Quantitative estimates of the spectral norm of random matrices with independent columns
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909556410417152 |
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| author | Dai, Guozheng Su, Zhonggen Wang, Hanchao |
| author_facet | Dai, Guozheng Su, Zhonggen Wang, Hanchao |
| contents | This paper investigates the nonasymptotic properties of the spectral norm of some random matrices with independent columns. In particular, we consider an $m\times n$ random matrix $BA$, where $A$ is an $N\times n$ random matrix with independent mean-zero subexponential entries, and $B$ is an $m\times N$ deterministic matrix. We prove that the $L_{p}$ norm of the spectral norm of $BA$ is upper bounded by $(\sqrt{m}+\sqrt{n})p$. It is remarkable that this result is independent of the dimension $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03069 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantitative estimates of the spectral norm of random matrices with independent columns Dai, Guozheng Su, Zhonggen Wang, Hanchao Probability 46B09, 46B20, 60E15 This paper investigates the nonasymptotic properties of the spectral norm of some random matrices with independent columns. In particular, we consider an $m\times n$ random matrix $BA$, where $A$ is an $N\times n$ random matrix with independent mean-zero subexponential entries, and $B$ is an $m\times N$ deterministic matrix. We prove that the $L_{p}$ norm of the spectral norm of $BA$ is upper bounded by $(\sqrt{m}+\sqrt{n})p$. It is remarkable that this result is independent of the dimension $N$. |
| title | Quantitative estimates of the spectral norm of random matrices with independent columns |
| topic | Probability 46B09, 46B20, 60E15 |
| url | https://arxiv.org/abs/2307.03069 |