matrix differentation

Question

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.

score 1 · Accepted Answer · edited Apr 13 '17 at 12:20

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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?

edited Apr 13 '17 at 12:20

Community

1

answered Feb 13 '15 at 21:39

Mathemagician1234

17,966

what is meant with nonsingular? – joog Feb 13 '15 at 22:23
Nonsingular means for a matrix A,$det(A)\neq 0$. It's proven in linear algebra this is equivalent to saying A is invertible. – Mathemagician1234 Feb 13 '15 at 22:52

matrix differentation

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