@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:-JR0BZJDR-C
  skos:prefLabel "square matrix"@en, "matrice carrée"@fr ;
  a skos:Concept ;
  skos:narrower psr:-SC8HM1Z6-2 .

psr: a skos:ConceptScheme .
psr:-C5Z50ZLJ-J
  skos:prefLabel "identity matrix"@en, "matrice identité"@fr ;
  a skos:Concept ;
  skos:broader psr:-SC8HM1Z6-2 .

psr:-SC8HM1Z6-2
  dc:modified "2024-10-18"^^xsd:date ;
  skos:definition """In linear algebra, a <b>diagonal matrix</b> is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is <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 \\\\left[{\\egin{smallmatrix}3&amp;0\\\\\\\\0&amp;2\\\\end{smallmatrix}}\\
ight]}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow>           <mo>[</mo>           <mrow class="MJX-TeXAtom-ORD">             <mstyle scriptlevel="1">               <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false">                 <mtr>                   <mtd>                     <mn>3</mn>                   </mtd>                   <mtd>                     <mn>0</mn>                   </mtd>                 </mtr>                 <mtr>                   <mtd>                     <mn>0</mn>                   </mtd>                   <mtd>                     <mn>2</mn>                   </mtd>                 </mtr>               </mtable>             </mstyle>           </mrow>           <mo>]</mo>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\left[{\\egin{smallmatrix}3&amp;0\\\\\\\\0&amp;2\\\\end{smallmatrix}}\\
ight]}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbd1681ed0048aa1b28a2e9b5f6bb834b1cc3b14" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:5.108ex; height:3.343ex;" alt="{\\\\displaystyle \\\\left[{\\egin{smallmatrix}3&amp;0\\\\\\\\0&amp;2\\\\end{smallmatrix}}\\
ight]}"></span>, while an example of a 3×3 diagonal matrix is<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 \\\\left[{\\egin{smallmatrix}6&amp;0&amp;0\\\\\\\\0&amp;5&amp;0\\\\\\\\0&amp;0&amp;4\\\\end{smallmatrix}}\\
ight]}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow>           <mo>[</mo>           <mrow class="MJX-TeXAtom-ORD">             <mstyle scriptlevel="1">               <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false">                 <mtr>                   <mtd>                     <mn>6</mn>                   </mtd>                   <mtd>                     <mn>0</mn>                   </mtd>                   <mtd>                     <mn>0</mn>                   </mtd>                 </mtr>                 <mtr>                   <mtd>                     <mn>0</mn>                   </mtd>                   <mtd>                     <mn>5</mn>                   </mtd>                   <mtd>                     <mn>0</mn>                   </mtd>                 </mtr>                 <mtr>                   <mtd>                     <mn>0</mn>                   </mtd>                   <mtd>                     <mn>0</mn>                   </mtd>                   <mtd>                     <mn>4</mn>                   </mtd>                 </mtr>               </mtable>             </mstyle>           </mrow>           <mo>]</mo>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\left[{\\egin{smallmatrix}6&amp;0&amp;0\\\\\\\\0&amp;5&amp;0\\\\\\\\0&amp;0&amp;4\\\\end{smallmatrix}}\\
ight]}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bad34bc0da45cc29d4095720a4a8c9b2cac2a26" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:7.219ex; height:6.176ex;" alt="{\\\\displaystyle \\\\left[{\\egin{smallmatrix}6&amp;0&amp;0\\\\\\\\0&amp;5&amp;0\\\\\\\\0&amp;0&amp;4\\\\end{smallmatrix}}\\
ight]}"></span>. An identity matrix of any size, or any multiple of it is a diagonal matrix called <i>scalar matrix</i>, for example, <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 \\\\left[{\\egin{smallmatrix}0.5&amp;0\\\\\\\\0&amp;0.5\\\\end{smallmatrix}}\\
ight]}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow>           <mo>[</mo>           <mrow class="MJX-TeXAtom-ORD">             <mstyle scriptlevel="1">               <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false">                 <mtr>                   <mtd>                     <mn>0.5</mn>                   </mtd>                   <mtd>                     <mn>0</mn>                   </mtd>                 </mtr>                 <mtr>                   <mtd>                     <mn>0</mn>                   </mtd>                   <mtd>                     <mn>0.5</mn>                   </mtd>                 </mtr>               </mtable>             </mstyle>           </mrow>           <mo>]</mo>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\left[{\\egin{smallmatrix}0.5&amp;0\\\\\\\\0&amp;0.5\\\\end{smallmatrix}}\\
ight]}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ae9d50cf77850fc91f92a367564eafc7f1f4718" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:7.667ex; height:3.343ex;" alt="{\\\\displaystyle \\\\left[{\\egin{smallmatrix}0.5&amp;0\\\\\\\\0&amp;0.5\\\\end{smallmatrix}}\\
ight]}"></span>.  In geometry, a diagonal matrix may be used as a <i>scaling matrix</i>, since matrix multiplication with it results in changing scale (size) and possibly also shape; only a scalar matrix results in uniform change in scale.  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Diagonal_matrix">https://en.wikipedia.org/wiki/Diagonal_matrix</a>)"""@en, """En algèbre linéaire, une matrice diagonale est une matrice carrée dont les coefficients en dehors de la diagonale principale sont nuls. Les coefficients de la diagonale peuvent être ou ne pas être nuls.
<br/>Une matrice diagonale est une matrice qui correspond à la représentation d'un endomorphisme diagonalisable dans une base de vecteurs propres. La matrice d'un endomorphisme diagonalisable est semblable à une matrice diagonale.
<br/>Toute matrice diagonale est symétrique, normale et triangulaire. La matrice identité In est diagonale. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Matrice_diagonale">https://fr.wikipedia.org/wiki/Matrice_diagonale</a>)"""@fr ;
  skos:broader psr:-JR0BZJDR-C ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Matrice_diagonale>, <https://en.wikipedia.org/wiki/Diagonal_matrix> ;
  skos:narrower psr:-C5Z50ZLJ-J ;
  skos:prefLabel "matrice diagonale"@fr, "diagonal matrix"@en ;
  skos:inScheme psr: ;
  a skos:Concept .