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On orthogonal matrices

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dc.contributor.advisor Kharaghani, Hadi
dc.contributor.advisor Holzmann, Wolf
dc.contributor.author Behbahani, Majid
dc.contributor.author University of Lethbridge. Faculty of Arts and Science
dc.date.accessioned 2007-05-12T20:34:17Z
dc.date.available 2007-05-12T20:34:17Z
dc.date.issued 2004
dc.identifier.uri http://hdl.handle.net/10133/213
dc.description iv, 64 leaves : ill., map ; 29 cm. en
dc.description.abstract Our main aim in this thesis is to study and search for orthogonal matrices which have a certain kind of block structure. The most desirable class of matrices for our purpose are orthogonal designs constructible from 16 circulant matrices. In studying these matrices, we show that the OD (12;1,1,1,9) is the only orthogonal design constructible from 16 circulant matrices of type OD (4n;1,1,1,4n-3), whenever n > 1 is an odd integer. We then use an exhaustive search to show that the only orthogonal design constructible from 16 circulant matrices of order 12 on 4 variables is the OD (12;1,1,1,9). It is known that by using of T-matrices and orthogonal designs constructible from 16 circulant matrices one can produce an infinite family of orthogonal designs. To complement our studies we reproduce and important recent construction of T-matrices by Xia and Xia. We then turn our attention to the applications of orthogonal matices. In some recent works productive regular Hadamard matrices are used to construct many new infinite families of symmetric designs. We show that for each integer n for which 4n is the order of a Hadamard matrix and 8n2 - 1 is a prime, there is a productive regular Hadamard matrix of order 16n2(82-1)2. As a corollary, we get many new infinite classes of symmetric designs whenever either of 4n(8n2-1)-1,4n(82-1) +1 is a prime power. We also review some other constructions of productive regular Hadamard matrices which are related to our work. en
dc.language.iso en_US en
dc.publisher Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2004 en
dc.relation.ispartofseries Thesis (University of Lethbridge. Faculty of Arts and Science) en
dc.subject Dissertations, Academic en
dc.subject Matrices en
dc.subject Hadamard matrices en
dc.title On orthogonal matrices en
dc.type Thesis en
dc.publisher.faculty Arts and Science
dc.publisher.department Department of Mathematics and Computer Science

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