W.Wang.J.Zhao Linear Algebra and its Applications 291 (1999)185-199 191 Proof.Let (Q()'=w then Eq.(13)gives 1=w(⑧) UR, andU=R-l.▣ Lemma 3.2.Assume that V=-R-TY,R given in Eq.(13),Q is M-invariant,and O=On..0,where Oi are M-invariant reflection with O2=I,such that e()=(8) (15) where Ik is the k x k identity matrix and D is a k xk matrix.Then ()-(8) If U is upper triangular,then U=R,and ()=() Proof.Since is M-invariant,then is M--invariant.We choose row M--invariant matrix O-T,such that e()(8) where D is nonsingular. For =I and the definition of V,we obtain e()() Let e-(888)adg-(88)