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Suppose $A_N$ is a positive definite matrix of size $N$ with eigenvalues $\Lambda=\{\lambda_1,\ldots,\lambda_N\}$. Let $D = \text{diag}\{d_1,\ldots,d_N\},\ d_i>0$ be a diagonal matrix. Can the eigenvalues of $A'_N=DAD$ be written in terms of $\Lambda$ and $d_i$?

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P.S. The above is related to this. I'm trying to further understand how to proceed analytically (instead of numerically, which is what I'm doing now). – user84825 Jul 3 '13 at 4:32
up vote 1 down vote accepted

(Unfortunately) No, the eigenvalues of $A_N'$ will also depend on the eigenvectors of $A_N$.

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