The matrix Sigma is positive definite and is decomposed as $\displaystyle \Sigma = AA^T$

Thus: $\displaystyle \Sigma^{-1} = A^{-T}A^{-1}$ and $\displaystyle A^{T}\Sigma^{-1} = A^{-1}$

What is $\displaystyle \frac{d A^{-1}}{d\Sigma}$ ?