Mathematics Homework Solutions
Problem
#24398

Verifying an inner product for continuous functions

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Problem1.doc
Suppose f(x) and g(x) are continuous real-valued functions defined for
[0,1]. Define vectors in (n, F= ( f(x1), f(x2), …,f(xn)) and G=
g(x1), g(x2), …,g(xn)), where xk = k/n. Why is n = 1/n ( f(xk)
g(xk) dx not an inner product for the space of continuous functions?
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