Linear Algebra Proof

  • #1
chill_factor
901
5

Homework Statement



L = lambda.

Prove: d(A^-1)/dL = -(A^-1)(dA/dL)(A^-1)

Homework Equations



?

The Attempt at a Solution



I did this as an analogy with function of numbers, but don't know how to extend this to matricies. for example:

lets say A = f(L)

d(f(L)^-1)/dL = - (f(L)^-2*d(f(L))/dL = -(A^-1)*dA/dL*(A^-1)

But what is the matrix form?
 

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,722

Homework Statement



L = lambda.

Prove: d(A^-1)/dL = -(A^-1)(dA/dL)(A^-1)

Homework Equations



?

The Attempt at a Solution



I did this as an analogy with function of numbers, but don't know how to extend this to matricies. for example:

lets say A = f(L)

d(f(L)^-1)/dL = - (f(L)^-2*d(f(L))/dL = -(A^-1)*dA/dL*(A^-1)

But what is the matrix form?

I'll use x instead of L, and let B(x) = Inv(A(x)); thus, A(x)*B(x) = I (identity matrix). Take the derivative.

RGV
 
  • #3
chill_factor
901
5
I'll use x instead of L, and let B(x) = Inv(A(x)); thus, A(x)*B(x) = I (identity matrix). Take the derivative.

RGV

Thanks greatly.
 

Suggested for: Linear Algebra Proof

  • Last Post
Replies
1
Views
644
Replies
5
Views
335
Replies
8
Views
798
  • Last Post
Replies
8
Views
201
  • Last Post
Replies
4
Views
412
  • Last Post
Replies
6
Views
546
Replies
2
Views
669
Replies
18
Views
494
Replies
8
Views
937
Replies
25
Views
1K
Top