Matrix positivity preservers in fixed dimension

Belton, Alexander and Guillot, Dominique and Khare, Apoorva and Putinar, Mihai (2016) Matrix positivity preservers in fixed dimension. Comptes Rendus Mathématique, 354 (2). pp. 143-148. ISSN 1631-073X

PDF (fixeddim_CRAS)
fixeddim_CRAS.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial-NoDerivs.

Download (291kB)


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.

Item Type:
Journal Article
Journal or Publication Title:
Comptes Rendus Mathématique
Additional Information:
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
Uncontrolled Keywords:
ID Code:
Deposited By:
Deposited On:
27 Nov 2015 14:04
Last Modified:
15 Jul 2020 05:24