Gradient of quadratic form

quarks

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Apr 28, 2012
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Hello,

I'm trying to solve a problem, where I have to maximise f(x):= Q(x)/|x|², for x=/=0,x€R^n
where Q(x) = x*A*x = sum(sum(aij*xi*xj)i)j) is a quadratic form
x = (xi,...,xn).T € R^n and A is a symmetric nxn matrix.

I found already, that it suffices to find sup f(x) for |x|=1 and defined g(x) := x²-1.
I want to find the maximum with Lagrange-multiplicators, so I think I need to solve
grad(Q(x)) = lambda*grad(g(x)).

My problem now is a bit embarrasing, but how do I find grad(Q(x)) ?
 
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