Definition:Matroid Induced by Linear Independence/Vector Space

Definition

Let $V$ be a vector space.

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

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

Then the ordered pair $\struct{S, \mathscr I}$ is called a matroid induced on $S$ by linear independence in $V$.

Also see

• Matroid Induced by Linear Independence in Vector Space is Matroid
• Definition:Vectorial Matroid

Sources

• 1976: Dominic Welsh: Matroid Theory Chapter $9.$ $\S 1.$ The representability problem