---
tag: 0ZD2CF6ZS0
kind: concept
name: Dual basis
msc: [15A04]
sources:
  - url: https://en.wikipedia.org/wiki/Dual_basis
    locator: Finite-dimensional vector spaces
same_as:
  wikidata: Q2297777
  wikipedia: Dual basis
---

## Summary

The dual basis of a basis $b_1, \dots, b_n$ is the family of linear forms $f_1, \dots, f_n$ with $f_i(b_j) = 1$ when $i = j$ and $0$ otherwise.