3.1.24 Prove that <f,g> = the integral f(x)*g(x)dx from 0 to 1 does not define an...

3.1.24 Prove that <f,g> = the integral f(x)*g(x)dx from 0 to 1 does not define an inner product on the vector space C0[-1,1]. Explain why this does not contradict the fact that it defines an inner product on the vector space C0[0,1]. Does it define an inner product on the subspace P(n) C C0[-1,1] consisting of all polynomial functions?

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Prove that

Colby Messinger answered 4 months ago

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