Does this statement hold?
If $$ \lambda_{\min}(B)\leq \lambda_{\min}(C),$$ then $$ \lambda_{\min}(BA)\leq \lambda_{\min}(CA),$$ where $A,B,C$ are symmetric Positive Definite Matrices.
2026-02-22 17:52:37.1771782757
A minimal eigenvalue inequality for Positive Definite Matrix
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There are easy counterexamples with $2 \times 2$ diagonal matrices.