| [ QuizWit ] in KIDS 글 쓴 이(By): jccha (잊으면그만) 날 짜 (Date): 1999년 5월 31일 월요일 오후 03시 36분 32초 제 목(Title): Re: [답] matrix derivative A known linear algebraic answer: View det A(t) as a composition of f:R->R^{n^2}, f(t)=a_ij(t) and g:R^{n^2}->R, g(x_ij)=det(x_ij). Partial derivatives are given by dx_ij/dt=da_ij/dt and dg/dx_ij = C_ji, where C_ij is the ij-cofactor of A. Then d/dt (det A(t)) = sum_ij (da_ij/dt)(C_ji) = trace (dA/dt A^adj) = (det A) trace(dA/dt A^{-1}) by the chain rule and the fact A A^adj = (det A)I, where A^adj=(C_ij) is the adjoint matrix of A, |