Order Relations of the Wasserstein mean and the spectral geometric mean
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911865937854464 |
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| author | Gan, Luyining Huang, Huajun |
| author_facet | Gan, Luyining Huang, Huajun |
| contents | On the space of positive definite matrices, several operator means are popular and have been studied extensively. In this paper, we investigate the near order and the Löwner order relations on the curves defined by the Wasserstein mean and the spectral geometric mean. We show that the near order $\preceq $ is stronger than the eigenvalue entrywise order, and that $A\natural_t B \preceq A\diamond_t B$ for $t\in [0,1]$. We prove the monotonicity properties of the curves originated from the Wasserstein mean and the spectral geometric mean in terms of the near order. The Löwner order properties of the Wasserstein mean and the spectral geometric mean are also explored. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15394 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Order Relations of the Wasserstein mean and the spectral geometric mean Gan, Luyining Huang, Huajun Functional Analysis 15A42, 15A45, 15B48 On the space of positive definite matrices, several operator means are popular and have been studied extensively. In this paper, we investigate the near order and the Löwner order relations on the curves defined by the Wasserstein mean and the spectral geometric mean. We show that the near order $\preceq $ is stronger than the eigenvalue entrywise order, and that $A\natural_t B \preceq A\diamond_t B$ for $t\in [0,1]$. We prove the monotonicity properties of the curves originated from the Wasserstein mean and the spectral geometric mean in terms of the near order. The Löwner order properties of the Wasserstein mean and the spectral geometric mean are also explored. |
| title | Order Relations of the Wasserstein mean and the spectral geometric mean |
| topic | Functional Analysis 15A42, 15A45, 15B48 |
| url | https://arxiv.org/abs/2312.15394 |