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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 .
- 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: