# Definition:P-Norm

## Definition

Let $p \ge 1$ be a real number.

Let $\ell^p$ denote the $p$-sequence space.

Let $\mathbf{x} = \langle{x_n}\rangle \in \ell^p$.

Then the $p$-norm of $\mathbf{x}$ is defined as:

$\displaystyle \left\Vert \mathbf{x} \right\Vert_p = \left({\sum_{n \mathop = 0}^\infty \left\vert x_n \right\vert^p}\right)^{1/p}$