We consider a matrix A such that QTAQ = diag()1, . .., Am), (1) where Q is orthogonal. We denote by qi the ith column of Q. We now consider the power method and the sequence D* defined as (k) = Au( k-1) (2) V (k) = 2 (1) / 112 (12) 1/2, (3) where we assume that |v) |2 = 1. Assume that we have Ox such that cos(Ok) = 91 1 I , ( k ) (4) with cos(60) * 0. Prove that m 2k 1 - cos(0k)2 5 ai = q v(0) a' E i (5) =2