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    Linear Algebra : Symmetric Polynomials and Inner products

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    Let be the real vector space of "symmetric" polynomials of degree at most 4, with inner product

    a. find a basis for V and determine dim V.
    b. viewing V as a subspace of R) with the same inner product, find the "closest" point in V to the polynomial.

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    Solution Preview

    Please see the attachment.

    from your solution..You noted that
    To minimize the above expression, we can minimize ||g1(x)||^2 to 0 by setting a=c=0.
    why do we set a=c=0?? is it just because to minimize???
    or it has to be 0??
    what if we ...

    Solution Summary

    Symmetric polynomials and inner products are investigated in the solution.