Let $V$ be a complex vector space and $A,B\in \operatorname{End}(V)$. Given that $\operatorname{Tr}(B)<0$, can we know the sign of $$\operatorname{Tr}(e^{-A^*A}B)$$ where $A^*$ denotes the conjugate transpose of $A$?
2026-04-03 21:30:40.1775251840
Sign of $\operatorname{Tr}(e^{-A^*A}B)$
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