Eigenvectors and Maximal Vectors in Boolean Vector Spaces

Boolean Vector Spaces

This article discusses the basic properties of finite-dimensional Boolean vector spaces and their linear transformations. We first introduce a natural Boolean-valued inner product and discuss orthonormal bases. We show that all bases are orthonormal and have the same cardinality. It is shown that the set of subspaces form an atomistic orthomodular poset. We then demonstrate that an operator tha...

Orbits of Maximal Vector Spaces

Let V∞ be a standard computable infinite-dimensional vector space over the rationals. The lattice L(V∞) of computably enumerable vector subspaces of V∞, and its quotient lattice modulo finite dimension, L(V∞), have been extensively studied. However, many important questions still remain open. In 1998, R. Downey and J. Remmel posed the question of finding meaningful orbits in L(V∞) (Question 5.8...

Vector cascade algorithms and refinable function vectors in Sobolev spaces

In this paper we shall study vector cascade algorithms and refinable function vectors with a general isotropic dilation matrix in Sobolev spaces. By investigating several properties of the initial function vectors in a vector cascade algorithm, we are able to take a relatively unified approach to study several questions such as convergence, rate of convergence and error estimate for a perturbed...

Bisimulations and Boolean Vectors

A modal accessibility relation is just a transition relation, and so can be represented by a {0,1} valued transition matrix. Starting from this observation, I first show that the machinery of matrices, over Boolean algebras more general than the two-valued one, is appropriate for investigating multi-modal semantics. Then I show that bisimulations have a rather elegant theory, when expressed in ...

Maximal irredundance and maximal ideal independence in Boolean algebras