Further results on the group inverses and Drazin inverses of anti-triangular block matrices

被引：35

作者：

Liu, Xifu ^{[1
,2
]}

Yang, Hu ^{[1
]}

机构：

[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

[2] E China Jiaotong Univ, Sch Basic Sci, Nanchang 330013, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 218卷 / 17期

基金：

中国国家自然科学基金;

关键词：

Drazin inverse; Group inverse; Block matrix; Idempotent matrix; REPRESENTATIONS;

D O I：

10.1016/j.amc.2012.02.058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the sufficient and necessary conditions for the existence of the group inverse for a class of 2 x 2 anti-triangular block matrices M with some certain conditions satisfied, and representations of the group inverse of M are obtained, which can be regarded as the extension of Bu et al. [C. Bu, J. Zhao, J. Zheng, Group inverse for a class 2 x 2 block matrices over skew fields, Appl. Math. Comput. 204 (2008) 45-49] and [C. Bu, J. Zhao, K. Zhang, Some results on group inverses of block matrices over skew fields, Electron. J. Linear Algebra, 18 (2009) 117-125]. Further, we use these results to determine the expressions of the Drazin inverse of M. Finally, two numerical examples are given to illustrate our results. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：8978 / 8986

页数：9

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