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ON THE GROUP INVERSE FOR THE SUM OF MATRICES
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 96 / Issue 1 / February 2014
- Published online by Cambridge University Press:
- 08 November 2013, pp. 36-43
- Print publication:
- February 2014
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- Article
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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} $.
