View source for Norm

==Definition==
A norm on a [[Vector space|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</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|absolute value]]
# <math>\forall x,y\in V\ \|x+y\|\le\|x\|+\|y\|</math> - a form of the [[Triangle inequality|triangle inequality]]

Often parts 1 and 2 are combined into the statement
* <math>\|x\|\ge 0\text{ and }\|x\|=0\iff x=0</math> so only 3 requirements will be stated.
I don't like this

==Examples==
===The Euclidean Norm===
The Euclidean norm is denoted <math>\|\cdot\|_2</math>


Here for <math>x\in\mathbb{R}^n</math> we have:

<math>\|x\|_2=\sqrt{\sum^n_{i=1}x_i^2}</math>
{{Todo|proof}}
{{Definition|Linear Algebra}}