19. Let X = (XI" . . , Xp ) and Y = (YI , .. . , ~) be independently distributed according to p-variate normal distributions with zero means and covariance matrices E(X;X.;) = aij and E(Y;lj) = !::J.a;j ' (i) The problem of testing H: !::J. s !::J.o remains invariant under the group G of transformations X· = XA, Y· = YA, where A = (ai j) is any nonsingular p X P matrix with aij = 0 for i > j , and there exists a UMP invariant test under G with rejection region yI 2 I xf > c.