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## problem with minimizing the matrix norm

Hello,

I have to to find the entries of a matrix $X\in \mathbb{R}^{n\times n}$ that minimize the functional: $Tr \{ (A-XB)(A-XB)^* \}$, 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 $a^{i}_{j}$ and set them all to zero. The expression becomes pretty cumbersome and error-prone.

I was wondering if there is an easier and/or known solution for this problem.
Thanks.
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