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arXiv · 1605.04416

On the similarity of AB and BA for normal and other matrices

Stephan Ramon Garcia·David Sherman·Gary Weiss
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Abstract

It is well-known that $AB$ and $BA$ are similar when $A$ and $B$ are complex square Hermitian matrices. In this note we answer a question of F. Zhang by demonstrating that similarity can fail if $A$ is Hermitian and $B$ is normal. Perhaps surprisingly, similarity does hold when $A$ is positive semidefinite and $B$ is normal.

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BibTeXRIS

Stephan Ramon Garcia, David Sherman, Gary Weiss. 2016-05-14. On the similarity of AB and BA for normal and other matrices. https://arxiv.org/abs/1605.04416

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