On the Submultiplicativity of Matrix Norms Induced by Random Vectors
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909105067655168 |
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| author | Bouthat, Ludovick |
| author_facet | Bouthat, Ludovick |
| contents | In a recent article, Chávez, Garcia and Hurley introduced a new family of norms $\|\cdot\|_{\mathbf{X},d}$ on the space of $n \times n$ complex matrices which are induced by random vectors $\mathbf{X}$ having finite $d$-moments. Therein, the authors asked under which conditions the norms induced by a scalar multiple of $\mathbf{X}$ are submultiplicative. In this paper, this question is completely answered by proving that this is always the case, as long as the entries of $\mathbf{X}$ have finite $p$-moments for $p=\max\{2+\varepsilon,d\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08173 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Submultiplicativity of Matrix Norms Induced by Random Vectors Bouthat, Ludovick Metric Geometry 47A30, 15A60, 15A18 In a recent article, Chávez, Garcia and Hurley introduced a new family of norms $\|\cdot\|_{\mathbf{X},d}$ on the space of $n \times n$ complex matrices which are induced by random vectors $\mathbf{X}$ having finite $d$-moments. Therein, the authors asked under which conditions the norms induced by a scalar multiple of $\mathbf{X}$ are submultiplicative. In this paper, this question is completely answered by proving that this is always the case, as long as the entries of $\mathbf{X}$ have finite $p$-moments for $p=\max\{2+\varepsilon,d\}$. |
| title | On the Submultiplicativity of Matrix Norms Induced by Random Vectors |
| topic | Metric Geometry 47A30, 15A60, 15A18 |
| url | https://arxiv.org/abs/2402.08173 |