# What is the derivative of the following matrix (See question)?

Is someone could help to answer what is the derivative for

$$\frac{\partial \log \text{det}(\boldsymbol \Sigma + \boldsymbol X \boldsymbol X^T)}{\partial \boldsymbol \Sigma}$$ and $$\frac{\partial \boldsymbol Y^T (\boldsymbol \Sigma + \boldsymbol X \boldsymbol X^T)^{-1} \boldsymbol Y}{\partial \boldsymbol \Sigma}$$ where $\boldsymbol \Sigma$ is $n \times n$, $\boldsymbol Y$ is a $n \times 1$ vector.

Thanks.

• – whuber
Oct 30 '16 at 17:44
• Thank you whuber. The reference is very useful. However, it is the exactly the same as my question here. Especially, I am wondering what is the $\partial (\boldsymbol \Sigma + \boldsymbol X \boldsymbol X^T) / \partial \boldsymbol \Sigma$. I hope this is not a stupid question. Oct 30 '16 at 18:56