---
tag: 000AYPA9AJ
kind: concept
name: Vector space
aliases: [linear-space]
msc: [15A03]
sources:
  - url: https://en.wikipedia.org/wiki/Vector_space
    locator: Definition and basic properties
same_as:
  wikidata: Q125977
  wikipedia: Vector space
---

## Summary

A vector space over a field is a set of vectors that can be added and multiplied by scalars, with the usual rules of arithmetic.
Vector spaces are the main objects of linear algebra.