An algorithm is sketched, which determines, up to an isomorphism, the matroid associated to a given matrix. A lemma which considerably shortens the corresponding computation time is used. The algorithm is given in detail for the matrices having at most 7 columns. Matroids on small ground-sets are represented by the following numerical parameters: cardinality of the ground-set, rank, number of bases and the vector of the sorted frequencies of elements w.r.t. the family of bases. It turns out that such a representation describes completely the matroids on at most 7 elements, while it is not sufficient on larger ground-sets.