A square matrix is congruent to its transpose

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A square matrix is congruent to its transpose

For any matrix X let X′ denote its transpose. We show that if A is an n by n matrix over a field K , then A and A′ are congruent over K , i.e., P ′AP =A′ for some P ∈ GLn(K).  2002 Elsevier Science (USA). All rights reserved.

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Ela an Algorithm That Carries a Square Matrix into Its Transpose by an Involutory Congruence

For any matrix X let X′ denote its transpose. It is known that if A is an n-by-n matrix over a field F , then A and A′ are congruent over F , i.e., XAX′ = A′ for some X ∈ GLn(F ). Moreover, X can be chosen so that X2 = In, where In is the identity matrix. An algorithm is constructed to compute such an X for a given matrix A. Consequently, a new and completely elementary proof of that result is ...

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ژورنال

عنوان ژورنال: Journal of Algebra

سال: 2002

ISSN: 0021-8693

DOI: 10.1016/s0021-8693(02)00126-6