Differentiation Involving Determinant.

Cynderella

New Member
I have to compute the following differentiation :

$$\frac{\partial}{\partial\sigma^2}\det[\mathbf X_{p\times n}'(\sigma^2 \mathbf I_{n}+\mathbf Z_{n\times q}\mathbf G_{q\times q}\mathbf Z_{q\times n}')^{-1}\mathbf X_{n\times p}],$$

where $$\sigma^2$$ is a scalar, $$\det$$ denotes determinant, $$\mathbf I_{n}$$ is a $n\times n$ identity matrix. Note that, $$\mathbf X$$, $$\mathbf Z$$, and $$\mathbf G$$ do NOT involve $$\sigma^2$$.

How can I do that?

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