Boolean Inner product Spaces and Boolean Matrices

Details Boolean Inner product Spaces and Boolean Matrices Boolean Inner product Spaces and Boolean Matrices

2009-02-08

arxiv.org/abs/0902.1290v1

Linear Algebra and Applications 431 (2009) 1-2, 272-296

Mathematics

Rings and Algebras

36 pages

Scientific paper

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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