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
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
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