@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:-L84V4M82-V
  skos:prefLabel "isomorphisme"@fr, "isomorphism"@en ;
  a skos:Concept ;
  skos:narrower psr:-FNGRLNXL-K .

psr:-VVTJ8P47-K
  skos:prefLabel "application linéaire"@fr, "linear map"@en ;
  a skos:Concept ;
  skos:narrower psr:-FNGRLNXL-K .

psr:-FNGRLNXL-K
  skos:definition """The <b>rank–nullity theorem</b> is a theorem in linear algebra, which asserts:  <ul><li>the number of columns of a matrix <span class="texhtml"><i>M</i></span> is the sum of the rank of <span class="texhtml"><i>M</i></span> and the nullity of <span class="texhtml"><i>M</i></span>; and</li> <li>the dimension of the domain of a linear transformation <span class="texhtml mvar" style="font-style:italic;">f</span> is the sum of the rank of <span class="texhtml mvar" style="font-style:italic;">f</span> (the dimension of the image of <span class="texhtml mvar" style="font-style:italic;">f</span>) and the nullity of <span class="texhtml mvar" style="font-style:italic;">f</span> (the dimension of the kernel of <span class="texhtml mvar" style="font-style:italic;">f</span>).</li></ul> It follows that for linear transformations of vector spaces of equal finite dimension, either injectivity or surjectivity implies bijectivity. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem">https://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem</a>)"""@en, """En mathématiques, et plus précisément en algèbre linéaire, le théorème du rang lie le rang d'une application linéaire et la dimension de son noyau. C'est un corollaire d'un théorème d'isomorphisme. Il peut être interprété par la notion d'indice d'application linéaire.
<br/>En dimension finie, il permet notamment de caractériser l'inversibilité d'une application linéaire ou d'une matrice par son rang. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_du_rang">https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_du_rang</a>)"""@fr ;
  skos:related psr:-FH5Q6VMW-P, psr:-BX545GQ6-L ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_du_rang>, <https://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem> ;
  skos:broader psr:-VVTJ8P47-K, psr:-L84V4M82-V ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:inScheme psr: ;
  a skos:Concept ;
  skos:prefLabel "rank-nullity theorem"@en, "théorème du rang"@fr .

psr:-BX545GQ6-L
  skos:prefLabel "rang"@fr, "rank"@en ;
  a skos:Concept ;
  skos:related psr:-FNGRLNXL-K .

psr: a skos:ConceptScheme .
psr:-FH5Q6VMW-P
  skos:prefLabel "kernel"@en, "noyau"@fr ;
  a skos:Concept ;
  skos:related psr:-FNGRLNXL-K .