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    Rights statement: This is the author’s version of a work that was accepted for publication in Comptes Rendus Mathématique. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Comptes Rendus Mathématique, ??, ?, 2016 DOI: 10.1016/j.crma.2015.11.006

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Matrix positivity preservers in fixed dimension

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<mark>Journal publication date</mark>02/2016
<mark>Journal</mark>Comptes Rendus Mathématique
Issue number2
Volume354
Number of pages6
Pages (from-to)143-148
Publication StatusPublished
Early online date18/01/16
<mark>Original language</mark>English

Abstract

A classical theorem of I.J. Schoenberg characterizes functions that preserve positivity when applied entrywise to positive semidefinite matrices of arbitrary size. Obtaining similar characterizations in fixed dimension is intricate. In this note, we provide a solution to this problem in the polynomial case. As consequences, we derive tight linear matrix inequalities for Hadamard powers of positive semidefinite matrices, and a sharp asymptotic bound for the matrix cube problem involving Hadamard powers.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Comptes Rendus Mathématique. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Comptes Rendus Mathématique 354 (2016), 143-148. DOI:10.1016/j.crma.2015.11.006