Rank Function of a Direct Sum of Matroids is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let and be matroids with disjoint ground sets . Let be their direct sum on the ground set , so that a subset is independent in if and only if is independent in and is independent in . Then for every subset , \begin{align } r M(A)=r {M.