@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:-BM60WV5C-0
  skos:prefLabel "forme sesquilinéaire"@fr, "sesquilinear form"@en ;
  a skos:Concept ;
  skos:broader psr:-Q8X6082L-Q .

psr:-Q8X6082L-Q
  skos:prefLabel "forme multilinéaire"@fr, "multilinear form"@en ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Multilinear_form>, <https://fr.wikipedia.org/wiki/Forme_multilin%C3%A9aire> ;
  skos:definition """In abstract algebra and multilinear algebra, a <b>multilinear form</b> on a vector space <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 V}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>V</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle V}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\\\\displaystyle V}"></span> over a field <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 K}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>K</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle K}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b76fce82a62ed5461908f0dc8f037de4e3686b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.066ex; height:2.176ex;" alt="{\\\\displaystyle K}"></span> is a map  <dl><dd><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 f\\\\colon V^{k}\\	o K}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>f</mi>         <mo>:<!-- : --></mo>         <msup>           <mi>V</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>k</mi>           </mrow>         </msup>         <mo stretchy="false">→<!-- → --></mo>         <mi>K</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle f\\\\colon V^{k}\\	o K}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08d4a04ab6d8e7573e087d155de44dccd8f0695d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.998ex; height:3.009ex;" alt="{\\\\displaystyle f\\\\colon V^{k}\\	o K}"></span></dd></dl> that is separately <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 K}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>K</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle K}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b76fce82a62ed5461908f0dc8f037de4e3686b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.066ex; height:2.176ex;" alt="{\\\\displaystyle K}"></span>-linear in each of its <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 k}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>k</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle k}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\\\\displaystyle k}"></span> arguments. More generally, one can define multilinear forms on a module over a commutative ring. The rest of this article, however, will only consider multilinear forms on finite-dimensional vector spaces.  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Multilinear_form">https://en.wikipedia.org/wiki/Multilinear_form</a>)"""@en, """En mathématiques, une forme multilinéaire est une application d'un produit d'espaces vectoriels dans leur corps de coefficients, qui est linéaire en chacune de ses variables. C'est donc un cas particulier d'application multilinéaire. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Forme_multilin%C3%A9aire">https://fr.wikipedia.org/wiki/Forme_multilin%C3%A9aire</a>)"""@fr ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:narrower psr:-X77F5QSS-2, psr:-BM60WV5C-0 ;
  skos:broader psr:-S7M9JFHC-2 ;
  skos:inScheme psr: ;
  a skos:Concept .

psr: a skos:ConceptScheme .
psr:-S7M9JFHC-2
  skos:prefLabel "application multilinéaire"@fr, "multilinear map"@en ;
  a skos:Concept ;
  skos:narrower psr:-Q8X6082L-Q .

psr:-X77F5QSS-2
  skos:prefLabel "bilinear form"@en, "forme bilinéaire"@fr ;
  a skos:Concept ;
  skos:broader psr:-Q8X6082L-Q .