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Suppose I have a square matrix $A \in \mathbb{R}^{mn \times mn}$. I want to find

$$\arg \min_{P, Q} \|A - P \otimes Q\|_F$$

where $P$ is an $m \times m$ permutation matrix and $Q$ is an $n \times n$ orthogonal matrix. I cannot find any research on problems like this. Does anyone have an idea for how to tackle this problem?

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  • $\begingroup$ What can you say in the degenerate cases m=1 or n=1? $\endgroup$
    – Yemon Choi
    Jan 11, 2016 at 4:14

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