On matrix polynomials and the joint spectral radius over max-algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918534933643264 |
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| author | M, Askar Ali Jayaraman, Sachindranath |
| author_facet | M, Askar Ali Jayaraman, Sachindranath |
| contents | Our aim is to study matrix polynomials over max-algebras and their growth in terms of max-induced seminorms. In particular, we compare the set growth of a bounded family $Ψ$ of matrix polynomials, measured in terms of the seminorms $η_{\|\cdot\|}$ and $\hatη_{\|\cdot\|}$ with the induced joint spectral radius of the coefficient pool $Ψ_0$ of the matrix polynomials. Dynamics of max-linear maps and convergence to periodic points under a single joint spectral radius condition and the existence of common max-eigenvectors of the coefficient pool are also brought out. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_27302 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On matrix polynomials and the joint spectral radius over max-algebras M, Askar Ali Jayaraman, Sachindranath Rings and Algebras Primary: 15A80, 11B83, 15A18 Secondary: 37C25 Our aim is to study matrix polynomials over max-algebras and their growth in terms of max-induced seminorms. In particular, we compare the set growth of a bounded family $Ψ$ of matrix polynomials, measured in terms of the seminorms $η_{\|\cdot\|}$ and $\hatη_{\|\cdot\|}$ with the induced joint spectral radius of the coefficient pool $Ψ_0$ of the matrix polynomials. Dynamics of max-linear maps and convergence to periodic points under a single joint spectral radius condition and the existence of common max-eigenvectors of the coefficient pool are also brought out. |
| title | On matrix polynomials and the joint spectral radius over max-algebras |
| topic | Rings and Algebras Primary: 15A80, 11B83, 15A18 Secondary: 37C25 |
| url | https://arxiv.org/abs/2605.27302 |