Contraction by a Nonloop Preserves Matroids is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let be a matroid on a finite ground set , and let be a nonloop of . Define the contraction to have ground set and independent sets \begin{align } \mathcal I(M/e) := \{I \subset E \setminus \{e\} : I \cup \{e\} \in \mathcal I\}. \end{align.