If $A,B$ are two PSD matrices, will $AB$ also be PSD?
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$AB$ need not be symmetric, try $A=\left(\begin{smallmatrix}1&1\\1&2\end{smallmatrix}\right)$ and $B=\left(\begin{smallmatrix}2&1\\1&1\end{smallmatrix}\right)$
user2097
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Why do we need symmetry? Is it part of the PSD definition? – An old man in the sea. Sep 06 '14 at 23:08
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@Anoldmaninthesea. Yes. – user2097 Sep 06 '14 at 23:11
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Ok. Thanks @user2097 – An old man in the sea. Sep 06 '14 at 23:25
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To whoever read this answer : symmetry has nothing to do with the definition of PSD. – Guillaume Oct 15 '20 at 17:33