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Thread: Differentiation Involving Determinant.

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    Differentiation Involving Determinant.




    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?
    Last edited by Cynderella; 05-23-2016 at 01:55 AM.

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