Non-archimedean valuations of eigenvalues of matrix polynomials

Abstract

We establish general weak majorization inequalities, relating the leading exponents of the eigenvalues of matrices or matrix polynomials over the field of Puiseux series with the tropical analogues of eigenvalues. We also show that these inequalities become equalities under genericity conditions, and that the leading coefficients of the eigenvalues are determined as the eigenvalues of auxiliary matrix polynomials.

31 pages, 2 figures. arXiv admin note: text overlap with arXiv:math/0402090

References in corpus (2)

• Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem
• Perturbation of eigenvalues of matrix pencils and optimal assignment problem

Cited by in corpus (2)

• Tropical totally positive matrices
• Tropical compound matrix identities