Date: Feb 26, 2013 10:19 AM
Author: Jose Carlos Santos
Subject: Unitary equivalence of real matrices

Hi all,

Let A an B be two square matrices over the reals with the same size and
suppose that they are unitarily equivalent, that is, that there is an
unitary matrix U such that U.A.U^{-1} = B. Does it follow that there is
an orthogonal real matrix M such that M.A.M^{-1} = B?

Best regards,

Jose Carlos Santos