| [ QuizWit ] in KIDS 글 쓴 이(By): guest (guest) 날 짜 (Date): 1998년 5월 3일 일요일 오전 10시 54분 05초 제 목(Title): Re: linear algebra 2. (A-B)C=C(A-B) -> AC-CA=BC-CB. Let X=AC-CA=BC-CB. Then AX = A(CB-BC) = ... = -XB Now X'AX = -X'XB, where X' is the transpose of X. Since LHS is symmetric, RHS is also symmetric. Therefore X'X and B commutes. Then X'XB has only nonnegative eigenvalues. -> X'XB=0 -> X'X=0 -> X=0. |