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    i have to orthonomalise a basis for a euclidean vector space using the Gram-Schmidt process.

    The vector space is (V,w). V is the space of real polynomials of degree at most 4. I am using the standard basis for this space to begin with.
    I have a function for w... w(f(X),g(X))=integral between -1 and 1 of f(X)g(X)dX.
    Now I know how to run Gram-Schmidt on a normal vector space but I'm a bit confused here, my confusion stems from this function w. what am i supposed to do with it and how does it affect my orthonormal basis.
    i dont want a full solution but tips and hints mainly geared towards w and its role in the vector space and the use of its function in this question would be very much appreciated!
    thanks
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    w is your inner product.

    An orthonormal basis is defined in terms of the inner product on the space.
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    so w is just my dot product?
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    Yes, w is your dot product/inner product/scalar product.

    So it defines what it means for two basis elements to be orthogonal in your space i.e. if w(f(X),g(X))=0
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    ok thanks, thats what i originally thought but the wording of the question confused me for ages!

    how would i actually normalise a polynomial? divide by w(f(x),f(x))?
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    So for example, f(X) = X and g(X) = X^2 + 1 aren't orthogonal as \displaystyle \int_{-1}^{1}(X^3 + X) \textrm{d}X \neq 0
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    (Original post by aqfrenzy)
    ok thanks, thats what i originally thought but the wording of the question confused me for ages!

    how would i actually normalise a polynomial? divide by w(f(x),f(x))?
    (Assuming you are using the norm induced by the inner product which is more than likely the case) - divide by the square root of w(f(X),f(X))
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    You really shouldn't be posting questions which are for credit...
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    i was mainly asking for help with notation here...didnt understand the (V,w) bit
 
 
 
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