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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.

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Exist matrices such that $f(X) = \sum_{j = j}A_jXB_j$ for all $X \in \text{M}_N(\mathbb{C})$? [closed]

Let $f: \text{M}_n(\mathbb{C}) \to \text{M}_n(\mathbb{C})$ be a $\mathbb{C}$-linear map (not necessarily an algebra homomorphism). Do there exist matrices $A_1, \ldots, A_d \in \text{M}_n(\mathbb{C})$ …
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