Hi. First of all I don't know if this belongs in the Linear Algebra forum or the Calculus forum (its a bit of both!) so apologies if its in the wrong place!

I am trying to find analytical expression for the derivative of the coherence (or correlation) function of a matrix.

So M(C) is the coherence matrix of some positive-definite, symmetrical, real or complex, matrix C. such that:

Is it possible to get an analytical expression for ? I'm not sure how differentiation works for matrix functions which operate on different elements within the matrix.

Any help you can offer would be greatly appreciated.

Thanks

Mark