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.

Norm (?), n. [L. norma a rule. See Normal, a.]

1.

A rule or authoritative standard; a model; a type.

2. Biol.

A typical, structural unit; a type.

Agassiz.

 

© Webster 1913.

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