Definition:Isomorphism (Matroid)

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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 if and only if:

$\forall X \subseteq S : X \in \mathscr I_1 \iff \map f X \in \mathscr I_2$

If $f$ is an isomorphism then $M_1$ is said to be isomorphic to $M_2$.