Dan Kučerovský, Aydin Sarraf
Abstract
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We give necessary and sufficient conditions for a Schur map to be a homomorphism, with some generalizations to the infinite-dimensional case. In the finite-dimensional case, we find that a Schur multiplier distributes over matrix multiplication if and only if the Schur matrix has a certain simple form.
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We give necessary and sufficient conditions for a Schur map to be a homomorphism, with some generalizations to the infinite-dimensional case. In the finite-dimensional case, we find that a Schur multiplier distributes over matrix multiplication if and only if the Schur matrix has a certain simple form.
Key concepts: Schur product theorem, Schur multiplier, Schur's theorem, Schur complement, Schur decomposition, Mathematics, Homomorphism, Schur's lemma