Displaying similar documents to “A generalization of a theorem of Boolean relation matrices”

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.

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.