@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:-JR0BZJDR-C
  skos:prefLabel "square matrix"@en, "matrice carrée"@fr ;
  a skos:Concept ;
  skos:narrower psr:-KGWKZXV3-R .

psr: a skos:ConceptScheme .
psr:-KGWKZXV3-R
  skos:inScheme psr: ;
  skos:altLabel "rational canonical form"@en ;
  a skos:Concept ;
  skos:prefLabel "décomposition de Frobenius"@fr, "Frobenius normal form"@en ;
  skos:broader psr:-JR0BZJDR-C ;
  skos:definition """In linear algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices obtained by conjugation by invertible matrices over F. The form reflects a minimal decomposition of the vector space into subspaces that are cyclic for A (i.e., spanned by some vector and its repeated images under A). Since only one normal form can be reached from a given matrix (whence the "canonical"), a matrix B is similar to A if and only if it has the same rational canonical form as A. Since this form can be found without any operations that might change when extending the field F (whence the "rational"), notably without factoring polynomials, this shows that whether two matrices are similar does not change upon field extensions. The form is named after German mathematician Ferdinand Georg Frobenius. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Frobenius_normal_form">https://en.wikipedia.org/wiki/Frobenius_normal_form</a>)"""@en, """On considère un K-espace vectoriel E de dimension finie et un endomorphisme u de cet espace. Une décomposition de Frobenius est une décomposition de E en somme directe de sous-espaces dits cycliques, telle que les polynômes minimaux (ou caractéristiques) respectifs des restrictions de u aux facteurs sont les facteurs invariants de u. La décomposition de Frobenius peut s'effectuer sur un corps quelconque : on ne suppose pas ici que K est algébriquement clos. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/D%C3%A9composition_de_Frobenius">https://fr.wikipedia.org/wiki/D%C3%A9composition_de_Frobenius</a>)"""@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/D%C3%A9composition_de_Frobenius>, <https://en.wikipedia.org/wiki/Frobenius_normal_form> ;
  dc:modified "2024-10-18"^^xsd:date .