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- Scales for real numbers , that is
- Function of sum is less than sum of functions, that is or the triangle inequality
- if and only if .
Definition[change | change source]
For a vector , the associated norm is written as or L where is some value. The value of the norm of with some length is as follows:
The most common usage of this is the Euclidean norm, also called the standard distance formula.
Examples[change | change source]
- 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
- Euclidean norm is the sum of the squares of the values:
- Maximum norm is the maximum absolute value:
- When applied to matrices, the Euclidean norm is referred to as the Frobenius norm
- L0 norm is the number of non-zero elements present in a vector