# Independence and orthogonality of algebraic eigenvectors over the max-plus algebra

@inproceedings{Nishida2021IndependenceAO, title={Independence and orthogonality of algebraic eigenvectors over the max-plus algebra}, author={Yuki Nishida and Sennosuke Watanabe and Yoshihide Watanabe}, year={2021} }

The max-plus algebra R ∪ {−∞} is a semiring with the two operations: addition a ⊕ b := max(a, b) and multiplication a ⊗ b := a + b. Roots of the characteristic polynomial of a max-plus matrix are called algebraic eigenvalues. Recently, algebraic eigenvectors with respect to algebraic eigenvalues were introduced as a generalized concept of eigenvectors. In this paper, we present properties of algebraic eigenvectors analogous to those of eigenvectors in the conventional linear algebra. First, we…

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