# Maximum likelihood covariance estimation of Gaussian

I was reading these notes on matrix calculus http://research.microsoft.com/en-us/um/people/minka/papers/matrix/minka-matrix.pdf

and I could not figure out how to go from equation (30) to (31). Any kind of help is appreciated.

Edit: The oI notation is defined in equation (21).

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You might also want to look at this: en.wikipedia.org/wiki/Estimation_of_covariance_matrices –  Michael Hardy Oct 22 '11 at 23:43
This is my summary on MLE of mean and covariance, shiyuzhao.files.wordpress.com/2011/10/mle-mean-variance.pdf. –  Shiyu Oct 23 '11 at 2:12
I am mostly interested in this ml estimate derivation as an application example of the constrained differential rule. Equation (30) constrains the differential to be symmetric, but it's not clear how the author moves to (31). –  Freddie Oct 24 '11 at 8:09