Biangular vectors
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Date
2013
Authors
Best, Darcy
University of Lethbridge. Faculty of Arts and Science
Journal Title
Journal ISSN
Volume Title
Publisher
Lethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science, 2013
Abstract
This thesis introduces unit weighing matrices, a generalization of Hadamard matrices.
When dealing with unit weighing matrices, a lot of the structure that is held by Hadamard
matrices is lost, but this loss of rigidity allows these matrices to be used in the construction
of certain combinatorial objects. We are able to fully classify these matrices for many small
values by defining equivalence classes analogous to those found with Hadamard matrices.
We then proceed to introduce an extension to mutually unbiased bases, called mutually unbiased
weighing matrices, by allowing for different subsets of vectors to be orthogonal. The
bounds on the size of these sets of matrices, both lower and upper, are examined. In many
situations, we are able to show that these bounds are sharp. Finally, we show how these sets
of matrices can be used to generate combinatorial objects such as strongly regular graphs
and association schemes.
Description
viii, 133 leaves ; 29 cm
Keywords
Unit weighing matrices , Hadamard matrices , Unbiased , Vectors , Dissertations, Academic , Mutually unbiased weighing matrices