Amicable T-matrices and applications

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dc.contributor.authorGholamiangonabadi, Hamed
dc.contributor.supervisorKharaghani, Hadi
dc.date.accessioned2013-09-11T22:24:55Z
dc.date.available2013-09-11T22:24:55Z
dc.date.issued2012
dc.degree.levelMasters
dc.descriptioniii, 49 leaves ; 29 cmen_US
dc.description.abstractOur main aim in this thesis is to produce new T-matrices from the set of existing T-matrices. In Theorem 4.3 a multiplication method is introduced to generate new T-matrices of order st, provided that there are some specially structured T-matrices of orders s and t. A class of properly amicable and double disjoint T-matrices are introduced. A number of properly amicable T-matrices are constructed which includes 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 18, 22. To keep the new matrices disjoint an extra condition is imposed on one set of T-matrices and named double disjoint T-matrices. It is shown that there are some T-matrices that are both double disjoint and properly amicable. Using these matrices an infinite family of new T-matrices are constructed. We then turn our attention to the application of T-matrices to construct orthogonal designs and complex Hadamard matrices. Using T-matrices some orthogonal designs constructed from 16 circulant matrices are constructed. It is known that having T-matrices of order t and orthogonal designs constructible from 16 circulant matrices lead to an infinite family of orthogonal designs. Using amicable T-matrices some complex Hadamard matrices are shown to exist.en_US
dc.identifier.urihttps://hdl.handle.net/10133/3262
dc.language.isoen_USen_US
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science, c2012en_US
dc.publisher.departmentDepartment of Mathematics and Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en_US
dc.subjectT-matrixen_US
dc.subjectHadamard matricesen_US
dc.subjectMatricesen_US
dc.subjectDissertations, Academicen_US
dc.titleAmicable T-matrices and applicationsen_US
dc.typeThesisen_US
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