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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.04101 |
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| _version_ | 1866913303471587328 |
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| author | Huang, Huajun Tam, Tin-Yau |
| author_facet | Huang, Huajun Tam, Tin-Yau |
| contents | A result of Nayak asserts that $\underset{m\to \infty}\lim |A^m|^{1/m}$ exists for each $n\times n$ complex matrix $A$, where $|A| = (A^*A)^{1/2}$, and the limit is given in terms of the spectral decomposition. We extend the result of Nayak, namely, we prove that the limit of $\underset{m\to \infty}\lim |BA^mC|^{1/m}$ exists for any $n\times n$ complex matrices $A$, $B$, and $C$ where $B$ and $C$ are nonsingular; the limit is obtained and is independent of $B$. We then provide generalization in the context of real semisimple Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04101 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extensions of Yamamoto-Nayak's Theorem Huang, Huajun Tam, Tin-Yau Group Theory Representation Theory 15A18 (Primary), 15A45, 22E46 (Secondary) A result of Nayak asserts that $\underset{m\to \infty}\lim |A^m|^{1/m}$ exists for each $n\times n$ complex matrix $A$, where $|A| = (A^*A)^{1/2}$, and the limit is given in terms of the spectral decomposition. We extend the result of Nayak, namely, we prove that the limit of $\underset{m\to \infty}\lim |BA^mC|^{1/m}$ exists for any $n\times n$ complex matrices $A$, $B$, and $C$ where $B$ and $C$ are nonsingular; the limit is obtained and is independent of $B$. We then provide generalization in the context of real semisimple Lie groups. |
| title | Extensions of Yamamoto-Nayak's Theorem |
| topic | Group Theory Representation Theory 15A18 (Primary), 15A45, 22E46 (Secondary) |
| url | https://arxiv.org/abs/2308.04101 |