Hello,
I have to to find the entries of a matrix [itex]X\in \mathbb{R}^{n\times n}[/itex] that minimize the functional: [itex]Tr \{ (AXB)(AXB)^* \}[/itex], where Tr denotes the trace operator, and ^{*} is the conjugate transpose of a matrix. The matrices A and B are complex and not necessarily square.
I tried to reformulate the problem with Einstein notation, then take the partial derivatives with respect to each [itex]a^{i}_{j}[/itex] and set them all to zero. The expression becomes pretty cumbersome and errorprone.
I was wondering if there is an easier and/or known solution for this problem.
Thanks.
