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Math Help - Definiteness of Constrained Quadratics - HELP

  1. #1
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    Exclamation Definiteness of Constrained Quadratics - HELP

    I am so stuck with these questions. Great appreciation for any help! Thanks

    Determine the definiteness of the following constrained quadratic:
    Q(x1,x2) = x12 +2x1x2 - x22 subject to x1 + x2 = 0
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  2. #2
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    Re: Definiteness of Constrained Quadratics - HELP

    Don't know what "definiteness" is (in a mathematical sense) but if you replace x_2 with -x_1 you obtain

    Q(x_1, x_2) = x_1^2 + 2x_1(-x_1) - (-x_1)^2

    Q(x_1, x_2) = -2x_1^2.
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  3. #3
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    Re: Definiteness of Constrained Quadratics - HELP

    If it's any use, you get a 'no, not positive definite' from testing by plugging the coefficients into the matrix shown in the result at the top of this pdf:

    http://www.google.co.uk/url?sa=t&rct...pRi9Hw&cad=rja

    Also,

    http://www.google.co.uk/url?sa=t&rct...nnH_gElX-UjLNA

    Positive definiteness - Wikipedia, the free encyclopedia
    Last edited by tom@ballooncalculus; August 7th 2012 at 10:53 AM.
    Thanks from bublemjj
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  4. #4
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    Re: Definiteness of Constrained Quadratics - HELP

    Quote Originally Posted by tom@ballooncalculus View Post
    You get a 'no, not positive definite' from testing by plugging the coefficients into the matrix shown in the result at the top of this pdf:

    http://www.google.co.uk/url?sa=t&rct...pRi9Hw&cad=rja

    Also,

    http://www.google.co.uk/url?sa=t&rct...nnH_gElX-UjLNA
    Thank you SOOO MUCH. The pdf does help a lot!!!
    May I ask for one more favour?
    Do you have a similar pdf related to "Continuous Differentiable Function" - kind of answering questions like whether a function is C^1 or C^k?
    You will be my life-saver.
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