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An algorithm that carries a square matrix into its transpose by an involutory congruence transformation

2003
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The Electronic Journal of Linear Algebra
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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 X 2 = 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 obtained. As a by-product another interesting result is also established. Let G be a semisimple complex

doi:10.13001/1081-3810.1116
fatcat:7qrhto6djjdmri6kyz67qlviti