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Non-archimedean valuations of eigenvalues of matrix polynomials

Marianne Akian 1, 2 Stéphane Gaubert 1, 2 Ravindra Bapat 3 
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
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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Submitted on : Wednesday, January 6, 2016 - 5:21:38 PM
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Marianne Akian, Stéphane Gaubert, Ravindra Bapat. Non-archimedean valuations of eigenvalues of matrix polynomials. Linear Algebra and its Applications, Elsevier, 2016, 498, pp.592-627. ⟨10.1016/j.laa.2016.02.036⟩. ⟨hal-01251803⟩



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