Commutator bounds and region of singular values of the commutator with a rank one matrix
| العنوان: | Commutator bounds and region of singular values of the commutator with a rank one matrix |
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| المؤلفون: | Daniel Oluwadamilare Akintoye, Che-Man Cheng, Ruiqiang Jiao |
| المصدر: | Linear Algebra and its Applications. 613:347-376 |
| بيانات النشر: | Elsevier BV, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Numerical Analysis, Algebra and Number Theory, General problem, 010102 general mathematics, Commutator (electric), 010103 numerical & computational mathematics, Rank (differential topology), 01 natural sciences, law.invention, Combinatorics, 2 × 2 real matrices, Singular value, Matrix (mathematics), law, Discrete Mathematics and Combinatorics, Geometry and Topology, 0101 mathematics, Constant (mathematics), Mathematics |
| الوصف: | The general problem under consideration is the determination of the best (i.e., smallest) constant C p , q , r such that ‖ X Y − Y X ‖ p ≤ C p , q , r ‖ X ‖ q ‖ Y ‖ r for all n × n matrices X and Y , where ‖ ⋅ ‖ p is the Schatten p-norm. Among the open situations, the problem is solved when (i) 2 p ∞ , q = r = 1 ; (ii) 2 p ∞ , q = 1 , 1 r 2 , and X, Y are 2 × 2 real matrices. The result for (i) is obtained via the study of the region (recently obtained in [5] ) of singular values of the commutator X Y − Y X , where X and Y are normalized rank one matrices. As a result of independent interest, for 2 × 2 real matrices, the region of singular values of the commutator X Y − Y X , where X is rank one and normalized, and ‖ Y ‖ r = 1 , is determined. The result for (ii) is a consequence of the case when r lies between 1 and 2. |
| تدمد: | 0024-3795 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::55b50f3fffb9c567e3f52abe95198d31 https://doi.org/10.1016/j.laa.2020.11.013 |
| حقوق: | CLOSED |
| رقم الأكسشن: | edsair.doi...........55b50f3fffb9c567e3f52abe95198d31 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 00243795 |
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