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- Matrix_congruence abstract "In mathematics, two matrices A and B over a field are called congruent if there exists an invertible matrix P over the same field such that PTAP = Bwhere "T" denotes the matrix transpose. Matrix congruence is an equivalence relation.Matrix congruence arises when considering the effect of change of basis on the Gram matrix attached to a bilinear form or quadratic form on a finite-dimensional vector space: two matrices are congruent if and only if they represent the same bilinear form with respect to different bases.Note that Halmos defines congruence in terms of conjugate transpose (with respect to a complex inner product space) rather than transpose, but this definition has not been adopted by most other authors.".
- Matrix_congruence wikiPageID "2383040".
- Matrix_congruence wikiPageRevisionID "540589913".
- Matrix_congruence hasPhotoCollection Matrix_congruence.
- Matrix_congruence subject Category:Linear_algebra.
- Matrix_congruence subject Category:Matrices.
- Matrix_congruence type Abstraction100002137.
- Matrix_congruence type Arrangement107938773.
- Matrix_congruence type Array107939382.
- Matrix_congruence type Group100031264.
- Matrix_congruence type Matrices.
- Matrix_congruence type Matrix108267640.
- Matrix_congruence comment "In mathematics, two matrices A and B over a field are called congruent if there exists an invertible matrix P over the same field such that PTAP = Bwhere "T" denotes the matrix transpose.".
- Matrix_congruence label "Congruenza fra matrici".
- Matrix_congruence label "Gelijkvormige matrices".
- Matrix_congruence label "Kongruenz (Matrix)".
- Matrix_congruence label "Matrices congruentes".
- Matrix_congruence label "Matrix congruence".
- Matrix_congruence label "合同矩阵".
- Matrix_congruence sameAs Kongruenz_(Matrix).
- Matrix_congruence sameAs Matrices_congruentes.
- Matrix_congruence sameAs Congruenza_fra_matrici.
- Matrix_congruence sameAs Gelijkvormige_matrices.
- Matrix_congruence sameAs m.0781y3.
- Matrix_congruence sameAs Q377286.
- Matrix_congruence sameAs Q377286.
- Matrix_congruence sameAs Matrix_congruence.
- Matrix_congruence wasDerivedFrom Matrix_congruence?oldid=540589913.
- Matrix_congruence isPrimaryTopicOf Matrix_congruence.