norm

n 1: a standard or model or pattern regarded as typical: "the

current middle-class norm of two children per family"

2: a statistic describing the location of a distribution: "it

set the norm for American homes" [syn: {average}]

norm

A real-valued function modelling the length of a

{vector}. The norm must be {homogeneous} and {symmetric} and

fulfil the following condition: the shortest way to reach a

point is to go straight towards it. Every {convex} symmetric

{closed} surface surrounding point 0 introduces a norm by

means of {Minkowski functional}; all vectors that end on the

surface have the same norm then.

The most popular norm is the {Euclidean norm}; it is

calculated by summing up squares of all coordinates and taking

the square root; this is the essence of {Pythagorus's

theorem}. In the infinite-dimensional case, the sum is

infinite or is replaced with an integral when the number of

dimensions is {uncountable}.

(1998-07-05)