# Linear Algebra Proof

## Homework Statement

L = lambda.

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

???

## 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?

Related Calculus and Beyond Homework Help News on Phys.org
Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

L = lambda.

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

???

## 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

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.