# Second Derivative of Determinant of Matrix?

by brydustin
Tags: derivative, determinant, matrix
 P: 209 Hi all.... I've read on wikipedia (facepalm) that the first derivative of a determinant is del(det(A))/del(A_ij) = det(A)*(inv(A))_j,i If we go to find the second derivative (applying power rule), we get: del^2(A) / (del(A)_pq) (del (A)_ij) = {del(det(A))/del(A_pq)}*(inv(A))_j,i + det(A)*{del(inv(A)_j,i) / del(A_pq)} I have no clue how to calculate the derivative of the inverse of a matrix with respect to changing the values in the original matrix: I.E. del(inv(A)_j,i) / del(A_pq) Also.... would be nice if someone could prove the first statement for the first derivative of the determinant. Thanks!

 Related Discussions Linear & Abstract Algebra 2 Calculus & Beyond Homework 3 Linear & Abstract Algebra 3 Calculus 1 Calculus 1