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name for a matrix operation

If $A$ is a matrix and $D$ is a diagonal matrix, is there some special name for $DAD$?

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The paternal matrix? ;) – Mark Grant Aug 24 at 12:47
Interesting idea :) – Felix Goldberg Aug 24 at 12:51
$A$ diagonally conjugated by $D$? – Igor Khavkine Aug 24 at 12:52
Or just $A$ conjugated by $D$. – Deane Yang Aug 24 at 13:09
I'd reserve the word "conjugated" for something like $DAD^{-1}$. – Andreas Blass Aug 24 at 14:32

it is called "diagonal congruence" here. This makes sense, at least when $D$ is real, since it is a congruence. "Conjugate" sounds more like $D^{-1}AD$ or $\overline{A}$ to me.