Graph of Linear Transformations over a Field
A Master of Science thesis in Mathematics by Yasmine Ahmed El-Ashi entitled, “Graph of Linear Transformations over a Field”, submitted in June 2019. Thesis advisor is Dr. Ayman Badawi. Soft and hard copy available.
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| Format: | doctoralThesis |
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2019
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| Online Access: | http://hdl.handle.net/11073/16476 |
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| _version_ | 1864513434960265216 |
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| author | El-Ashi, Yasmine Ahmed |
| author_facet | El-Ashi, Yasmine Ahmed |
| author_role | author |
| dc.contributor.none.fl_str_mv | Badawi, Ayman |
| dc.creator.none.fl_str_mv | El-Ashi, Yasmine Ahmed |
| dc.date.none.fl_str_mv | 2019-09-03T07:33:03Z 2019-09-03T07:33:03Z 2019-06 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | 29.232-2019.01 http://hdl.handle.net/11073/16476 |
| dc.language.none.fl_str_mv | en_US |
| dc.subject.none.fl_str_mv | Graph theory Linear transformations Mathematics Graph theory Transformations (Mathematics) |
| dc.title.none.fl_str_mv | Graph of Linear Transformations over a Field |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/doctoralThesis |
| description | A Master of Science thesis in Mathematics by Yasmine Ahmed El-Ashi entitled, “Graph of Linear Transformations over a Field”, submitted in June 2019. Thesis advisor is Dr. Ayman Badawi. Soft and hard copy available. |
| format | doctoralThesis |
| id | aus_bcf4ce0abdc037c4c025ab8c18e893b2 |
| identifier_str_mv | 29.232-2019.01 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/16476 |
| publishDate | 2019 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
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| spelling | Graph of Linear Transformations over a FieldEl-Ashi, Yasmine AhmedGraph theoryLinear transformationsMathematicsGraph theoryTransformations (Mathematics)A Master of Science thesis in Mathematics by Yasmine Ahmed El-Ashi entitled, “Graph of Linear Transformations over a Field”, submitted in June 2019. Thesis advisor is Dr. Ayman Badawi. Soft and hard copy available.This research is an attempt to introduce a connection between graph theory and linear transformations of finite dimensional vector spaces over a field F (in our case we will be considering R). Let Rᵐ, Rⁿ be finite vector spaces over R, and let L be the set of all non-trivial linear transformations from Rᵐ to Rⁿ. An equivalence relation ~ is defined on L such that two elements f, k ϵ L are equivalent, f ~ k, if and only if ker (f) = ker (k). Let V be the set of all equivalence classes of ~. We define a new graph, G([t] : Rᵐ → Rⁿ), to be the undirected graph with vertex set equal to V , such that two vertices, [x] ; [y] ϵ G([t] : Rᵐ → Rⁿ) are adjacent if and only if ker (x) ∩ ker (y) ≠ 0. The relationship between the connectivity of the graph G([t] : Rᵐ → Rⁿ) and the values of m and n has been investigated. In addition, we determine the values of m and n for a complete and totally disconnected graph, as well as the diameter and girth of the graph if connected.College of Arts and SciencesDepartment of Mathematics and StatisticsMaster of Science in Mathematics (MSMTH)Badawi, Ayman2019-09-03T07:33:03Z2019-09-03T07:33:03Z2019-06info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdf29.232-2019.01http://hdl.handle.net/11073/16476en_USoai:repository.aus.edu:11073/164762025-06-26T12:36:35Z |
| spellingShingle | Graph of Linear Transformations over a Field El-Ashi, Yasmine Ahmed Graph theory Linear transformations Mathematics Graph theory Transformations (Mathematics) |
| status_str | publishedVersion |
| title | Graph of Linear Transformations over a Field |
| title_full | Graph of Linear Transformations over a Field |
| title_fullStr | Graph of Linear Transformations over a Field |
| title_full_unstemmed | Graph of Linear Transformations over a Field |
| title_short | Graph of Linear Transformations over a Field |
| title_sort | Graph of Linear Transformations over a Field |
| topic | Graph theory Linear transformations Mathematics Graph theory Transformations (Mathematics) |
| url | http://hdl.handle.net/11073/16476 |