Expression for the Group Inverse of the 2 ×2 Block Matrix

DU Fa-peng

doi:10.13371/j.cnki.chin.q.j.m.2016.04.010

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 4: 412 - 421

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.04.010

Expression for the Group Inverse of the 2 ×2 Block Matrix

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Department of Mathematics,Southeast University, School of Mathematical and Physical Sciences,Xuzhou Institute of Technology

DU Fa-peng(1974-), male, native of Xuzhou, Jiangsu, an associate professor of Xuzhou Institute of Technology, Ph.D., engages in functional analysis application and operator algebra.

Received date: 2014-11-30

Online published: 2020-11-03

Supported by

Supported by the Fund for Postdoctoral of China(2015M581688)； Supported by the National Natural Science Foundation of China(11371089)； Supported by the Specialized Research Fund for the Doctoral Program of Higher Education(20120092110020)； Supported by the Natural Science Foundation of Jiangsu Province(BK20141327)； Supported by the Foundation of Xuzhou Institute of Technology(XKY2014207)；

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Abstract

In this paper, we present a method how to get the expression for the group inverse of 2×2 block matrix and get the explicit expressions of the block matrix (A C B D) under some conditions.

Key words： generalized inverse; group inverse; block matrix

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DU Fa-peng . Expression for the Group Inverse of the 2 ×2 Block Matrix[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(4) : 412 -421 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.04.010

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