Non-archimedean valuations of eigenvalues of matrix polynomials

Also arXiv:1601.00438International audienceWe establish general weak majorization inequalities, relating the leadingexponents of the eigenvalues of matrices or matrix polynomials over the fieldof Puiseux series with the tropical analogues of eigenvalues. We also show thatthese inequalities become equalities under genericity conditions, and that theleading coefficients of the eigenvalues are determined as the eigenvalues ofauxiliary matrix polynomials