norm

Length in a vector space

Also known as length · magnitude

Instance of: concept
, function
Subclass of: seminorm
, functional
, quasinorm
+1 more
Part of: normed vector space

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the Euclidean norm, the 2-norm, or, sometimes, the magnitude or length of the vector. This norm can be defined as the square root of the inner product of a vector with itself.

Overview

All data

19 statements · 11% with external sources · numbers in brackets are citations

Different from: norm
standard
Definition domain: vector space
Codomain: set of non-negative real numbers

On other databases

9 identifiers linking norm across the web's reference databases

Data quality

statements

11%

externally sourced

Source last edited October 3, 2026. AIDB refreshes this page daily.

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AIDB. (2026). norm (Q956437). Retrieved from https://aidb.si/e/norm-Q956437