Norm (mathematics)

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In mathematics, the norm of a vector is its length. For the real numbers the only norm is the absolute value. For spaces with more dimensions the norm can be any function with

  1. Scales for real numbers , that is
  2. Function of sum is less than sum of functions, that is or the triangle inequality
  3. if and only if .

Examples[change | change source]

  1. The one-norm is the sum of absolute values: This is like finding the distance from one place on a grid to another by summing together the distances in all directions the grid goes; see Manhattan Distance
  2. Euclidean norm is the sum of the squares of the values:
  3. Maximum norm is the maximum absolute value: