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I have the following scalar function:

$$f\left(\mathbf{X}\right) = \left\|\mathbf{A} - e^{i\mathbf{X}}\mathbf{B}\right\|_{F}^{2} $$

where the matrices $\mathbf{A}$ and $\mathbf{B}$ inside the squared Frobenius norm have complex-valued entries, the matrix $\mathbf{X}$ has real-valued entries, and $i$ is the imaginary unit. Let's assume, for convenience, that all matrices are square and have dimensions $n \times n$.

I want to compute the gradient of this scalar function $f\left(\mathbf{X}\right)$ with respect to the matrix $\mathbf{X}$.

I tried several things but I wasn't able to solve this problem. Any help / hint / guidance would be appreciated.

operatorerror
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Kotsos
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  • Related: https://math.stackexchange.com/questions/2962817/gradient-of-a-complex-valued-matrix-function-but-with-real-domain – user550103 Oct 22 '18 at 04:46
  • Thank you very much! Although I did a search on relevant questions before posting, I didn't find this one. – Kotsos Oct 22 '18 at 12:30

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