ON COMPUTATION OF SKEW-SYMMETRIC GENERATOR FOR AN ORTHOGONAL MATRIX

In this paper, we constructively prove that for any matrix A over a _eld of characteristic 0 and its eigenvalue _ 6= 0 there exists a diago-nal matrix D with diagonal coe_cients _1 such that DA has no eigenvalue_. Hence and by the canonical result on Cayley transformation, for each or-thogonal matrix U one can _nd a diagonal matrix D and a skew-symmetric matrix S such that U = D(S - I)-1(S + I).