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

Lookup NU author(s): Professor Mihai Putinar


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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


DOI: 10.1016/j.crma.2015.11.006


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