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mathematical physics > dynamical systems theory > Perron-Frobenius theorem
algebra > linear algebra > matrix > square matrix > Perron-Frobenius theorem
graph theory > Perron-Frobenius theorem
probability theory > stochastic process > Markov process > Perron-Frobenius theorem

Terme préférentiel

Perron-Frobenius theorem  

Définition(s)

  • In matrix theory, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique eigenvalue of largest magnitude and that eigenvalue is real. The corresponding eigenvector can be chosen to have strictly positive components, and also asserts a similar statement for certain classes of nonnegative matrices. This theorem has important applications to probability theory (ergodicity of Markov chains); to the theory of dynamical systems (subshifts of finite type); to economics (Okishio's theorem, Hawkins–Simon condition); to demography (Leslie population age distribution model); to social networks (DeGroot learning process); to Internet search engines (PageRank); and even to ranking of football teams. The first to discuss the ordering of players within tournaments using Perron–Frobenius eigenvectors is Edmund Landau.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Perron%E2%80%93Frobenius_theorem)

Concept(s) générique(s)

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http://data.loterre.fr/ark:/67375/PSR-HWJ1H8L3-4

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RDF/XML TURTLE JSON-LD Date de création 28/07/2023, dernière modif. 24/08/2023