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Math Help - Orthonormal basis

  1. #1
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    Orthonormal basis

    Define an inner product on P2 by <p,q> = ʃ (-1 to 1) p(x)q(x) dx. Let U (element of) P2 be the subspace spanned by {x,x^2}

    (a) Find an orthonormal basis for U
    (b) Find the polynomial in U that is as close as possible to f(x)=1 (for the norm corresponding to the above inner product).

    Can someone help me solve this question? Thank you in advance.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ghadz7 View Post
    Define an inner product on P2 by <p,q> = ʃ (-1 to 1) p(x)q(x) dx. Let U (element of) P2 be the subspace spanned by {x,x^2}

    (a) Find an orthonormal basis for U
    Use the Gramm-Schmidt process on \{x,x^2\}

    (b) Find the polynomial in U that is as close as possible to f(x)=1 (for the norm corresponding to the above inner product).
    Once you have the orthonormal basis elements \{p_1(x), p_2(x)\} the polynomial is:

    P(x)=\langle f,p_1\rangle p_1(x)+\langle f,p_2\rangle p_2(x)

    CB
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  3. #3
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    I am a year 12 student who made the mistake of undertaking a university subject. I am absolutely clueless in applying the Gramm-Schmidt process.

    I have managed to solve section a but I'm facing difficulties with section b.
    Last edited by ghadz7; August 30th 2010 at 05:29 AM.
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  4. #4
    A Plied Mathematician
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    You say you got section a. What did you get for your basis?
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  5. #5
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    { root(3/2)x , x^2 } was I right?
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  6. #6
    A Plied Mathematician
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    That's not quite what I get. Can you show me your steps?
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