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On the vectors associated with the roots of max-plus characteristic polynomials

Yuki Nishida; Sennosuke Watanabe; Yoshihide Watanabe — 2020

Applications of Mathematics

We discuss the eigenvalue problem in the max-plus algebra. For a max-plus square matrix, the roots of its characteristic polynomial are not its eigenvalues. In this paper, we give the notion of algebraic eigenvectors associated with the roots of characteristic polynomials. Algebraic eigenvectors are the analogues of the usual eigenvectors in the following three senses: (1) An algebraic eigenvector satisfies an equation similar to the equation $A \otimes x = λ \otimes x$ for usual eigenvectors. Under a suitable assumption,...

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