Let $A,C$ be given positive semidefinite matrices, $B$ be an arbitrary positive definite matrix. How can I estimate the value of $\DeclareMathOperator{tr}{tr}\tr(AB)\tr(CB^{-1})$ ? Is that true $\tr(AB)\tr(CB^{-1}) \geq \tr(AC)$ ?
Thank you !
2026-03-30 17:03:30.1774890210
Evaluate the product $\operatorname{tr}(AB)\operatorname{tr}(CB^{-1})$
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