Norm (mathematics)

In mathematics, the norm of a vector is its length. A vector is a mathematical object that has a size, called the "magnitude", and a direction. For the real numbers, the only norm is the absolute value. For spaces with more dimensions, the norm can be any function formula_1 with the following three properties:
Definition.
For a vector formula_7, the associated norm is written as formula_8, or Lformula_1 where formula_1 is some value. The value of the norm of formula_7 with some length formula_12 is as follows:
formula_13
The most common usage of this is the Euclidean norm, also called the standard distance formula.