 Rank of a matroid

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 $A$: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.