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Math Help - Derivative of matrix function

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    Derivative of quadratic form

    Seeking some serious help:

    The positive definite (hence symmetric) matrix Sigma is decomposed as \Sigma = AA^T, where A has rows a_i^T for which a_i^T a_i = \Sigma_{ii}

    Given r and t as constant, be the vector \mu(\Sigma) = [r -\frac{1}{2} \Sigma_{ii}]t linear function of the vector [\Sigma_{ii}], i.e. the diagonal elements of Sigma.
    Be g(x, \Sigma) = -\frac{1}{2} [(x - \mu(\Sigma))^T\ \Sigma^{-1}\ (x - \mu(\Sigma))] the quadratic form.

    I'm struggling to derive \frac{d}{d\Sigma} g(x, \Sigma) and \frac{d}{d\Sigma} \mu(\Sigma). I do need both.

    I would appreciate some help. Thanks in advance!
    Last edited by paolopiace; February 26th 2010 at 10:54 AM.
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