I want to find the derivative of the $f:X→(X′X)^{-1}$ where $X$ is a $m×n$ matrix.
Now I know that the differential of $d(X^{−1})=−X^{−1}(dX)X^{−1}$. Can I use this directly to get the differential for the function I want to differentiate above?
Any derivations of this differential and derivative would be appreciated.
As long as the matrix for the given linear transformation on Euclidean space is nonsingular, I don't see why not. Some clear and detailed discussions can be found here. I particularly recommend Richard Schoonhoven's wonderful response,I think you'll find it exactly what you're looking for.
Hey,why waste a perfectly good answer someone worked hard posting?