The dual matroid 
of a matroid 
on a ground set 
is the matroid whose matroid
bases are the complements 
of the matroid bases 
of 
. Duality is an involution,
so 
. The matroid
circuits of 
are the matroid cocircuits of 
(Fu 2026).
Dual Matroid
See also
Matroid, Matroid Basis, Matroid Circuit, Matroid CocircuitExplore with Wolfram|Alpha
References
Fu, H. "A Counterexample to the Circuit-Cocircuit Intersection Conjecture." 5 Oct 2026. https://arxiv.org/abs/2610.06033.Cite this as:
Weisstein, Eric W. "Dual Matroid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DualMatroid.html