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arXiv · 2503.07980

A similarity canonical form for max-plus matrices and its eigenproblem

Haicheng Zhang·Xiyan Zhu
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Abstract

We provide a necessary and sufficient condition for matrices in the max-plus algebra to be pseudo-diagonalizable, calculate the powers of pseudo-diagonal matrices and prove the invariance of optimal-node matrices and separable matrices under similarity. As an application, we determine the eigenvalues and eigenspaces of pseudo-diagonalizable matrices.

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Haicheng Zhang, Xiyan Zhu. 2025-03-11. A similarity canonical form for max-plus matrices and its eigenproblem. https://arxiv.org/abs/2503.07980

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