Is there any theorem which can put a bound on $$ Tr (V_1 V_2 \dots V_n) $$ as a function of product of $$ Tr (V_1)^{p_1} Tr (V_2)^{p_2} \dots Tr (V_n)^{p_n} $$ where $V_i$ are hermitian matrices.
2026-03-25 11:14:46.1774437286
Bounds on trace of product of hermitian matrices.
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No. Consider $$V=\begin{bmatrix}1&1\\1&-1\end{bmatrix}, \ \ W=\begin{bmatrix}1&0\\0&-1\end{bmatrix}.$$ Then $$\text {Tr}\,(VW)=2, \ \ \text {Tr}\,(V)=\text {Tr}\,(W)=0.$$