How do I calculate the derivative of matrix? I'd like to expand a real, symmetric and positive definite Matrix M into a Taylor series. I'm trying to do M (T) = M(T_0) + (del M)/(del T) (T-T_0) + ... T is a algebraic vector of parameters (e.g. temperatures at finite element nodes). I'm only interested in the first order term, i.e. the derivative of M at T_0. My Professor tried to do this, but used unclear notation.

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$$\left[\begin{array}{cccc}1& 3& 0& -4\\ 2& 6& 0& -8\end{array}\right]$$

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