On a generalization of the Johnson-Newman theorem to multiple rank-one perturbations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917146453344256 |
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| author | Wang, Wei Wu, Siqi |
| author_facet | Wang, Wei Wu, Siqi |
| contents | Wang and Zhao (Adv. Appl. Math. 173 (2026) 102994) generalized the classic Johnson-Newman theorem on simultaneous similarity of symmetric matrices from a single rank-one perturbation to multiple rank-one perturbations. However, their result applies only to specific rank-one perturbations, and the given condition is quite involved as it relies on multivariate polynomials. We provide a simple proof of their result, leading to an improved version with a simplified condition that holds for arbitrary rank-one perturbations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a generalization of the Johnson-Newman theorem to multiple rank-one perturbations Wang, Wei Wu, Siqi Combinatorics 05C50 Wang and Zhao (Adv. Appl. Math. 173 (2026) 102994) generalized the classic Johnson-Newman theorem on simultaneous similarity of symmetric matrices from a single rank-one perturbation to multiple rank-one perturbations. However, their result applies only to specific rank-one perturbations, and the given condition is quite involved as it relies on multivariate polynomials. We provide a simple proof of their result, leading to an improved version with a simplified condition that holds for arbitrary rank-one perturbations. |
| title | On a generalization of the Johnson-Newman theorem to multiple rank-one perturbations |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2512.12599 |