Matrix/Vector Differentiation: Proving the Derivative of x'Mx

[wu_weidong]

Homework Statement

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.

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.

Regards,
Rayne

 

[Dick]

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?