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Boolean inner-product spaces and Boolean matrices

✍ Scribed by Stan Gudder; Frédéric Latrémolière

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
289 KB
Volume
431
Category
Article
ISSN
0024-3795

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✦ Synopsis

This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and stochastic and unitary Boolean matrices are studied. A dimension theorem for orthonormal bases of a Boolean space is proven. We characterize the invariant stochastic Boolean vectors for a Boolean stochastic matrix and show that they can be used to reduce a unitary matrix. Finally, we obtain a result on powers of stochastic and unitary matrices.

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## Abstract We investigate bounds on the chromatic number of a graph __G__ derived from the nonexistence of homomorphisms from some path \documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}\begin{eqnarray\*}\vec{P}\end{eqnarray\*}\end{document} into some orientation \documentclass{