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Math Help - Inner product space help

  1. #1
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    Inner product space help

    There are two continuous function p and q in the continuous interval[-1,1] , prove the following inner product space is undefined

    Integrate (x*p(x)*q(x)) d(x) (from -1 to 1)

    I have no clue in how to prove this =(
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  2. #2
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    Quote Originally Posted by MichaelChun View Post
    There are two continuous function p and q in the continuous interval[-1,1] , prove the following inner product space is undefined

    Integrate (x*p(x)*q(x)) d(x) (from -1 to 1)

    I have no clue in how to prove this =(
    <p,p> \geq 0 and 0 iff p=0
    <p,q>=<q,p>
    <\alpha x+\beta y,z>=\alpha <x,z>+\beta <y,z>
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  3. #3
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    Quote Originally Posted by MichaelChun View Post
    There are two continuous function p and q in the continuous interval[-1,1] , prove the following inner product space is undefined
    Is "undefined"???

    Integrate (x*p(x)*q(x)) d(x) (from -1 to 1)

    I have no clue in how to prove this =(
    Surely you mean just "show that the integral defines an inner product on that space". And you do that, as dwsmith said, by showing that the "rules" for an inner product are satisfies.
    Last edited by HallsofIvy; May 7th 2010 at 03:27 AM.
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  4. #4
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    Quote Originally Posted by HallsofIvy View Post
    Is "undefined"???


    Surely you mean just "show that the integral defines an inner product on that space. And you do that, as dwsmith said, by showing that the "rules" for an inner product are satisfies.
    cannot be defined, someone told me because in this case <p,p> is not a positive definite, but why?
    I don't know how to show it
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    Nice! Which means when p is not 0 and the inner product is zero so we cannot define it as inner product?? That's smart
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  7. #7
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    Quote Originally Posted by MichaelChun View Post
    Nice! Which means when p is not 0 and the inner product is zero so we cannot define it as inner product?? That's smart
    Correct, 0 iff p=0
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