In mathematics, a norm is a function on a vector space that generalizes to vector spaces the notion of the distance from a point of a Euclidean space to the origin.
Formal definition of norm
Let X be a vector space over some subfield F of the complex numbers. Then a norm on X is any function having the following four properties:
- for all (positivity)
- if and only if x=0
- for all (triangular inequality)
- for all
A norm on X also defines a metric on X as . Hence a normed space is also a metric space.