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While trying to solve an optimization problem for a MIMO linear precoder, I have encountered the need to compute the eigenvalues of a matrix [itex]D^{H}A^{H}AD[/itex] where the matrix [itex]A[/itex] is known and the matrix [itex]D[/itex] is a diagonal matrix whose entries contain the variables that need to be optimized (those variables can be assumed to be real without loss of generality).

At first sight, I thought it would be easy but I'm finding myself stuck since any of the ideas I had in mind to do that have been useless.

Any help or idea on how to proceed will be much appreciated.

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# Effect on eigenvalues of multiplying by a diagonal matrix

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