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A is an m-by-n matrix and M is an n-by-n matrix, $\det M \neq 0$. Is it possible to write the singular values of $AM$ as a function of the singular values of $A$? The entries of M can be regarded as known parameters.

Thanks!

Sinbaski
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1 Answers1

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No. For example, if $M = \pmatrix{1 & 0\cr 0 & 2\cr}$ and the singular values of $A$ are $1$ and $2$, the singular values of $AM$ could be $4, 1$ (for $A = M$) or $2,2$ (for $A = 2 M^{-1}$).

Robert Israel
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