@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:-QGSG5CF3-S .

psr: a skos:ConceptScheme .
psr:-QGSG5CF3-S
  skos:broader psr:-KSXWNH06-H ;
  skos:definition """In mathematics, Specht's theorem gives a necessary and sufficient condition for two complex matrices to be unitarily equivalent. It is named after Wilhelm Specht, who proved the theorem in 1940.
<br/>Two matrices A and B with complex number entries are said to be unitarily equivalent if there exists a unitary matrix U such that B = U *AU. Two matrices which are unitarily equivalent are also similar. Two similar matrices represent the same linear map, but with respect to a different basis; unitary equivalence corresponds to a change from an orthonormal basis to another orthonormal basis.
<br/>If A and B are unitarily equivalent, then tr AA* = tr BB*, where tr denotes the trace (in other words, the Frobenius norm is a unitary invariant). This follows from the cyclic invariance of the trace: if B = U *AU, then tr BB* = tr U *AUU *A*U = tr AUU *A*UU * = tr AA*, where the second equality is cyclic invariance. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Specht%27s_theorem">https://en.wikipedia.org/wiki/Specht%27s_theorem</a>)"""@en, """En mathématiques, le théorème de Specht donne une condition nécessaire et suffisante pour que deux matrices soient unitairement équivalentes . Il porte le nom de Wilhelm Specht, qui a prouvé le théorème en 1940. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Specht">https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Specht</a>)"""@fr ;
  a skos:Concept ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:prefLabel "Specht's theorem"@en, "théorème de Specht"@fr ;
  dc:created "2023-07-28"^^xsd:date ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Specht%27s_theorem>, <https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Specht> .