{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/71017"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/71017","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Involutory matrices, modulo m","abstract":"Given the prime power factorization of a positive integer m, a method for calculating the number of all distinct n x n - involutory matrices (mod m) is derived. This is done by first developing a method for the construction and enumeration of involutory matrices (mod P<sup>α</sup>), without duplication, for each prime power modulus P<sup>α</sup>. Using these results, formulas for the number of distinct involutory matrices (mod P<sup>α</sup>) of order n are given where p is an odd prime, p=2, α= 1 and α > 1. The concept of a fixed group associated with an involutory matrix (mod P<sup>α</sup>) is used to characterize such matrices. Involutory matrices (mod P<sup>α</sup>) of order n are considered as linear transformations on a vector space of n-tuples to provide uncomplicated proofs for the basic results concerning involutory matrices over a finite field.","abstract_html":"Given the prime power factorization of a positive integer m, a method for calculating the number of all distinct n x n - involutory matrices (mod m) is derived. This is done by first developing a method for the construction and enumeration of involutory matrices (mod P&lt;sup&gt;α&lt;/sup&gt;), without duplication, for each prime power modulus P&lt;sup&gt;α&lt;/sup&gt;. Using these results, formulas for the number of distinct involutory matrices (mod P&lt;sup&gt;α&lt;/sup&gt;) of order n are given where p is an odd prime, p=2, α= 1 and α &gt; 1. The concept of a fixed group associated with an involutory matrix (mod P&lt;sup&gt;α&lt;/sup&gt;) is used to characterize such matrices. Involutory matrices (mod P&lt;sup&gt;α&lt;/sup&gt;) of order n are considered as linear transformations on a vector space of n-tuples to provide uncomplicated proofs for the basic results concerning involutory matrices over a finite field.","abstract_has_math":false,"creators":["Amey, Dorothy Mae"],"institution":"Virginia Polytechnic Institute","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1969,"date_issued":"1969","date_published":"1969","updated_at":"2026-07-22T22:18:53Z","subjects":[],"languages":["en_US"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10919/71017","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Amey, Dorothy Mae"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-05-23T14:57:10Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-05-23T14:57:10Z"]},{"key":"dc:date.issued","label":"Date","values":["1969"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/71017"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Given the prime power factorization of a positive integer m, a method for calculating the number of all distinct n x n - involutory matrices (mod m) is derived. This is done by first developing a method for the construction and enumeration of involutory matrices (mod P<sup>α</sup>), without duplication, for each prime power modulus P<sup>α</sup>. Using these results, formulas for the number of distinct involutory matrices (mod P<sup>α</sup>) of order n are given where p is an odd prime, p=2, α= 1 and α > 1. The concept of a fixed group associated with an involutory matrix (mod P<sup>α</sup>) is used to characterize such matrices. Involutory matrices (mod P<sup>α</sup>) of order n are considered as linear transformations on a vector space of n-tuples to provide uncomplicated proofs for the basic results concerning involutory matrices over a finite field."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Involutory matrices, modulo m"]}]}],"canonical_facts":{"dc:contributor.department":["Mathematics"],"dc:creator":["Amey, Dorothy Mae"],"dc:date.accessioned":["2016-05-23T14:57:10Z"],"dc:date.available":["2016-05-23T14:57:10Z"],"dc:date.issued":["1969"],"dc:description.abstract":["Given the prime power factorization of a positive integer m, a method for calculating the number of all distinct n x n - involutory matrices (mod m) is derived. This is done by first developing a method for the construction and enumeration of involutory matrices (mod P<sup>α</sup>), without duplication, for each prime power modulus P<sup>α</sup>. Using these results, formulas for the number of distinct involutory matrices (mod P<sup>α</sup>) of order n are given where p is an odd prime, p=2, α= 1 and α > 1. The concept of a fixed group associated with an involutory matrix (mod P<sup>α</sup>) is used to characterize such matrices. Involutory matrices (mod P<sup>α</sup>) of order n are considered as linear transformations on a vector space of n-tuples to provide uncomplicated proofs for the basic results concerning involutory matrices over a finite field."],"dc:description.degree":["Master of Science"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/71017"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Involutory matrices, modulo m"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute"]},"updated_at":"2026-07-22T22:18:53Z"}