Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala

Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala

We prove that the coefficient of \(t^2\) in \(\mathsf{trace}((A+tB)^6)\) is a sum of squares in the entries of the symmetric matrices \(A\) and \(B\).

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Bibliographic Details
Date:2024
Main Authors: Green, Nathaniel K., Kim, Edward D.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2024
Subjects:
semidefinite programming
sum of squares
positivity of multivariate polynomials
roots of polynomials
11C99
15A42
15A10
26C10
90C22
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2125
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-2125
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spelling oai:ojs.admjournal.luguniv.edu.ua:article-21252024-06-27T08:42:43Z Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala Green, Nathaniel K. Kim, Edward D. semidefinite programming, sum of squares, positivity of multivariate polynomials, roots of polynomials 11C99, 15A42, 15A10, 26C10, 90C22 We prove that the coefficient of \(t^2\) in \(\mathsf{trace}((A+tB)^6)\) is a sum of squares in the entries of the symmetric matrices \(A\) and \(B\). Lugansk National Taras Shevchenko University University of Wisconsin-La Crosse 2024-06-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2125 10.12958/adm2125 Algebra and Discrete Mathematics; Vol 37, No 2 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2125/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2125/1087 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2125/1088 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2125/1089 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2125/1090 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2125/1091 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2125/1092 Copyright (c) 2024 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2024-06-27T08:42:43Z
collection OJS
language English
topic semidefinite programming
sum of squares
positivity of multivariate polynomials
roots of polynomials
11C99
15A42
15A10
26C10
90C22
spellingShingle semidefinite programming
sum of squares
positivity of multivariate polynomials
roots of polynomials
11C99
15A42
15A10
26C10
90C22
Green, Nathaniel K.
Kim, Edward D.
Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala
topic_facet semidefinite programming
sum of squares
positivity of multivariate polynomials
roots of polynomials
11C99
15A42
15A10
26C10
90C22
format Article
author Green, Nathaniel K.
Kim, Edward D.
author_facet Green, Nathaniel K.
Kim, Edward D.
author_sort Green, Nathaniel K.
title Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala
title_short Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala
title_full Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala
title_fullStr Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala
title_full_unstemmed Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala
title_sort further techniques on a polynomial positivity question of collins, dykema, and torres-ayala
description We prove that the coefficient of \(t^2\) in \(\mathsf{trace}((A+tB)^6)\) is a sum of squares in the entries of the symmetric matrices \(A\) and \(B\).
publisher Lugansk National Taras Shevchenko University
publishDate 2024
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2125
work_keys_str_mv AT greennathanielk furthertechniquesonapolynomialpositivityquestionofcollinsdykemaandtorresayala
AT kimedwardd furthertechniquesonapolynomialpositivityquestionofcollinsdykemaandtorresayala
first_indexed 2024-06-28T04:03:55Z
last_indexed 2024-06-28T04:03:55Z
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