Non-archimedean valuations of eigenvalues of matrix polynomials

Marianne Akian; Ravindra Bapat; Stéphane Gaubert

doi:10.1016/j.laa.2016.02.036

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arXiv · 1601.00438

Non-archimedean valuations of eigenvalues of matrix polynomials

Marianne Akian·Ravindra Bapat·Stéphane Gaubert

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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.

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BibTeX RIS

Marianne Akian, Ravindra Bapat, Stéphane Gaubert. 2016-01-04. Non-archimedean valuations of eigenvalues of matrix polynomials. https://doi.org/10.1016/j.laa.2016.02.036

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