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Seminorm
Definition
| $F$ … subfield of $\mathbb{C}$ |
| $V$ … $F$-vector space |
| $p\in \mathrm{SemiNorm}(V)$ |
| $p:V\to \mathbb R $ |
| $v,w\in V$ |
| $p(v+w) \le p(v)+p(w)$ |
| $\lambda\in F$ |
| $p(\lambda\cdot v) = |\lambda|\cdot p(v)$ |
Discussion
A Norm is a seminorm with the adition axiom
$p(v)=0 \implies v=0$
Reference
Wikipedia: Norm
Context
Requirements
