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I have a square symmetric matrix $A$ with real non negative entries, a diagonal matrix $D$ with real positive entries. I mark the diagonal of $D$ as $d$. I am interested in the matrix $DAD$: is there anyway to represent this matrix as by using $d$ and not $D$? I am looking for a solution without using the $E_{ij}$ matrices.

I am also interested in such a representation for the term $diag(DADB)$, where $B$ is a symmetric binary matrix.

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