| [ QuizWit ] in KIDS 글 쓴 이(By): jaekun (Yossarian) 날 짜 (Date): 2003년 10월 18일 토요일 오후 08시 38분 04초 제 목(Title): Re: 수학 질문 (product of p.d. matrices) Sorry, I cannot write Korean right now. Now I see that unlike the complex case, a positive definite matrix need not be symmetric, although many standard text books on linear algebra impose symmetry when defining positive definite matrices (See, for example, Anton). Hence the following holds (am i right?) If A and B are symmetric positive definite, then so is AB if and only if AB=BA. Then the problem we have is: Suppose A and B are positive, not necessarily symmetric matices. Can AB be positive definite if AB \neq BA? Mr. illusion may answer this question. ps. Mr. illusion, I don't understand your determinant argument. If A is positive symmetric, then surely its determinant is positive, but not vice versa. |