Register to reply

Second Derivative of Determinant of Matrix?

by brydustin
Tags: derivative, determinant, matrix
Share this thread:
brydustin
#1
Dec31-11, 03:51 PM
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!
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100

Register to reply

Related Discussions
NxN-complex matrix, identified 2Nx2N-real matrix, determinant Linear & Abstract Algebra 2
Finding determinant given determinant of another matrix Calculus & Beyond Homework 3
Derivative of determinant wrt matrix Linear & Abstract Algebra 3
Derivative of Log Determinant of a Matrix w.r.t a parameter Calculus 1
A SPECIAL Derivative of Matrix Determinant (tensor involved) Calculus 1