Definition:Inner Product/Integrable Functions
< Definition:Inner Product(Redirected from Definition:Inner Product of Integrable Functions)
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Definition
Let $f$ and $g$ be real functions that are integrable over the closed real interval $\closedint a b$.
The inner product $\innerprod f g$ is defined as:
- $\innerprod f g = \ds \int_a^b \map f x \map g x \rd x$
Also see
- Results about inner products of integrable functions can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): orthogonal functions
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): orthogonal functions