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Homework Statement
Let f: R^nxn -> R^nxn be the function f(A) = A^-1. ie f is the inverse function for some nxn matrix. Show it is differentiable and find the derivative.
Homework Equations
The Attempt at a Solution
I need to do something along the lines of (A + H)^-1 = A^-1 + f'(A)H + p(H) where p is a remainder term. I'm not sure how to expand this. I've looked in my notes and our lecturer did something along the lines of (A + H)^-1 - A^-1 = (A+H)^-1(I - (A+H)A^-1) = (A+H)^-1(-HA^-1). I can't really figure out what to do next since it doesn't seem easy to expand (A+H)^-1.