Non-archimedean valuations of eigenvalues of matrix polynomials

Authors

Marianne Akian, Centre de Mathématiques Appliquées
Ravindra Bapat, Indian Statistical Institute (Delhi Centre)
Stéphane Gaubert, Centre de Mathématiques Appliquées

Article Type

Research Article

Publication Title

Linear Algebra and Its Applications

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.

First Page

592

Last Page

627

DOI

10.1016/j.laa.2016.02.036

Publication Date

6-1-2016

Comments

Open Access; Green Open Access

Recommended Citation

Akian, Marianne; Bapat, Ravindra; and Gaubert, Stéphane, "Non-archimedean valuations of eigenvalues of matrix polynomials" (2016). Journal Articles. 4317.
https://digitalcommons.isical.ac.in/journal-articles/4317