A relation between the concepts of transposition, similarity, and symmetry, as well as matrix equations
Treść / Zawartość
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.