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eigenvalues of matrices or operators

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How the eigenvalues change when a Hermitian matrix is left multiplied and right multiplied b...

Suppose there is a Hermitian matrix $S$ with eigenvalues $\lambda_1, \lambda_2, \dots, \lambda_K$. There is a diagonal matrix $D$ whose entries on the main diagonal are positive. … What are the eigenvalues of $DSD$? The answer is obvious when all entries of $D$ are equal, but how about beyond this case? …
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