Decompositions of Schur block products

Erik Christensen

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arXiv · 1811.03668

Decompositions of Schur block products

Erik Christensen

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Abstract

Given two m x n matrices A = (a_{ij}) and B=(b_{ij}) with entries in B(H), the Schur block product is the m x n matrix A \square B := (a_{ij}b_{ij}). There exists an m x n contraction matrix S = (s_{ij}), such that A \square B = diag(AA*)^(1/2) S diag(B*B)^(1/2). This decomposition is also valid for the block Schur tensor product. It is shown, via the theory of random matrices, that the set of contractions S, which may appear in such a decomposition, is a very thin subset of the unit ball of M_n(B(H)).

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BibTeX RIS

Erik Christensen. 2018-11-08. Decompositions of Schur block products. https://arxiv.org/abs/1811.03668

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