Editing Affine transformation (section)

===Alternative definition===
Given two [[affine space]]s <math>\mathcal{A}</math> and <math>\mathcal{B}</math>, over the same field, a function <math>f\colon \mathcal{A} \to \mathcal{B}</math> is an affine map [[if and only if]] for every family <math>\{(a_i, \lambda_i)\}_{i\in I}</math> of weighted points in <math>\mathcal{A}</math> such that 
: <math>\sum_{i\in I}\lambda_i = 1</math>,

we have<ref>
{{cite book|author1=Schneider, Philip K. |author2=Eberly, David H.|title=Geometric Tools for Computer Graphics|publisher=Morgan Kaufmann|year=2003|isbn=978-1-55860-594-7|page=98|url=https://books.google.com/books?id=3Q7HGBx1uLIC&pg=PA98}}</ref>

: <math>f\left(\sum_{i\in I}\lambda_i a_i\right)=\sum_{i\in I}\lambda_i f(a_i)</math>.

In other words, <math>f</math> preserves [[Barycentric_coordinate_system|barycenters]].