Rank of a matroid
= Rank of a matroid
{title2=$r_M(A)$}
For a <subset> $A$ of the <ground set>, the <rank of a matroid> on $A$ is the maximum <cardinality> of a <matroid independent set> contained in $A$:
$$
r_M(A)=\max\{\,|I|: I\subseteq A,\ I\in\mathcal I\,\}.
$$
Thus $r_M(E)$ is the common size of the <matroid bases>, and $r_M(\varnothing)=0$. The <weighted three-vector matroid> has $r_M(E)=2$, even though its <ground set> has three labels.