Normed vector space
id:
normed-vector-space-249-17806222
title:
Normed vector space
text:
In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If V is a vector space over K , where K is a field equal to R or to C , then a norm on V is a map V → R , typically denoted by ‖ ⋅ ‖ , satisfying the following four axioms: Non-negativity: for every x ∈ V , ‖ x ‖ ≥ 0 .
Positive definiteness: for every x ∈ V , ‖ x ‖ = 0 if and only
brand slug:
wiki
category slug:
encyclopedia
description:
Vector space on which a distance is defined
original url:
https://en.wikipedia.org/wiki/Normed_vector_space
date created:
date modified:
2024-02-21T22:11:31Z
main entity:
{"identifier":"Q726210","url":"https://www.wikidata.org/entity/Q726210"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/7/74/Mathematical_Spaces.png","width":505,"height":505}
fields total:
13
integrity:
15