Definition:Vectorial Matroid

Definition
Let $V$ be a vector space.

Let $S$ be a finite subset of $V$.

Let $\struct{S, \mathscr I}$ be the matroid induced by $V$ on $S$.

From Matroid Induced by Vector Space is Matroid, $\struct{S, \mathscr I}$ is a matroid.

Then any matroid isomorphic to $\struct{S, \mathscr I}$ is called a vectorial matroid.

Also see

 * Leigh.Samphier/Sandbox/Definition:Matroid Induced by Vector Space
 * Matroid Induced by Vector Space is Matroid