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.