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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.

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  • $\begingroup$ See stats.stackexchange.com/questions/214676. $\endgroup$
    – whuber ♦
    Oct 30, 2016 at 17:44
  • $\begingroup$ 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. $\endgroup$
    – Po Ning
    Oct 30, 2016 at 18:56
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    $\begingroup$ Did you see the answer in that thread? $\endgroup$
    – whuber ♦
    Oct 30, 2016 at 21:00

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