# What is the euclidean norm?

In $\mathbb{R}$, ${\mathbb{R}}^{2}$ and ${\mathbb{R}}^{3}$ The euclidean norm is quite simply the distance between coordinates
This is further extended for some vector $\vec{x} = \left({x}_{1} , {x}_{2} , \ldots , {x}_{n}\right) \in {\mathbb{R}}^{n}$ by:
$| | \vec{x} | | = \sqrt{{x}_{1}^{2} + {x}_{2}^{2} + \ldots + {x}_{n}^{2}}$