Dual Matroid Basis Construction is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let be a matroid on a finite ground set , and let denote the set of bases of . Define \begin{align } \mathcal{B}^ (M) := \{E \setminus B : B \in \mathcal{B}(M)\}. \end{align } Then is the set of bases of a matroid on.