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Existence of a linear map resulting in the determinant being an elementary symmetric polynomial

Such a map $\Phi$ does not exist for $n=5$ and $k=2$. Let me in fact show a stronger claim: There exist no two matrices $U\in\mathbb{C}^{5\times2}$ and $V\in\mathbb{C}^{2\times5}$ such that every five ...
darij grinberg's user avatar

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