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Math Help - Inner product of polynomial

  1. #1
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    Inner product of polynomial

    Hey everyone,

    My teacher gave a problem to show that p = 1 + x and q = 1 - x are orthogonal, but he says let <p,q> = a0b0 + a1b1 be the inner product. How do I do this with out integrating? I'm a little confused.

    Thanks
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  2. #2
    A Plied Mathematician
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    What are a_{0}, b_{0}, a_{1}, b_{1}? I would assume you have something like p(x)=a_{0}+a_{1}x, and q(x)=b_{0}+b_{1}x. If that's so, then the inner product \langle p,q\rangle=a_{0}b_{0}+a_{1}b_{1} will definitely give you orthogonality of those two polynomials. Do you see how?
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  3. #3
    Super Member girdav's Avatar
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    You don't have to integrate because the inner product is not defined by an integral. You only have to apply the definition and see what a_0, a_1, b_0 and b_1 are.
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  4. #4
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    I see it. It was like you said it was. It would be (1)(1) + ((1)(-1) = 0.
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  5. #5
    A Plied Mathematician
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    That's right.
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  6. #6
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  7. #7
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    You're welcome!
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