Matroid isomorphism
= Matroid isomorphism
{title2=$\phi:E\to E'$}
A <matroid isomorphism> between $(E,\mathcal I)$ and $(E',\mathcal I')$ is a <bijection> $\phi$ such that $I\in\mathcal I$ if and only if $\phi(I)\in\mathcal I'$. It relabels the <ground set> without changing independence. The number of labelled <matroids> therefore differs from the number of types up to <matroid isomorphism>.