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Vidéo Année : 2013

Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 4)

Afficher 

Mike Boyle
  • Fonction : Orateur
  • PersonId : 828899
Fanny Bastien
Vanille Beaumont
  • Fonction : Monteur

Résumé

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.

Dates et versions

medihal-01319278 , version 1 (20-05-2016)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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  • HAL Id : medihal-01319278 , version 1

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Mike Boyle, Fanny Bastien, Vanille Beaumont. Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 4) : Summer School 2013 - Number theory and dynamics. 2013. ⟨medihal-01319278⟩
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