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

psr: a skos:ConceptScheme .
psr:-H51QJWDQ-L
  skos:prefLabel "espace de Minkowski"@fr, "Minkowski space"@en ;
  a skos:Concept ;
  skos:broader psr:-MKZ7N5M3-5 .

psr:-MKZ7N5M3-5
  skos:exactMatch <https://en.wikipedia.org/wiki/Pseudo-Euclidean_space>, <https://fr.wikipedia.org/wiki/Espace_pseudo-euclidien> ;
  skos:narrower psr:-H51QJWDQ-L ;
  skos:inScheme psr: ;
  skos:definition """En mathématiques, et plus particulièrement en géométrie, un espace pseudo-euclidien est une extension du concept d'espace euclidien, c'est-à-dire que c'est un espace vectoriel muni d'une forme bilinéaire (qui définirait la métrique dans le cas d'un espace euclidien), mais cette forme n'est pas définie positive, ni même positive. L'espace de Minkowski est un exemple d'espace pseudo-euclidien. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Espace_pseudo-euclidien">https://fr.wikipedia.org/wiki/Espace_pseudo-euclidien</a>)"""@fr, """In mathematics and theoretical physics, a <b>pseudo-Euclidean space</b> is a finite-dimensional real <span class="texhtml"><i>n</i></span>-space together with a non-degenerate quadratic form <span class="texhtml"><i>q</i></span>. Such a quadratic form can, given a suitable choice of basis <span class="texhtml">(<i>e</i><sub>1</sub>, …, <i>e</i><sub><i>n</i></sub>)</span>, be applied to a vector <span class="texhtml"><i>x</i> = <i>x</i><sub>1</sub><i>e</i><sub>1</sub> + ⋯ + <i>x</i><sub><i>n</i></sub><i>e</i><sub><i>n</i></sub></span>, giving
<br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle q(x)=\\\\left(x_{1}^{2}+\\\\dots +x_{k}^{2}\\
ight)-\\\\left(x_{k+1}^{2}+\\\\dots +x_{n}^{2}\\
ight)}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>q</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mrow>
<br/>          <mo>(</mo>
<br/>          <mrow>
<br/>            <msubsup>
<br/>              <mi>x</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>1</mn>
<br/>              </mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>2</mn>
<br/>              </mrow>
<br/>            </msubsup>
<br/>            <mo>+</mo>
<br/>            <mo>⋯<!-- ⋯ --></mo>
<br/>            <mo>+</mo>
<br/>            <msubsup>
<br/>              <mi>x</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>k</mi>
<br/>              </mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>2</mn>
<br/>              </mrow>
<br/>            </msubsup>
<br/>          </mrow>
<br/>          <mo>)</mo>
<br/>        </mrow>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mrow>
<br/>          <mo>(</mo>
<br/>          <mrow>
<br/>            <msubsup>
<br/>              <mi>x</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>k</mi>
<br/>                <mo>+</mo>
<br/>                <mn>1</mn>
<br/>              </mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>2</mn>
<br/>              </mrow>
<br/>            </msubsup>
<br/>            <mo>+</mo>
<br/>            <mo>⋯<!-- ⋯ --></mo>
<br/>            <mo>+</mo>
<br/>            <msubsup>
<br/>              <mi>x</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>n</mi>
<br/>              </mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>2</mn>
<br/>              </mrow>
<br/>            </msubsup>
<br/>          </mrow>
<br/>          <mo>)</mo>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle q(x)=\\\\left(x_{1}^{2}+\\\\dots +x_{k}^{2}\\
ight)-\\\\left(x_{k+1}^{2}+\\\\dots +x_{n}^{2}\\
ight)}</annotation>
<br/>  </semantics>
<br/></math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1156c830a451f8538a95e64d233dd9d18555eba8" class="mwe-math-fallback-image-display" aria-hidden="true" style="vertical-align: -1.171ex; width:43.085ex; height:3.343ex;" alt="{\\\\displaystyle q(x)=\\\\left(x_{1}^{2}+\\\\dots +x_{k}^{2}\\
ight)-\\\\left(x_{k+1}^{2}+\\\\dots +x_{n}^{2}\\
ight)}"></div> which is called the <i>scalar square</i> of the vector <span class="texhtml"><i>x</i></span>. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Pseudo-Euclidean_space">https://en.wikipedia.org/wiki/Pseudo-Euclidean_space</a>)"""@en ;
  skos:prefLabel "espace pseudo-euclidien"@fr, "pseudo-Euclidean space"@en ;
  skos:broader psr:-TJ9ZMMDF-W ;
  a skos:Concept .

psr:-TJ9ZMMDF-W
  skos:prefLabel "géométrie"@fr, "geometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-MKZ7N5M3-5 .