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Keywords:
$W$-core inverse; reverse order law; perturbation; spectral norm
$W$-core inverse; reverse order law; perturbation; spectral norm
Summary:
Let $A$, $W$ be two $n\times n$ complex matrices. We present the expression of the $W$-core inverse of $A$ by Hartwig and Spindelböck's decompositions and full rank decompositions. It is also proved that $A$ is $W$-core invertible if and only if $A$ is right $W$-core invertible. This equivalence may not be true in a general $*$-ring, see H. H. Zhu, L. Y. Wu, D. Mosić (2023). Then, several results for the reverse order law of the $W$-core inverse are given. Another accomplishment of this paper is to establish some perturbation properties and perturbation bounds for the $W$-core inverse, under some conditions. Finally, the necessary and sufficient condition for the continuity of the $W$-core inverse is derived.
References:
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