Missouri Journal of Mathematical Sciences

The Nullity and Rank of Combinations of Two Outer Inverses of a Given Matrix

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 $c\neq a+b$.

Article information

Source
Missouri J. Math. Sci., Volume 22, Issue 1 (2010), 19-22.

Dates
First available in Project Euclid: 1 August 2011

https://projecteuclid.org/euclid.mjms/1312232717

Digital Object Identifier
doi:10.35834/mjms/1312232717

Mathematical Reviews number (MathSciNet)
MR2650058

Zentralblatt MATH identifier
1202.15007

Subjects
Primary: 15A03: Vector spaces, linear dependence, rank
Secondary: 15A03: Vector spaces, linear dependence, rank

Citation

Zuo, Kezheng; Xie, Tao. The Nullity and Rank of Combinations of Two Outer Inverses of a Given Matrix. Missouri J. Math. Sci. 22 (2010), no. 1, 19--22. doi:10.35834/mjms/1312232717. https://projecteuclid.org/euclid.mjms/1312232717

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