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I'd like to define a vector valued function in mathematica 7 as the exponential of a quadratic form, defined with respect to a purely symbolic matrix. What I want to do with it is to take derivatives with respect to the components of my vector, and evaluate the result when all components of the vector vanish (i.e. the result will just be a sum of products of matrix components). I'm struggling to define a function that takes a vector as an argument- can anyone tell me a good way of doing this?

It would also be helpful to me if I could construct a symmetric symbolic matrix (in a slightly less messy way than adding a symbolic matrix to its transpose), so that it presents an answer in the most simple form, although that's not so essential as I can simplify the result myself if needs be.

Many thanks in advance.