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Math Help - Differential problem

  1. #1
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    Differential problem

    Let A \in M_n(\mathbb{R} ) and let T(A) = \left( A^{-1} \right) ^T .

    Prove that trace[\mathcal{D} T(A)] = -trace[A^{-1} \cdot (A^T)^{-1}],

    Where \mathcal{D}f(p) is the Jacobian of f(p).

    Already proved prior to this that the determinant transformation is continuous and that GL_n( \mathbb{R}) is an open set. Don't really have a clue how to approach this -- a direction would be nice.

    Thanks.
    Last edited by Defunkt; November 17th 2009 at 05:11 PM.
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