Circuit Characterization of Matroid Closure is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let be a matroid on a ground set , and let denote its closure operator. For every subset and every element , \begin{align } e \in \operatorname{cl} M(A) \end{align } if and only if either , or there exists a circuit of such that.