norm

mathematics 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 toward 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'stheorem. 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)