| [ QuizWit ] in KIDS 글 쓴 이(By): guest (wiking) 날 짜 (Date): 1998년 5월 6일 수요일 오전 12시 01분 24초 제 목(Title): Re: linear algebra 4. Define: N! = conjugate transpose of N. Claim1: If [N, N!] = 0, N can be diagonalized under Unitary Transform. Claim2: For a set of non-zero complex numbers, C = {ci} where |C| = m, {Ci = (cj^(i-1))} spans C^m Proof> W/O L.G, N can be written Diag(di) (and N! = Diag(di*)) from Claim1. From Claim2, there exists {bi} s.t (di*) = Sum(j)(bj*Cj) for distinct di's. In other words, N! = Sum(bj*N^(j-1)) = p(N) where |p| < m. |