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Homework Help: Matrix/Vector differentiation

  1. Sep 18, 2007 #1
    1. The problem statement, all variables and given/known data

    Hi all,
    I need help proving the result:

    Let g(x) = x'Mx, where M is a n-by-n real constant matrix and x' denotes the transpose of vector x. Then the derivative of g(x) = (M + M')x.

    3. The attempt at a solution

    I was thinking of using product rule on x'(Mx) to get Mx + x'M, but apparently this is incorrect as the dimensions of Mx and x'M don't even match and so cannot be grouped together to get (M + M')x.

    Please help.

    Thank you.

  2. jcsd
  3. Sep 18, 2007 #2


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    Science Advisor
    Homework Helper

    Think indices. x'Mx=x_i*M_ik*x_k (summed over i and k). What's the derivative of that wrt, say, x_n?
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