# Definition:Rank (Matroid)

Let $M = \struct{S, \mathscr I}$ be a matroid.
Let $\rho : \powerset S \to \Z$ be the rank function of $M$.
The rank of $M$, denoted by $\map \rho M$, is the image of $S$ under $\rho$, that is:
$\map \rho M = \map \rho S$.