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inner product (of functions)

A way of pairing two functions to produce a single number, built from an integral instead of a finite sum.

The inner product of two functions f,g on an interval [a,b] is \langle f,g\rangle=\int_a^bf(x)g(x)\,dx -- the continuous analog of the dot product \mathbf u\cdot\mathbf v=\sum_iu_iv_i, a sum over infinitely many points instead of finitely many.

See also

orthogonal functions
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