In mathematics, a generalization of the concept of absolute value. A norm || || on a vector space E over a field k is a way of measuring the distance of elements of E from zero. Usually norms are required to satisfy the following axioms:

Weakening one or another of these

axioms yields various

generalizations such as

quasinorms,

pseudonorms, etc. A

vector space endowed with a

norm is called a

normed linear space. See

Banach space for more and examples.