---
tag: 0KCQ9Y3QKA
kind: concept
name: Basis
msc: [15A03]
sources:
  - url: https://en.wikipedia.org/wiki/Basis_(linear_algebra)
    locator: Definition
same_as:
  wikidata: Q189569
  wikipedia: Basis (linear algebra)
---

## Summary

A basis of a vector space is a linearly independent family of vectors that spans the space.
Each vector of the space is then a linear combination of the basis vectors in exactly one way.