{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/8447"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/8447","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Calculating and Preserving Star Sets and Star Complements of General Matrices","abstract":"This thesis presents several results relating to star sets and star complements of graphs. While a method for calculating star sets and star complements involving pro- jection matrices has been known since their introduction, a second method involving determinants is demonstrated and shown to be equivalent to the rst method. Some of the theory for star sets and star complements is expanded to general diagonalizable matrices, regardless of symmetry. The concept of preserving star sets between two general matrices is introduced and shown to be an equivalence relation, and attempts are made to classify what types of matrices can preserve the star sets of a general matrix. Finally, we determine some results for general matrices that occur when star set preservation overlaps with other equivalence relations.","abstract_html":"This thesis presents several results relating to star sets and star complements of graphs. While a method for calculating star sets and star complements involving pro- jection matrices has been known since their introduction, a second method involving determinants is demonstrated and shown to be equivalent to the rst method. Some of the theory for star sets and star complements is expanded to general diagonalizable matrices, regardless of symmetry. The concept of preserving star sets between two general matrices is introduced and shown to be an equivalence relation, and attempts are made to classify what types of matrices can preserve the star sets of a general matrix. Finally, we determine some results for general matrices that occur when star set preservation overlaps with other equivalence relations.","abstract_has_math":false,"creators":["Bergen, Ryan Paul"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Master of Science (MSc)","degree_level":"Master's","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Fallat, Shaun"],"committee_chairs":[],"committee_members":["Meagher, Karen"],"year":2017,"date_issued":"2017-08-18","date_published":"2017-08-18","updated_at":"2026-07-24T04:03:30Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4060"],"render_values":[{"text":"https://doi.org/10.82465/4060","href":"https://doi.org/10.82465/4060","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/8447","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Fallat, Shaun"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Meagher, Karen"]},{"key":"dc:creator","label":"Author","values":["Bergen, Ryan Paul"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-11-22T21:45:13Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-11-22T21:45:13Z"]},{"key":"dc:date.issued","label":"Date","values":["2017-08-18"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MSc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4060"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/8447"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematicss, University of Regina. v, 75 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["This thesis presents several results relating to star sets and star complements of graphs. While a method for calculating star sets and star complements involving pro- jection matrices has been known since their introduction, a second method involving determinants is demonstrated and shown to be equivalent to the rst method. Some of the theory for star sets and star complements is expanded to general diagonalizable matrices, regardless of symmetry. The concept of preserving star sets between two general matrices is introduced and shown to be an equivalence relation, and attempts are made to classify what types of matrices can preserve the star sets of a general matrix. Finally, we determine some results for general matrices that occur when star set preservation overlaps with other equivalence relations."]},{"key":"dc:title","label":"Title","values":["Calculating and Preserving Star Sets and Star Complements of General Matrices"]}]}],"canonical_facts":{"dc:contributor.advisor":["Fallat, Shaun"],"dc:contributor.committeemember":["Meagher, Karen"],"dc:creator":["Bergen, Ryan Paul"],"dc:date.accessioned":["2018-11-22T21:45:13Z"],"dc:date.available":["2018-11-22T21:45:13Z"],"dc:date.issued":["2017-08-18"],"dc:description":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematicss, University of Regina. v, 75 p."],"dc:description.abstract":["This thesis presents several results relating to star sets and star complements of graphs. While a method for calculating star sets and star complements involving pro- jection matrices has been known since their introduction, a second method involving determinants is demonstrated and shown to be equivalent to the rst method. Some of the theory for star sets and star complements is expanded to general diagonalizable matrices, regardless of symmetry. The concept of preserving star sets between two general matrices is introduced and shown to be an equivalence relation, and attempts are made to classify what types of matrices can preserve the star sets of a general matrix. Finally, we determine some results for general matrices that occur when star set preservation overlaps with other equivalence relations."],"dc:identifier.doi":["https://doi.org/10.82465/4060"],"dc:identifier.uri":["https://hdl.handle.net/10294/8447"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Calculating and Preserving Star Sets and Star Complements of General Matrices"],"dc:type":["master thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:30Z"}