# Inner Product

### From MATH213

Used in Fourier Series analysis.

Theorem 1: Existence of Inner Product

If $f,gāL_{2}([a,b])$ then $<f,g>$ exists and is finite.

Definition 2: Standard Inner product on

`L^2([a, b])`

If $f$ and $g$ are complex valued functions in $L_{2}([a,b])$ then the standard inner product is $<f,g>=bāa1āā«_{a}f(t)g(t)ādt$

- See L2 Function

Is the Inner product the same as the Dot Product?

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar.