Definition:Matroid Induced by Affine Independence

Definition
Let $\R^n$ be the $n$-dimensional real Euclidean space.

Let $S = \set{x_1, \dots, x_r}$ be a finite subset of $\R^n$.

Let $\mathscr I$ be the set of affinely independent subsets of $S$.

Then $\struct{S, \mathscr I}$ is called the matroid induced by affine independence on $S$.

Also see

 * Matroid Induced by Affine Independence is Matroid