\begin{definition}[Definition:Isomorphism (Matroid)]
Let $M_1 = \struct{S_1, \mathscr I_1}$ and $M_2 = \struct{S_2, \mathscr I_2}$ be matroids.
Let $f : S_1 \to S_2$ be a bijection.
Then $f$ is called an '''isomorphism''' {{iff}}:
:$\forall X \subseteq S : X \in \mathscr I_1 \iff \map f X \in \mathscr I_2$
If $f$ is an '''isomorphism''' then $M_1$ is said to be '''isomorphic''' to $M_2$.
\end{definition}