Multi Variable Derivatives
Multi-variable derivative To the people that are not used to matrix derivatives (like me) it could be useful to see how $$ \frac{ \partial u^{T}Su }{ \partial u } = 2Su $$ First, we note that if you derive with respect to some matrix, the output will be of the same dimension of that matrix. That notation is just deriving every single component independently and then joining them together, so it will be better understood as as $$ \frac{ \partial u^{T}Su }{ \partial u } = \begin{bmatrix} \frac{ \partial u^{T}Su }{ \partial u_{1} } \ \dots \ \frac{ \partial u^{T}Su }{ \partial u_{M} } \ \end{bmatrix} \begin{bmatrix} 2(Su){1} \ \dots \ 2(Su){M} \end{bmatrix} = 2Su $$ So we can prove each derivative independently, it's just a lot of manual work!...