VERIFYING UNITARY CONGRUENCE OF CONINVOLUTIONS, SKEW-CONINVOLUTIONS, AND CONNILPOTENT MATRICES OF INDEX TWO

摘要

It is shown that n x n solutions A and B of the matrix equationrnXX = δI,rnwhere δ is one and the same for both matrices, are unitarily congruent if and only ifrntr(A~*A)~k =tT(B~*B)~k, k = 1,2,…,n.