| [ QuizWit ] in KIDS 글 쓴 이(By): jccha (잊으면그만) 날 짜 (Date): 1998년 5월 6일 수요일 오후 12시 37분 21초 제 목(Title): Re: 나도 선형대수 Linear algrbra becomes very popular! :) Answer: min(p,q) The key facts are sylvester's law of intertia and the observation that we can choose a basis of R^n so that Q is represented by [ 0 I 0 ] [ I 0 0 ] [ 0 0 X ] where the first block represents the restriction of Q on H, because Q is nondegenerated. (Do you know the proof of the existence of a sympletic basis for a skew-symmetric form? :) From the fact that [1 0] becomes [0 1] by adding the first row to the [0 -1] [1 0] other row and performing the same column operation, [0 I] becomes [I 0] [I 0] [0 -I] and so |p-q| = (signature of Q) = (signature of X) <= p+q - 2 dim H. Conversely, a metabolizer with the maximal dimension is easily realized, using the above matrix similarity relation. |