Non-archimedean valuations of eigenvalues of matrix polynomials
Résumé
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.