Displaying similar documents to “Power indices of trace zero symmetric Boolean matrices”

Boolean matrices ... neither Boolean nor matrices

Gabriele Ricci (2000)

Discussiones Mathematicae - General Algebra and Applications

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Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.

Linear operators preserving maximal column ranks of nonbinary boolean matrices

Seok-Zun Song, Sung-Dae Yang, Sung-Min Hong, Young-Bae Jun, Seon-Jeong Kim (2000)

Discussiones Mathematicae - General Algebra and Applications

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The maximal column rank of an m by n matrix is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.

Generalized indices of Boolean matrices

Bo Zhou (2002)

Czechoslovak Mathematical Journal

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We obtain upper bounds for generalized indices of matrices in the class of nearly reducible Boolean matrices and in the class of critically reducible Boolean matrices, and prove that these bounds are the best possible.

Completely positive matrices over Boolean algebras and their CP-rank

Preeti Mohindru (2015)

Special Matrices

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Drew, Johnson and Loewy conjectured that for n ≥ 4, the CP-rank of every n × n completely positive real matrix is at most [n2/4]. In this paper, we prove this conjecture for n × n completely positive matrices over Boolean algebras (finite or infinite). In addition,we formulate various CP-rank inequalities of completely positive matrices over special semirings using semiring homomorphisms.