@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:-C4BXTZC6-H
  skos:prefLabel "geometric figure"@en, "figure géométrique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-FC1QRB6L-7 .

psr:-ZTD7VMDS-3
  skos:prefLabel "analyse convexe"@fr, "convex analysis"@en ;
  a skos:Concept ;
  skos:narrower psr:-FC1QRB6L-7 .

psr: a skos:ConceptScheme .
psr:-KRMCJZW3-1
  skos:prefLabel "symmetric cone"@en, "cône symétrique"@fr ;
  a skos:Concept ;
  skos:broader psr:-FC1QRB6L-7 .

psr:-FC1QRB6L-7
  skos:prefLabel "convex cone"@en, "cône convexe"@fr ;
  dc:created "2023-07-28"^^xsd:date ;
  skos:broader psr:-C4BXTZC6-H, psr:-W0JJX1W8-X, psr:-ZTD7VMDS-3 ;
  skos:definition """En algèbre linéaire, un cône convexe est une partie d'un espace vectoriel sur un corps ordonné qui est stable par combinaisons linéaires à coefficients strictement positifs. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/C%C3%B4ne_convexe">https://fr.wikipedia.org/wiki/C%C3%B4ne_convexe</a>)"""@fr, """In linear algebra, a cone—sometimes called a linear cone for distinguishing it from other sorts of cones—is a subset of a vector space that is closed under positive scalar multiplication; that is, <span class="texhtml mvar" style="font-style:italic;">C</span> is a cone if <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle x\\\\in C}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>x</mi>
         <mo>∈<!-- ∈ --></mo>
         <mi>C</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle x\\\\in C}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7fc788379bff7289bdf694ffd68ee690e999eb7" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.937ex; height:2.176ex;" alt="x\\\\in C"></span> implies <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle sx\\\\in C}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>s</mi>
         <mi>x</mi>
         <mo>∈<!-- ∈ --></mo>
         <mi>C</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle sx\\\\in C}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3fea2be1b29260df5b8ada71962e13c08a04a77" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.027ex; height:2.176ex;" alt="{\\\\displaystyle sx\\\\in C}"></span> for every <span class="nowrap">positive scalar <span class="texhtml mvar" style="font-style:italic;">s</span></span>. When the scalars are real numbers, or belong to an ordered field, one generally calls a cone a subset of a vector space that is closed under multiplication by a positive scalar. In this context, a convex cone is a cone that is closed under addition, or, equivalently, a subset of a vector space that is closed under linear combinations with positive coefficients. It follows that convex cones are convex sets. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Convex_cone">https://en.wikipedia.org/wiki/Convex_cone</a>)"""@en ;
  dc:modified "2023-07-28"^^xsd:date ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/C%C3%B4ne_convexe>, <https://en.wikipedia.org/wiki/Convex_cone> ;
  skos:inScheme psr: ;
  a skos:Concept ;
  skos:narrower psr:-KRMCJZW3-1 .

psr:-W0JJX1W8-X
  skos:prefLabel "vector space"@en, "espace vectoriel"@fr ;
  a skos:Concept ;
  skos:narrower psr:-FC1QRB6L-7 .