2026-09-19T15:01:33.958239800Zhttps://opus.uleth.ca/server/oai/requestoai:opus.uleth.ca:10133/35602019-02-06T06:06:25Zcom_10133_3346com_10133_1com_10133_296col_10133_3347col_10133_298
ULethbridge OPUS Repository
supervisor
Kharaghani, Hadi
author
Best, Darcy
author
University of Lethbridge. Faculty of Arts and Science
2014-10-24T22:47:27Z
2014-10-24T22:47:27Z
2013
https://hdl.handle.net/10133/3560
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.
en_CA
Unit weighing matrices
Hadamard matrices
Unbiased
Vectors
Dissertations, Academic
Mutually unbiased weighing matrices
Biangular vectors
Thesis
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URL
http://localhost:4000/bitstreams/cef4c6a4-712b-4886-b9ca-4fb5523eb98c/download
File
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URL
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BEST_DARCY_MSC_2013.pdf.txt