ePrints

Matrix positivity preservers in fixed dimension. Sur les transformations positives des matrices d'une dimension donnée.

Lookup NU author(s): Professor Mihai Putinar

Downloads

Full text for this publication is not currently held within this repository. Alternative links are provided below where available.

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.

Publication metadata

Author(s): Belton A, Guillot D, Khare A, Putinar M

Publication type: Article

Publication status: Published

Journal: Comptes Rendus Mathematique

Year: 2016

Volume: 354

Issue: 2

Pages: 143–148

Print publication date: 01/02/2016

Online publication date: 18/01/2016

Acceptance date: 22/11/2015

ISSN (print): 1631-073X

ISSN (electronic): 1778-3569

Publisher: Elsevier Masson

URL: http://dx.doi.org/10.1016/j.crma.2015.11.006

DOI: 10.1016/j.crma.2015.11.006

Altmetrics

Share