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.

Matroid duals go back to the original paper by Hassler Whitney defining matroids. They generalize to matroids the notions of planar graph duality and of dual spaces in linear algebra.

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