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Derivative with respect to matrix

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Derivative with respect to matrix

Hello,
1- How to determine a derivative of a function with respect to matrix?
2- For example let a function f such that
f(C)= x'Cy + x'C'y + x'C'ACy
where x and y are vectors and C and A are matrix and (') is the opertor transpose.
what is the derivative of f with respect to C?

Thank you.


Hello,
If I understand there isn't a derivative with respect to matrix like my example.

There is.
http://en.wikipedia.org/wiki/Fréchet_derivative

At point C in direction B the derivative is
Df(C)(B)=x'By+x'B'y+x'B'ACy+x'C'ABy

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