Geodesic
An algorithm that carries a square matrix into its transpose by an involutory congruence transformation
The electronic journal of linear algebra, Tome 10 (2003), pp. 320-340.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For any matrix X let X0 denote its transpose. It is known that if A is an n-by-n matrix over a field F , then A and A0 are congruent over F , i.e., XAX0 = A0 for some X $2 G\Ln (F )$. 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 obtained.
Classification : 11E39, 15A63, 15A22
Keywords: congruence of matrices, transpose, rational solution, symplectic group 
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     title = {An algorithm that carries a square matrix into its transpose by an involutory congruence transformation},
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Djoković, Dragomir Ž.; Szechtman, F.; Zhao, K. An algorithm that carries a square matrix into its transpose by an involutory congruence transformation. The electronic journal of linear algebra, Tome 10 (2003), pp. 320-340. http://geodesic.mathdoc.fr/item/ELA_2003__10__a0/