Norm

The Norm of A Function

The norm of f is analogous to the magnitude of a vector $v=v\_1,...v\_n$ where $|v|=\sqrt{\sum \_{k=1}^{d}v\_k^2}$. As vectors have a finite amount of values, whereas functions just like $f(x)$ have an infinite amount of outputs in any bounded region, the norm is

$$||f||=\sqrt{\int \_0^{2\pi }f(x{)}^{2}dx}$$

• $f$ is a unit function if $||f||=0$