@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-STXWBZP3-1
  skos:prefLabel "théorie des systèmes dynamiques"@fr, "dynamical systems theory"@en ;
  a skos:Concept ;
  skos:narrower psr:-HWJ1H8L3-4 .

psr:-JR0BZJDR-C
  skos:prefLabel "square matrix"@en, "matrice carrée"@fr ;
  a skos:Concept ;
  skos:narrower psr:-HWJ1H8L3-4 .

psr:-HWJ1H8L3-4
  skos:prefLabel "Perron-Frobenius theorem"@en, "théorème de Perron-Frobenius"@fr ;
  dc:created "2023-07-28"^^xsd:date ;
  skos:inScheme psr: ;
  a skos:Concept ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Perron%E2%80%93Frobenius_theorem>, <https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Perron-Frobenius> ;
  skos:broader psr:-STXWBZP3-1, psr:-J8SLM0HB-6, psr:-KQDNC91K-9, psr:-JR0BZJDR-C ;
  dc:modified "2023-08-24"^^xsd:date ;
  skos:definition """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. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Perron%E2%80%93Frobenius_theorem">https://en.wikipedia.org/wiki/Perron%E2%80%93Frobenius_theorem</a>)"""@en, """En algèbre linéaire et en théorie des graphes, le théorème de Perron-Frobenius, démontré par Oskar Perron et Ferdinand Georg Frobenius, a d'importantes applications en théorie des probabilités (chaînes de Markov), en théorie des systèmes dynamiques, en économie (analyse entrée-sortie), en théorie des graphes, en dynamique des populations (matrices de Leslie) et dans l'aspect mathématique du calcul des pagerank de Google. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Perron-Frobenius">https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Perron-Frobenius</a>)"""@fr .

psr: a skos:ConceptScheme .
psr:-KQDNC91K-9
  skos:prefLabel "processus de Markov"@fr, "Markov process"@en ;
  a skos:Concept ;
  skos:narrower psr:-HWJ1H8L3-4 .

psr:-J8SLM0HB-6
  skos:prefLabel "graph theory"@en, "théorie des graphes"@fr ;
  a skos:Concept ;
  skos:narrower psr:-HWJ1H8L3-4 .