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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'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)


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