@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr: a skos:ConceptScheme .
psr:-F16NMHR3-3
  skos:exactMatch <https://en.wikipedia.org/wiki/Symmetric_tensor>, <https://fr.wikipedia.org/wiki/Tenseur_sym%C3%A9trique> ;
  skos:prefLabel "tenseur symétrique"@fr, "symmetric tensor"@en ;
  a skos:Concept ;
  skos:definition """Un tenseur <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 \\\\mathrm {A} }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="normal">A</mi>
         </mrow>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathrm {A} }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff6366939c4ebbd4e8494d0dedc54c4b8dd7135a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\\\\mathrm  A}"></span> d'ordre 2 est dit symétrique si la forme bilinéaire associée est symétrique. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Tenseur_sym%C3%A9trique">https://fr.wikipedia.org/wiki/Tenseur_sym%C3%A9trique</a>)"""@fr, """In mathematics, a <b>symmetric tensor</b> is a tensor that is invariant under a permutation of its vector arguments:
<br/>
<br/><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 T(v_{1},v_{2},\\\\ldots ,v_{r})=T(v_{\\\\sigma 1},v_{\\\\sigma 2},\\\\ldots ,v_{\\\\sigma r})}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>T</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <msub>
<br/>          <mi>v</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>,</mo>
<br/>        <msub>
<br/>          <mi>v</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>,</mo>
<br/>        <mo>…<!-- … --></mo>
<br/>        <mo>,</mo>
<br/>        <msub>
<br/>          <mi>v</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>r</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mi>T</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <msub>
<br/>          <mi>v</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>σ<!-- σ --></mi>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>,</mo>
<br/>        <msub>
<br/>          <mi>v</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>σ<!-- σ --></mi>
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>,</mo>
<br/>        <mo>…<!-- … --></mo>
<br/>        <mo>,</mo>
<br/>        <msub>
<br/>          <mi>v</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>σ<!-- σ --></mi>
<br/>            <mi>r</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle T(v_{1},v_{2},\\\\ldots ,v_{r})=T(v_{\\\\sigma 1},v_{\\\\sigma 2},\\\\ldots ,v_{\\\\sigma r})}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103d7912c013f8cd6df2b9c5848d29e5e501989a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:38.165ex; height:2.843ex;" alt="{\\\\displaystyle T(v_{1},v_{2},\\\\ldots ,v_{r})=T(v_{\\\\sigma 1},v_{\\\\sigma 2},\\\\ldots ,v_{\\\\sigma r})}"></span></dd></dl>
<br/>for every permutation <i>σ</i> of the symbols <span class="nowrap">{1, 2, ..., <i>r</i>}.</span>  Alternatively, a symmetric tensor of order <i>r</i> represented in coordinates as a quantity with <i>r</i> indices satisfies
<br/>
<br/><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 T_{i_{1}i_{2}\\\\cdots i_{r}}=T_{i_{\\\\sigma 1}i_{\\\\sigma 2}\\\\cdots i_{\\\\sigma r}}.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>T</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <msub>
<br/>              <mi>i</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>1</mn>
<br/>              </mrow>
<br/>            </msub>
<br/>            <msub>
<br/>              <mi>i</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>2</mn>
<br/>              </mrow>
<br/>            </msub>
<br/>            <mo>⋯<!-- ⋯ --></mo>
<br/>            <msub>
<br/>              <mi>i</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>r</mi>
<br/>              </mrow>
<br/>            </msub>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>=</mo>
<br/>        <msub>
<br/>          <mi>T</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <msub>
<br/>              <mi>i</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>σ<!-- σ --></mi>
<br/>                <mn>1</mn>
<br/>              </mrow>
<br/>            </msub>
<br/>            <msub>
<br/>              <mi>i</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>σ<!-- σ --></mi>
<br/>                <mn>2</mn>
<br/>              </mrow>
<br/>            </msub>
<br/>            <mo>⋯<!-- ⋯ --></mo>
<br/>            <msub>
<br/>              <mi>i</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>σ<!-- σ --></mi>
<br/>                <mi>r</mi>
<br/>              </mrow>
<br/>            </msub>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle T_{i_{1}i_{2}\\\\cdots i_{r}}=T_{i_{\\\\sigma 1}i_{\\\\sigma 2}\\\\cdots i_{\\\\sigma r}}.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/495e48164fb9dd9afedee585e5d3262baf5d47e4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:21.329ex; height:2.843ex;" alt="{\\\\displaystyle T_{i_{1}i_{2}\\\\cdots i_{r}}=T_{i_{\\\\sigma 1}i_{\\\\sigma 2}\\\\cdots i_{\\\\sigma r}}.}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Symmetric_tensor">https://en.wikipedia.org/wiki/Symmetric_tensor</a>)"""@en ;
  skos:related psr:-P3L2KQWH-H ;
  skos:inScheme psr: ;
  skos:broader psr:-WVKDMZRV-6 .

psr:-P3L2KQWH-H
  skos:prefLabel "notation de Voigt"@fr, "Voigt notation"@en ;
  a skos:Concept ;
  skos:related psr:-F16NMHR3-3 .

psr:-WVKDMZRV-6
  skos:prefLabel "tenseur"@fr, "tensor"@en ;
  a skos:Concept ;
  skos:narrower psr:-F16NMHR3-3 .