Norm
From Maths
Revision as of 16:04, 7 March 2015 by Alec (Talk | contribs) (Created page with "==Definition== A norm on a vector space {{M|(V,F)}} is a function <math>\|\cdot\|:V\rightarrow\mathbb{R}</math> such that: # <math>\forall x\in V\ \|x\|\ge 0<...")
Definition
A norm on a vector space [ilmath](V,F)[/ilmath] is a function [math]\|\cdot\|:V\rightarrow\mathbb{R}[/math] such that:
- [math]\forall x\in V\ \|x\|\ge 0[/math]
- [math]\|x\|=0\iff x=0[/math]
- [math]\forall \lambda\in F, x\in V\ \|\lambda x\|=|\lambda|\|x\|[/math] where [math]|\cdot|[/math] denotes absolute value
