A Matrix Generalization of the Hardy-Littlewood-Pólya Rearrangement Inequality and Its Applications
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917086777835520 |
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| author | Yue, Man-Chung |
| author_facet | Yue, Man-Chung |
| contents | By analyzing an optimization problem over orthogonal matrices, we prove a generalization of the Hardy-Littlewood-Pólya rearrangement inequality to positive definite matrices. The inequality is then extended to rectangular matrices. Using our main results, we derive new inequalities for several distance-like functions encountered in various signal processing or machine learning applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_08144 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Matrix Generalization of the Hardy-Littlewood-Pólya Rearrangement Inequality and Its Applications Yue, Man-Chung Functional Analysis By analyzing an optimization problem over orthogonal matrices, we prove a generalization of the Hardy-Littlewood-Pólya rearrangement inequality to positive definite matrices. The inequality is then extended to rectangular matrices. Using our main results, we derive new inequalities for several distance-like functions encountered in various signal processing or machine learning applications. |
| title | A Matrix Generalization of the Hardy-Littlewood-Pólya Rearrangement Inequality and Its Applications |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2006.08144 |