Linear mappings preserving the copositive cone
| العنوان: | Linear mappings preserving the copositive cone |
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| المؤلفون: | Yaroslav Shitov |
| المصدر: | Proceedings of the American Mathematical Society. 149:3173-3176 |
| بيانات النشر: | American Mathematical Society (AMS), 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Linear map, Combinatorics, Monomial, 2 × 2 real matrices, Matrix (mathematics), Cone (topology), Applied Mathematics, General Mathematics, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Mathematics |
| الوصف: | Let $\mathcal{S}_n$ be the set of all $n$-by-$n$ symmetric real matrices, and let $\mathcal{C}_n$ be the copositive cone, that is, the set of all matrices $a\in\mathcal{S}_n$ that fulfill the condition $u^\top a u\geqslant0$ for all $n$-vectors $u$ with nonnegative entries. We prove that a linear mapping $\varphi:\mathcal{S}_n\to \mathcal{S}_n$ satisfies $\varphi(\mathcal{C}_n)=\mathcal{C}_n$ if and only if $$\varphi(x)=m^\top xm$$ for a fixed monomial matrix $m$ with nonnegative entries. Comment: 5 pages |
| تدمد: | 1088-6826 0002-9939 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d639b3b818da768373129334e70e964e https://doi.org/10.1090/proc/15432 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....d639b3b818da768373129334e70e964e |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 10886826 00029939 |
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