Show that C(X) (exercise 2.85) is not an inner product space.
Two vectors x and y in an inner product space X are orthogonal if xT y = 0. We symbolize this by x Š¥ y The orthogonal complement SŠ¥ of a subset S Š‚ X as the set of all vectors that are orthogonal to every vector in S, that is,
SŠ¥ = {x ˆŠ X : xT y = 0 for every y ˆŠ S}
A set of vectors {x1, x2,..., xn} is called pairwise orthogonal if xi Š¥ xj for every i ‰  j. A set of vectors {x1, x2,..., xn} is called orthonormal if it is pairwise orthogonal and each vector has unit length so that

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if ij otherwise