For positive-definite matrices $A$ and $B$ the following inequalities hold: $$ 0\leq\lambda_{\min}(A)\lambda_{\max}(B)\leq\lambda_{\min}(A){\rm Tr}(B)\leq{\rm Tr} (AB)\leq\lambda_{\max}(A){\rm Tr} B\leq{\rm Tr}(A){\rm Tr}(B). $$ Сan they (or some of them) be valid for the case of semi-definite (or indefinite) matrices?
2026-04-23 15:47:29.1776959249
Inequalities for trace of a product
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