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Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 1) | |
| Auteur(s) : BOYLE MIKE
18-06-2013
Éditeur(s) : Fanny Bastien; Description : Lecture I. I’ll give a complete elementary presentation of the essential features of the Perron Frobenius theory of nonnegative matrices for the central case of primitive matrices (the "Perron" part). (The "Frobenius" part, for irreducible matrices, and finally the case for general nonnegative matrices, will be described, with proofs left to accompanying notes.) For integer matrices we’ll relate "Perron numbers" to this and Mahler measures. Lecture II. I’ll describe how the Perron-Frobenius theory generalizes (and fails to generalize) to 1,2,... x 1,2,... nonnegative matrices. Lecture III. We’ll see the simple, potent formalism by which a certain zeta function can be associated to a nonnegative matrix, and its relation to the nonzero spectrum of the matrix, and how polynomial matrices can be used in this setting for constructions and conciseness. Lecture IV. We’ll describe a natural algebraic equivalence relation on finite square matrices over a semiring (such as Z, Z_+, R, ... ) which refines the nonzero spectrum and is related to K-theory. Mots-clés libres : Mathèmatiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory Classification générale : Mathématiques Accès à la ressource : http://www.canal-u.tv/video/institut_fourier/mike_... rtmpt://fms2.cerimes.fr:80/vod/institut_fourier/mi... Conditions d'utilisation : Droits réservés à l'éditeur et aux auteurs. CC BY-NC-ND 4.0 | DONNEES PEDAGOGIQUES Type pédagogique : cours / présentation Niveau : doctorat DONNEES TECHNIQUES Format : video/x-flv Taille : 2.31 Go Durée d'exécution : 1 heure 3 minutes 44 secondes |
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