A norm on a vector space $V$ is a real-valued functional $\vert \vert \cdot\vert \vert $ such that for all $v,w \in V$ and $\alpha \in \mathbb R$, the following properties hold:
- $\vert \vert v+w\vert \vert \leq \vert \vert v\vert \vert + \vert \vert w\vert \vert $;
- $\vert \vert \alpha v\vert \vert = \vert \alpha\vert \cdot \vert \vert v\vert \vert $;
- $\vert \vert v\vert \vert \geq 0$ and $\vert \vert v\vert \vert = 0$ if and only if $v=0$.
Wikidata ID: Q956437