# Fisher matrix for multivariate normal distribution

1. ### hdb

3
The fisher information matrix for multivariate normal distribution is said at many places to be simplified as:
$$\mathcal{I}_{m,n} = \frac{\partial \mu^\mathrm{T}}{\partial \theta_m} \Sigma^{-1} \frac{\partial \mu}{\partial \theta_n}.\$$
even on
http://en.wikipedia.org/wiki/Fisher_information#Multivariate_normal_distribution
I am trying to come up with the derivation, but no luck so far. Does anyone have any ideas / hints / references, how to do this?

Thank you

5

5. ### hdb

3
Thank you for the answers, in between I have found an another reference, which is a direct derivation of the same result, for me this one seems to be easier to interpret:

Klein, A., and H. Neudecker. “A direct derivation of the exact Fisher information matrix of Gaussian vector state space models.” Linear Algebra and its Applications 321, no. 1-3

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