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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| Дата: | 2024 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2024
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2125 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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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 |
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Algebra and Discrete Mathematics |
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|
| 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 |
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AT greennathanielk furthertechniquesonapolynomialpositivityquestionofcollinsdykemaandtorresayala AT kimedwardd furthertechniquesonapolynomialpositivityquestionofcollinsdykemaandtorresayala |
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2024-06-28T04:03:55Z |
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2024-06-28T04:03:55Z |
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