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ON THE GROUP INVERSE FOR THE SUM OF MATRICES

Part of: Basic linear algebra

Published online by Cambridge University Press:  08 November 2013

CHANGJIANG BU ,
XIUQING ZHOU ,
LIANG MA  and
JIANG ZHOU
CHANGJIANG BU*
Affiliation:
College of Science, Harbin Engineering University, Harbin 150001, PR China
XIUQING ZHOU
Affiliation:
College of Science, Harbin Engineering University, Harbin 150001, PR China
LIANG MA
Affiliation:
College of Science, Harbin Engineering University, Harbin 150001, PR China
JIANG ZHOU
Affiliation:
College of Science, Harbin Engineering University, Harbin 150001, PR China
*
✉buchangjiang@hrbeu.edu.cn
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Abstract

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Let ${ \mathbb{K} }^{m\times n} $ denote the set of all $m\times n$ matrices over a skew field $ \mathbb{K} $. In this paper, we give a necessary and sufficient condition for the existence of the group inverse of $P+ Q$ and its representation under the condition $PQ= 0$, where $P, Q\in { \mathbb{K} }^{n\times n} $. In addition, in view of the natural characters of block matrices, we give the existence and representation for the group inverse of $P+ Q$ and $P+ Q+ R$ under some conditions, where $P, Q, R\in { \mathbb{K} }^{n\times n} $.

Keywords

group inversegroup invertibilityskew field

MSC classification

Secondary: 15A09: Matrix inversion, generalized inverses
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 96 , Issue 1 , February 2014 , pp. 36 - 43
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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