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Math Help - Gram-Schmidt Process on these Vectors

  1. #1
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    Gram-Schmidt Process on these Vectors

    I have a vector space of polynomials at most second degree with basis (1,x,x^2) with the inner product defined as

    \langle{p,q}\rangle=\int^{10}_{0}p(x)q(x)dx

    and I want to find an orthonormal basis using the Gram-Schmidt process.

    I've found that e_1=1/10

    For e_2 I have

    e_2=(x-\langle{x},\frac{1}{10}\rangle\frac{1}{10})/||x-\langle{x},\frac{1}{10}\rangle\frac{1}{10}||

    e_2=(x-1/2)/||x-1/2||
    e_2=(x-1/2)/16.90661

    However when I take the inner product between e_1 and e_2 the result is not zero, but it should be since they're orthogonal. However if I take the inner product with the upper limit at 1 they are zero.

    I'm pretty sure I've been applying the Gram-Schmidt process using the inner product I defined above. Does anyone know what I did wrong?
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  2. #2
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    \displaystyle e_1=\frac{1}{\sqrt{10}}
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    \displaystyle e_1=\frac{1}{\sqrt{10}}
    I cannot believe I overlooked the square root step even though I constantly reminded myself to take the square root.

    Thank you very much!
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  4. #4
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    No problem.
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