.com organization: School of Mathematics, Southeast University, Nanjing, 210096, China and School of Science, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, 530006, China – sequence: 2 givenname: Jianlong surname: Chen fullname: Chen, Jianlong email: jlchen@seu.edu.cn organization: School of Mathematics, Southeast University, Nanning, 210096, China |
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| Cites_doi | 10.1016/j.amc.2013.02.010 10.1016/j.laa.2016.08.008 10.1080/03081088308817561 10.1016/0024-3795(78)90048-4 10.1080/03081087.2013.791690 10.2989/16073606.2017.1377779 10.1007/s10092-015-0151-2 10.1016/j.amc.2013.10.060 10.1016/j.amc.2014.03.048 10.4171/JST/207 10.1080/03081080902778222 10.1016/j.laa.2015.09.046 10.1080/03081087.2013.839676 |
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| References | (ref51) 2018; 41 (ref131) 1978; 20 (ref31) 2014; 236 (ref61) 2013; 219 (ref121) 2016; 508 (ref21) 2014; 226 (ref141) 2009 (ref71) 2014; 62 (ref91) 2016; 53 (ref01) 2003 (ref101) 1983; 14 (ref81) 2018; 8 (ref11) 2010; 58 (ref151) 2016; 488 (ref41) 2014; 62 (ref111) 2010 |
| References_xml | – volume: 219 start-page: 7310 year: 2013 ident: ref61 article-title: On a partial order defined by the weighted Moore-Penrose inverse publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2013.02.010 – volume: 508 start-page: 289 year: 2016 ident: ref121 article-title: Core-EP decomposition and its applications publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2016.08.008 – volume: 14 start-page: 241 year: 1983 ident: ref101 article-title: Matrices for which A* and A† commute publication-title: Linear and Multilinear Algebra doi: 10.1080/03081088308817561 – volume-title: Generalized inverses: theory and applications year: 2003 ident: ref01 – volume: 20 start-page: 167 year: 1978 ident: ref131 article-title: Weak Drazin inverses publication-title: Linear Algebra and Appl. doi: 10.1016/0024-3795(78)90048-4 – volume: 62 start-page: 792 year: 2014 ident: ref41 article-title: Core-EP inverse publication-title: Linear Multilinear Algebra doi: 10.1080/03081087.2013.791690 – volume: 41 start-page: 265 year: 2018 ident: ref51 article-title: Revisiting the core EP inverse and its extension to rectangular matrices publication-title: Quaest. Math. doi: 10.2989/16073606.2017.1377779 – volume-title: Generalized inverses of linear transformations year: 2009 ident: ref141 – volume: 53 start-page: 331 year: 2016 ident: ref91 article-title: Characterizations of DMP inverse in a Hilbert space publication-title: Calcolo doi: 10.1007/s10092-015-0151-2 – volume: 226 start-page: 575 year: 2014 ident: ref21 article-title: On a new generalized inverse for matrices of an arbitrary index publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2013.10.060 – volume: 236 start-page: 450 year: 2014 ident: ref31 article-title: On a generalized core inverse publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2014.03.048 – volume-title: Matrix partial orders, shorted operators and applications year: 2010 ident: ref111 – volume: 8 start-page: 555 year: 2018 ident: ref81 article-title: The gDMP inverse of Hilbert space operators publication-title: J. Spectr. Theory doi: 10.4171/JST/207 – volume: 58 start-page: 681 year: 2010 ident: ref11 article-title: Core inverse of matrices publication-title: Linear Multilinear Algebra doi: 10.1080/03081080902778222 – volume: 488 start-page: 235 year: 2016 ident: ref151 article-title: Partial orders based on core-nilpotent decomposition publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2015.09.046 – volume: 62 start-page: 1629 year: 2014 ident: ref71 article-title: Further properties on the core partial order and other matrix partial orders publication-title: Linear Multilinear Algebra doi: 10.1080/03081087.2013.839676 |
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