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Math Help - Finding infinum and supremum of over the quadratic q(x)

  1. #1
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    Red face Finding infinum and supremum of over the quadratic q(x)

    Let A denote the matrix

    A=
    1 1 -12
    -1 1 0
    0 0 2
    and define the quadratic
    q(x):= <x,Ax>
    where<> defines the inner product

    Determine the supremum and infimum of q(x) over all unitx vectors x

    By definiton we know that the infinum and supremum are interrelated by being the smallest and largest numbers that are less than all elements or greater than all elements in a set t.
    I am a bit confused since x is only unit so its range of values should not be infinite (so my logic tells me) and this is the time we use the infimum and supremum.

    I am having trouble starting the problem.

    Thank you very much for any help,
    -Carlos
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  2. #2
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
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    Re: Finding infinum and supremum of over the quadratic q(x)

    If you multiply it out, you'll get that q(x,y,z) is a polynomial in the three variables. You want to find the extrema in 3-space subject to the constraint x^2+y^2+z^2=1. Check out "Lagrange multipliers" for a method.
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