Dual matroid

In matroid theory, the dual of a matroid ${\displaystyle M}$ is another matroid ${\displaystyle M^{\ast }}$ that has the same elements as ${\displaystyle M}$, and in which a set is independent if and only if ${\displaystyle M}$ has a basis set disjoint from it.^[1][2][3]

Matroid duals go back to the original paper by Hassler Whitney defining matroids.^[4] They generalize to matroids the notions of plane graph duality.