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

• Published in: arXiv.org
• Main Authors: Nishida, Yuki, Watanabe, Sennosuke, Watanabe, Yoshihide
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 04.10.2021
• Subjects: Eigenvalues; Eigenvectors; Linear algebra; Mathematical analysis; Matrices (mathematics); Matrix algebra; Multiplication; Orthogonality; Polynomials

The max-plus algebra \(\mathbb{R}\cup \{-\infty \}\) is a semiring with the two operations: addition \(a \oplus b := \max(a,b)\) and multiplication \(a \otimes b := a + b\). Roots of the characteristic polynomial of a max-plus matrix are called algebraic eigenvalues. Recently, algebraic eigenvectors...