===== Seminorm =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $F$ ... subfield of $\mathbb{C}$ |
| @#55CCEE: context     | @#55CCEE: $V$ ... $F$-vector space |
| @#FFBB00: definiendum | @#FFBB00: $p\in \mathrm{SemiNorm}(V)$ |
| @#55EE55: postulate   | @#55EE55: $p:V\to \mathbb R $ |
| $v,w\in V$ | |
| @#55EE55: postulate   | @#55EE55: $p(v+w) \le p(v)+p(w)$ |
| $\lambda\in F$ | |
| @#55EE55: postulate   | @#55EE55: $p(\lambda\cdot v) = |\lambda|\cdot p(v)$ |

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=== Discussion ===
A [[Norm]] is a seminorm with the adition axiom

$p(v)=0 \implies v=0$

(which I also write as $p(!0)=0$.)
 
=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Norm_%28mathematics%29|Norm]]
==== Parents ====
=== Context ===
[[Vector space]]