Displaying similar documents to “Linear operators preserving maximal column ranks of nonbinary boolean matrices”

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.

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.

Power indices of trace zero symmetric Boolean matrices

Bo Zhou (2004)

Discussiones Mathematicae - General Algebra and Applications

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The power index of a square Boolean matrix A is the least integer d such that Ad is a linear combination of previous nonnegative powers of A. We determine the maximum power indices for the class of n×n primitive symmetric Boolean matrices of trace zero, the class of n×n irreducible nonprimitive symmetric Boolean matrices, and the class of n×n reducible symmetric Boolean matrices of trace zero, and characterize the extreme matrices respectively.

Linear operators that preserve Boolean rank of Boolean matrices

LeRoy B. Beasley, Seok-Zun Song (2013)

Czechoslovak Mathematical Journal

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The Boolean rank of a nonzero m × n Boolean matrix A is the minimum number k such that there exist an m × k Boolean matrix B and a k × n Boolean matrix C such that A = B C . In the previous research L. B. Beasley and N. J. Pullman obtained that a linear operator preserves Boolean rank if and only if it preserves Boolean ranks 1 and 2 . In this paper we extend this characterizations of linear operators that preserve the Boolean ranks of Boolean matrices. That is, we obtain that a linear operator preserves...

Boolean differential operators

Jorge Catumba, Rafael Díaz (2014)

Commentationes Mathematicae Universitatis Carolinae

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We consider four combinatorial interpretations for the algebra of Boolean differential operators and construct, for each interpretation, a matrix representation for the algebra of Boolean differential operators.