Geodesic
A relation between the concepts of transposition, similarity, and symmetry, as well as matrix equations
Mathematica Applicanda, Tome 33 (2005) no. 47/06, pp. 21-28.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

The author studies relationships among the notions of transpose, similarity, and symmetrization of matrices. It is shown that a square matrix is similar to its transpose, and that there exists a matrix that, simultaneously, carries this similarity transformation and symmetrizes the matrix. Furthermore, some equalities involving adjoint matrices are established as well. The proofs of the results are formulated for complex matrices, but they are valid also for other algebraically closed fields.
DOI : 10.14708/ma.v33i47/06.1349
Classification : 15A24 (15A18)
Mots-clés : Matrix equations and identities, Eigenvalues, singular values, and eigenvectors 
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Tadeusz Kaczorek. A relation between the concepts of transposition, similarity, and symmetry, as well as matrix equations. Mathematica Applicanda, Tome 33 (2005) no. 47/06, pp.  21-28. doi : 10.14708/ma.v33i47/06.1349. http://geodesic.mathdoc.fr/articles/10.14708/ma.v33i47/06.1349/

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