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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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    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).2011-10-24

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OK, it's more trivial than I thought: (30) is in the form of A = (A o I)/2, which is satisfied only if A=0, which is a simplified form of (30). Working with A=0, then (31) follows.