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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

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Matrix positivity preservers in fixed dimension. / Belton, Alexander; Guillot, Dominique; Khare, Apoorva et al.
In: Comptes Rendus Mathématique, Vol. 354, No. 2, 02.2016, p. 143-148.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Belton, A, Guillot, D, Khare, A & Putinar, M 2016, 'Matrix positivity preservers in fixed dimension', Comptes Rendus Mathématique, vol. 354, no. 2, pp. 143-148. https://doi.org/10.1016/j.crma.2015.11.006

APA

Belton, A., Guillot, D., Khare, A., & Putinar, M. (2016). Matrix positivity preservers in fixed dimension. Comptes Rendus Mathématique, 354(2), 143-148. https://doi.org/10.1016/j.crma.2015.11.006

Vancouver

Belton A, Guillot D, Khare A, Putinar M. Matrix positivity preservers in fixed dimension. Comptes Rendus Mathématique. 2016 Feb;354(2):143-148. Epub 2016 Jan 18. doi: 10.1016/j.crma.2015.11.006

Author

Belton, Alexander ; Guillot, Dominique ; Khare, Apoorva et al. / Matrix positivity preservers in fixed dimension. In: Comptes Rendus Mathématique. 2016 ; Vol. 354, No. 2. pp. 143-148.

Bibtex

@article{a0662d7019884842b94ab6f6e3f9d6e1,
title = "Matrix positivity preservers in fixed dimension",
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.",
author = "Alexander Belton and Dominique Guillot and Apoorva Khare and Mihai Putinar",
note = "This is the author{\textquoteright}s version of a work that was accepted for publication in Comptes Rendus Math{\'e}matique. 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 Math{\'e}matique 354 (2016), 143-148. DOI:10.1016/j.crma.2015.11.006",
year = "2016",
month = feb,
doi = "10.1016/j.crma.2015.11.006",
language = "English",
volume = "354",
pages = "143--148",
journal = "Comptes Rendus Math{\'e}matique",
issn = "1631-073X",
publisher = "Elsevier Masson",
number = "2",

}

RIS

TY - JOUR

T1 - Matrix positivity preservers in fixed dimension

AU - Belton, Alexander

AU - Guillot, Dominique

AU - Khare, Apoorva

AU - Putinar, Mihai

N1 - 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

PY - 2016/2

Y1 - 2016/2

N2 - 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.

AB - 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.

U2 - 10.1016/j.crma.2015.11.006

DO - 10.1016/j.crma.2015.11.006

M3 - Journal article

VL - 354

SP - 143

EP - 148

JO - Comptes Rendus Mathématique

JF - Comptes Rendus Mathématique

SN - 1631-073X

IS - 2

ER -