@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:-KSXWNH06-H
  skos:prefLabel "matrix"@en, "matrice"@fr ;
  a skos:Concept ;
  skos:narrower psr:-KS49LW2Q-H .

psr: a skos:ConceptScheme .
psr:-KS49LW2Q-H
  skos:altLabel "matrice transposée"@fr ;
  skos:prefLabel "transpose"@en, "transposée"@fr ;
  skos:inScheme psr: ;
  a skos:Concept ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:definition """In linear algebra,  the <b>transpose</b> of a matrix is an operator which flips a matrix over its diagonal;  that is, it switches the row and column indices of the matrix <span class="texhtml"><b>A</b></span> by producing another matrix, often denoted by <span class="texhtml"><b>A</b><sup>T</sup></span> (among other notations).  The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. In the case of a logical matrix representing a binary relation R, the transpose corresponds to the converse relation R<sup>T</sup>.  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Transpose">https://en.wikipedia.org/wiki/Transpose</a>)"""@en, """En mathématiques, la <b>matrice transposée</b> (ou la <b>transposée</b>) d'une matrice <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 A\\\\in \\\\mathrm {M} _{m,n}(K)}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>A</mi>         <mo>∈<!-- ∈ --></mo>         <msub>           <mrow class="MJX-TeXAtom-ORD">             <mi mathvariant="normal">M</mi>           </mrow>           <mrow class="MJX-TeXAtom-ORD">             <mi>m</mi>             <mo>,</mo>             <mi>n</mi>           </mrow>         </msub>         <mo stretchy="false">(</mo>         <mi>K</mi>         <mo stretchy="false">)</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle A\\\\in \\\\mathrm {M} _{m,n}(K)}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a7c5c3e34ba8aecc5b0531f78687664cb1f5f0" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.709ex; height:3.009ex;" alt="{\\\\displaystyle A\\\\in \\\\mathrm {M} _{m,n}(K)}"></span> est la matrice <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 A^{\\\\mathsf {T}}\\\\in \\\\mathrm {M} _{n,m}(K)}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi>A</mi>           <mrow class="MJX-TeXAtom-ORD">             <mrow class="MJX-TeXAtom-ORD">               <mi mathvariant="sans-serif">T</mi>             </mrow>           </mrow>         </msup>         <mo>∈<!-- ∈ --></mo>         <msub>           <mrow class="MJX-TeXAtom-ORD">             <mi mathvariant="normal">M</mi>           </mrow>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>             <mo>,</mo>             <mi>m</mi>           </mrow>         </msub>         <mo stretchy="false">(</mo>         <mi>K</mi>         <mo stretchy="false">)</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle A^{\\\\mathsf {T}}\\\\in \\\\mathrm {M} _{n,m}(K)}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e975cb4d0716601229d4e948fbd5bcd684e13d99" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.06ex; height:3.343ex;" alt="{\\\\displaystyle A^{\\\\mathsf {T}}\\\\in \\\\mathrm {M} _{n,m}(K)}"></span>, également notée <span class="nowrap"><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 A^{\\\\operatorname {t} }}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi>A</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi mathvariant="normal">t</mi>           </mrow>         </msup>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle A^{\\\\operatorname {t} }}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab2f79932cebe05278538ba0867518813cd2081b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.615ex; height:2.509ex;" alt="{\\\\displaystyle A^{\\\\operatorname {t} }}"></span>,</span> <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 ^{\\\\operatorname {t} }\\\\!A}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi></mi>           <mrow class="MJX-TeXAtom-ORD">             <mi mathvariant="normal">t</mi>           </mrow>         </msup>         <mspace width="negativethinmathspace"></mspace>         <mi>A</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle ^{\\\\operatorname {t} }\\\\!A}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4812e26e6031a77dbf2993e7bfb4368b6ed85f4" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.228ex; height:2.509ex;" alt="{\\\\displaystyle ^{\\\\operatorname {t} }\\\\!A}"></span> ou <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 A'}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi>A</mi>           <mo>′</mo>         </msup>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle A'}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98a12527148d6ed68adc91d9b419eb4b92d58ef6" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.428ex; height:2.509ex;" alt="{\\\\displaystyle A'}"></span></span>, obtenue en échangeant les lignes et les colonnes de <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 A}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>A</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle A}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\\\\displaystyle A}"></span>.  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Matrice_transpos%C3%A9e">https://fr.wikipedia.org/wiki/Matrice_transpos%C3%A9e</a>)"""@fr ;
  skos:broader psr:-KSXWNH06-H ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Matrice_transpos%C3%A9e>, <https://en.wikipedia.org/wiki/Transpose> .