I wonder how to differentiate with respect to the diagonal matrix $X_d$, the following matrix :

$$ X_d^T (\Sigma_d + X_d C X_d)^{-1} X_d $$

where $X_d$ and $\Sigma_d$ are diagonal matrices with striclty positive diagonal entries and $C$ is a positive definite matrix. Any hint would be appreciated.

  • $\begingroup$ How to derive this from what? What do each of the terms represent? $\endgroup$ – Tom Jun 4 '14 at 13:41
  • $\begingroup$ @Tom. Does the edit help ? Thanks. $\endgroup$ – peuhp Jun 4 '14 at 13:47

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