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arXiv · 2410.20112

Extremal Schur Multipliers

Erik Christensen
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Abstract

The Schur product of two complex m x n matrices is their entry wise product. We show that an extremal element X in the convex set of m x n complex matrices of Schur multiplier norm at most 1 satisfies the inequality rank(X) =< (m +n)^(1/2) . For positive n x n matrices with unit diagonal, we give a characterization of the extremal elements, and show that such a matrix satisfies rank(X) =< n^(1/2).

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BibTeXRIS

Erik Christensen. 2024-10-26. Extremal Schur Multipliers. https://arxiv.org/abs/2410.20112

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