On cardinalities of row spaces of Boolean matrices
Copyright policy )On cardinalities of row spaces of Boolean matrices
The author shows that if the row space of an \(n\times n\) matrix exceeds in cardinality \(2^{n-1}\) then it is \(2^{n-1}\) plus a power of 2 which is not greater. He applies this to finite topologies and the height of the poset of \(\mathcal D\) classes in the semigroup of \(n\times n\) Boolean matrices.
- DigiZeitschriften Germany
- Pennsylvania State University United States
Several topologies on one set (change of topology, comparison of topologies, lattices of topologies), Algebraic systems of matrices, finite topologies, Transformation groups and semigroups (topological aspects), Article, row space, Semigroups of transformations, relations, partitions, etc., 510.mathematics, Cardinality properties (cardinal functions and inequalities, discrete subsets), semigroup of Boolean matrices, height of the poset of \(\mathcal D\) classes, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
Several topologies on one set (change of topology, comparison of topologies, lattices of topologies), Algebraic systems of matrices, finite topologies, Transformation groups and semigroups (topological aspects), Article, row space, Semigroups of transformations, relations, partitions, etc., 510.mathematics, Cardinality properties (cardinal functions and inequalities, discrete subsets), semigroup of Boolean matrices, height of the poset of \(\mathcal D\) classes, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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