VDict mobile



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)