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arXiv · 2605.27302

On matrix polynomials and the joint spectral radius over max-algebras

Askar Ali M·Sachindranath Jayaraman
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Abstract

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 $\Psi$ of matrix polynomials, measured in terms of the seminorms $\eta_{\|\cdot\|}$ and $\hat{\eta}_{\|\cdot\|}$ with the induced joint spectral radius of the coefficient pool $\Psi_0$ 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.

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Askar Ali M, Sachindranath Jayaraman. 2026-05-26. On matrix polynomials and the joint spectral radius over max-algebras. https://arxiv.org/abs/2605.27302

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