| [ QuizWit ] in KIDS 글 쓴 이(By): guest (wiking) 날 짜 (Date): 1998년 5월 4일 월요일 오전 07시 54분 47초 제 목(Title): Re: linear algebra 3. Known Fact: A=(Aij = xi^(j-1)) where xi's are different is non-singular. Claim: rank(H) = rank(H2) where H2 = (1/(i+j)) Now I want to show H2 is positive-definite. First we observe <e|H2|e> = int[a in [0,1]](a*(sum(ei*a^(i-1)))^2). Using Known Fact, we know the intergral should be positive for all non zero e. As a result, rank(H) = n. |