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    Let Ω = [−1, 1] ⊂ R and consider Π2(Ω) and given that B = {p1, p2, p3} is a basis of Π2(Ω) and that <f|g>= f(−1)g(−1) + f(0)g(0) + f(1)g(1) does defines an inner product on Π2(Ω), consider the following:

    Show that B is not an orthonormal basis of (Π2(Ω),<.,.>.

    I'm not very confident with orthonormal basis' so any help to try and make me answer this question will be much appreciated.
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    (Original post by AFraggers)
    Let Ω = [−1, 1] ⊂ R and consider Π2(Ω) and given that B = {p1, p2, p3} is a basis of Π2(Ω) and that <f|g>= f(−1)g(−1) + f(0)g(0) + f(1)g(1) does defines an inner product on Π2(Ω), consider the following:

    Show that B is not an orthonormal basis of (Π2(Ω),<.,.>.

    I'm not very confident with orthonormal basis' so any help to try and make me answer this question will be much appreciated.
    It would be a good idea if you were to attach a photo of the question, or to reproduce the question in full, as there are too many undefined terms in what you have asked above. What is Π2(Ω)? What are p1, p2 and p3?

    Your other posts in this thread concern orthogonalization of this set; does this carry on from the same question? If so, post it whole in one thread.
 
 
 
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