Determining the Schein Rank of Boolean Matrices - Marenich, Evgeny E. (Matrix Methods: Theory, Algorithms And Applications, 2010)
In this paper we present some results of Schein rank of Boolean matrices. A notion of the intersection number of a bipartite graph is defined and its applications to Schein rank of Boolean matrices are derived. We discuss minimal and maximal matrices of given Schein rank, the number of m × n Boolean matrices with given Schein rank. The Schein ranks of some m × n Boolean matrices are determined. In the last section, we give some further result concerning the Schein rank of Boolean matrices.