---
tag: JWK49HMHYT
kind: concept
name: Affine independence
msc: [51N10, 15A03]
sources:
  - url: https://en.wikipedia.org/wiki/Affine_space
---

## Summary

Points of an [[affine space|09XNAPTJQ7]] are affinely independent if none of them is an [[affine combination|0KJH6SRFZK]] of the others.
Equivalently, the vectors from one of the points to the others are [[linearly independent|0CRMGPAH83]].
Affinely independent points are the vertices of a simplex.
In an $n$-dimensional space, $n + 1$ of them form an affine frame, in which barycentric coordinates are defined.

## Explanations

### L1 human

Two points are affinely independent when they are different.
Three points are affinely independent when they do not lie on one line, so they span a triangle.
Four points are affinely independent when they do not lie in one plane, so they span a tetrahedron.
In general, affinely independent points are in "general position": no one of them lies in the flat spanned by the others.