normed plane

A normed plane is a pair (2,||||), where the function x||x|| is a norm.

If we define a distance function d(x,y)=||x-y|| then the metric space (2,d) is called a Minkowski plane or a Minkowski geometry.

The classical examples of Minkowski and normed planes are the p-norm ||x||p=(|x1|p+|x2|p)1/p where 1p< and the maximum or supremum normMathworldPlanetmath ||x||=max{|x1|,|x2|}.

Title normed plane
Canonical name NormedPlane
Date of creation 2013-03-22 16:50:30
Last modified on 2013-03-22 16:50:30
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 6
Author Mathprof (13753)
Entry type Definition
Classification msc 46B20
Defines Minkowski plane
Defines Minkowski geometry