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February 2010 The Nullity and Rank of Combinations of Two Outer Inverses of a Given Matrix
Kezheng Zuo, Tao Xie
Missouri J. Math. Sci. 22(1): 19-22 (February 2010). DOI: 10.35834/mjms/1312232717

Abstract

This paper shows that the nullity and rank of $aP+bQ-cQAP$ is a constant, where $P$ and $Q$ are outer inverses of a given matrix $A$, $c=a+b$ ($a,b\neq 0$) or $c\neq a+b$, $a, b, c \in \mathbb{C}$. In addition, the rank of $aP+bQ-cQAP$ is equal to the rank of $P-Q$ if $c=a+b$ and to $P+Q$ if $c\neq a+b$.

Citation

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Kezheng Zuo. Tao Xie. "The Nullity and Rank of Combinations of Two Outer Inverses of a Given Matrix." Missouri J. Math. Sci. 22 (1) 19 - 22, February 2010. https://doi.org/10.35834/mjms/1312232717

Information

Published: February 2010
First available in Project Euclid: 1 August 2011

zbMATH: 1202.15007
MathSciNet: MR2650058
Digital Object Identifier: 10.35834/mjms/1312232717

Subjects:
Primary: 15A03
Secondary: 15A03

Rights: Copyright © 2010 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.22 • No. 1 • February 2010
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