Dual Matroid Rank Formula is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let be a matroid on a finite ground set , with rank function . Let denote the dual matroid of , and let be the rank function of . Then, for every subset , \begin{align } r^ (A)=|A| r(E)+r(E\setminus A). \end{align.