Definition:Free Matroid

Definition
Let $S$ be a finite set of cardinality $n$.

Let $\mathscr I = \powerset S$ be the power set of $S$.

That is, let $\mathscr I$ be the set of all subsets of $S$:
 * $\mathscr I := \set {X: X \subseteq S}$

Then the ordered pair $\struct{S, \mathscr I}$ is called the free matroid of $S$.

Also see

 * Leigh.Samphier/Sandbox/Free Matroid is Matroid