A matroid basis is an independent subset of a matroid that is maximal with respect to inclusion. All bases of a matroid have the same number of elements, called its matroid rank.
The bases determine the matroid, since a subset is independent iff it is contained in a basis. For a matroid represented by columns of a matrix, the bases correspond to maximal linearly independent collections of columns. In the graphic matroid of a connected graph, the bases are its spanning trees.
