Basic concepts in matroid theory

Abstract

Since the introduction of 2-isomorphism we saw several examples, both in the theory and its applications, where not all the properties of a graph play a role; in most cases only subgraphs with or without circuits need to be distinguished. Similarly, sign conventions or the underlying field for the matrices of the graphs were not important; we did not care about the numerical values of the entries of the matrices, only the linear dependence or independence of the columns of the matrices.