# Math Help - Derivative of matrix function

1. ## Derivative of quadratic form

Seeking some serious help:

The positive definite (hence symmetric) matrix Sigma is decomposed as $\Sigma = AA^T$, where A has rows $a_i^T$ for which $a_i^T a_i = \Sigma_{ii}$

Given r and t as constant, be the vector $\mu(\Sigma) = [r -\frac{1}{2} \Sigma_{ii}]t$ linear function of the vector $[\Sigma_{ii}]$, i.e. the diagonal elements of Sigma.
Be $g(x, \Sigma) = -\frac{1}{2} [(x - \mu(\Sigma))^T\ \Sigma^{-1}\ (x - \mu(\Sigma))]$ the quadratic form.

I'm struggling to derive $\frac{d}{d\Sigma} g(x, \Sigma)$ and $\frac{d}{d\Sigma} \mu(\Sigma)$. I do need both.

I would appreciate some help. Thanks in advance!