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On the similarity of AB and BA for normal and other matrices
classification
math.FA
keywords
normalsimilarityhermitianmatriceswhenanswercomplexdemonstrating
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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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