Majorization inequalities for valuations of eigenvalues using tropical algebra - Département de mathématiques appliquées Accéder directement au contenu
Communication Dans Un Congrès Année : 2015

Majorization inequalities for valuations of eigenvalues using tropical algebra

Résumé

We consider a matrix with entries over the field of Puiseux series, equipped with its non-archimedean valuation (the leading exponent). We establish majorization inequalities relating the sequence of the valuations of the eigenvalues of a matrix with the tropical eigenvalues of its valuation matrix (the latter is obtained by taking the valuation entrywise). We also show that, generically in the leading coefficients of the Puiseux series, the precise asymptotics of eigenvalues, eigenvectors and condition numbers can be determined. For this, we apply diagonal scalings constructed from the dual variables of a parametric optimal assignment constructed from the valuation matrix. Next, we establish an archimedean analogue of the above inequalities, which applies to matrix polynomials with coefficients in the field of complex numbers, equipped with the modulus as its valuation. This talk covers joint works with Ravindra Bapat, Stéphane Gaubert, Andrea Marchesini, and Francoise Tisseur.
Fichier non déposé

Dates et versions

hal-01252363 , version 1 (07-01-2016)

Identifiants

  • HAL Id : hal-01252363 , version 1

Citer

Marianne Akian. Majorization inequalities for valuations of eigenvalues using tropical algebra. 4th International Conference on Matrix methods in Mathematics and Applications (MMMA-2015), Aug 2015, Moscow, Russia. ⟨hal-01252363⟩
276 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More