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 linear independence in $V$ on $S$.

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

Also see

• Definition:Matroid Induced by Linear Independence (Vector Space)
• Matroid Induced by Linear Independence in Vector Space is Matroid, which demonstrates that $\struct {S, \mathscr I}$ is a matroid

Sources

• 1976: Dominic Welsh: Matroid Theory ... (previous) ... (next) Chapter $1.$ $\S 3.$ Examples of Matroids