Derivative of matrix inversion
= Derivative of matrix inversion
On the open set of invertible square matrices, the inversion map is <differentiable map>[differentiable] and
$$
D(A\mapsto A^{-1})_A[H]=-A^{-1}HA^{-1}.
$$
= Derivative of matrix inversion
On the open set of invertible square matrices, the inversion map is <differentiable map>[differentiable] and
$$
D(A\mapsto A^{-1})_A[H]=-A^{-1}HA^{-1}.
$$