Non-archimedean valuations of eigenvalues of matrix polynomials

作者：Akian Marianne; Bapat Ravindra; Gaubert Stephan

来源：Linear Algebra and Its Applications, 2016, 498: 592-627.

DOI：10.1016/j.laa.2016.02.036

• Perturbation theory
• Max-plus algebra
• Tropical semifield
• Spectral theory
• Newton-Puiseux theorem
• Amoeba
• Majorization
• Graphs
• Optimal assignment

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.

• 出版日期2016-6-1
• 单位INRIA