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 with the following three properties:[1]
For a vector , the associated norm is written as ,[2] or L where is some value. The value of the norm of with some length is as follows:[3]
The most common usage of this is the Euclidean norm, also called the standard distance formula.