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Math Help - Orthonormal Set

  1. #1
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    Orthonormal Set

    I have this problem that says show that \left \{ \frac12, sin(x), cos(x) \right \} is an orthonormal set relative to the inner product defined by \frac1\pi  \int_{-\pi}^{\pi}f(x)g(x)dx. When I take the norms of each item in the set I get 1/2, 1, 1 respectively. Could someone point out to what I am doing wrong?

    Thanks
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  2. #2
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    Are you sure it's supposed to be an orthonormal set and not just an orthogonal set? I get what you get for the norms, so the set is definitely not orthonormal w.r.t. that inner product. Maybe they meant to have the set

    \left\{\frac{\sqrt{2}}{2},\sin(x),\cos(x)\right\},

    which I believe is orthonormal w.r.t. that inner product.
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  3. #3
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    I went ahead and made it orthonormal and I got the same set that you derived. I am not sure if my teacher made a mistake or he wanted us to make them orthonormal. Thanks for your help!
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  4. #4
    A Plied Mathematician
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    You're welcome!
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