On the contribution of cardinalities of row space of Boolean matrices Original Research Article

Let Bn be the set of all n × n Boolean matrices, R(A) denote the row space of A set membership, variant Bn R(A) denote the cardinality of R(A). In this paper, we show the following two facts. 31) For any m set membership, variant [1, 46], [1, 78], [1, 120], there are A set membership, variant B7, A set membership, variant B8, A set membership, variant B9 respectively, such that R(A) = m. (2) If n greater-or-equal, slanted 10, then for any m set membership, variant [1,2[(n − 10)/2] + 6 + 2[((n − 1) − 10)/2]+6 + … + 2 [(11 − 10)/2]+6 + 2[(10 − 10)/2]+6 + 26 + 25 + 24 + 23], there is A set membership, variant Bn, such that R(A) = m.