Dual matroid

Summary

The dual of a matroid $M$ is the matroid $M^*$ on the same ground set whose bases are the complements of the bases of $M$. Duality is an involution, $M^{**} = M$, and it exchanges deletion and contraction of minors. For a planar graph, the dual of its graphic matroid is the graphic matroid of the dual graph. So matroid duality extends planar graph duality to all matroids.