About: Dieudonné determinant

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In linear algebra, the Dieudonné determinant is a generalization of the determinant of a matrix to matrices over division rings and local rings. It was introduced by Dieudonné. If K is a division ring, then the Dieudonné determinant is a homomorphism of groups from the group GLn(K) of invertible n by n matrices over K onto the abelianization K×/[K×, K×] of the multiplicative group K× of K. For example, the Dieudonné determinant for a 2-by-2 matrix is the residue class, in K×/[K×, K×], of

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  • In linear algebra, the Dieudonné determinant is a generalization of the determinant of a matrix to matrices over division rings and local rings. It was introduced by Dieudonné. If K is a division ring, then the Dieudonné determinant is a homomorphism of groups from the group GLn(K) of invertible n by n matrices over K onto the abelianization K×/[K×, K×] of the multiplicative group K× of K. For example, the Dieudonné determinant for a 2-by-2 matrix is the residue class, in K×/[K×, K×], of (en)
  • En algèbre linéaire, le déterminant de Dieudonné est une généralisation du déterminant aux corps gauches et plus généralement aux anneaux locaux non nécessairement commutatifs. (fr)
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  • Determinant (en)
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  • In linear algebra, the Dieudonné determinant is a generalization of the determinant of a matrix to matrices over division rings and local rings. It was introduced by Dieudonné. If K is a division ring, then the Dieudonné determinant is a homomorphism of groups from the group GLn(K) of invertible n by n matrices over K onto the abelianization K×/[K×, K×] of the multiplicative group K× of K. For example, the Dieudonné determinant for a 2-by-2 matrix is the residue class, in K×/[K×, K×], of (en)
  • En algèbre linéaire, le déterminant de Dieudonné est une généralisation du déterminant aux corps gauches et plus généralement aux anneaux locaux non nécessairement commutatifs. (fr)
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  • Dieudonné determinant (en)
  • Déterminant de Dieudonné (fr)
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