\begin{definition}[Definition:Matroid Induced by Linear Independence/Vector Space]
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 $V$'''.
\end{definition}