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arXiv · 0902.1290

Boolean Inner product Spaces and Boolean Matrices

Stan Gudder·Frederic Latremoliere
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Abstract

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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Stan Gudder, Frederic Latremoliere. 2009-02-08. Boolean Inner product Spaces and Boolean Matrices. https://arxiv.org/abs/0902.1290

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