How to show $\frac {\partial a^{T}X^{-1}b}{\partial X} = -\left( X^{-1}\right) ^{T}ab^{T}\left( X^{-1}\right) ^{T}$?
Prove that $\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$