{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/70494"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/70494","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Determinants of matrices over lattices","abstract":"Three different definitions for the determinant of a matrix over arbitrary lattices have been developed to determine which properties and relations were reminiscent of the determinant or permanent of elementary algebra. In each determinant there are properties concerning: the elements of the matrix in the expansion of its determinant; the determinant of a matrix and its transpose; a principle of duality for rows and columns; the interchange of rows and columns; the determinant of a matrix formed from another by a row or column meet of certain elements; and evaluations of certain special matrices. An expansion by row or column is given for one determinant and a lemma on inverses is proven in light of another. A preliminary section on Lattice Theory is also included.","abstract_html":"Three different definitions for the determinant of a matrix over arbitrary lattices have been developed to determine which properties and relations were reminiscent of the determinant or permanent of elementary algebra. In each determinant there are properties concerning: the elements of the matrix in the expansion of its determinant; the determinant of a matrix and its transpose; a principle of duality for rows and columns; the interchange of rows and columns; the determinant of a matrix formed from another by a row or column meet of certain elements; and evaluations of certain special matrices. An expansion by row or column is given for one determinant and a lemma on inverses is proven in light of another. A preliminary section on Lattice Theory is also included.","abstract_has_math":false,"creators":["Chesley, Daniel Sprigg"],"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":1967,"date_issued":"1967","date_published":"1967","updated_at":"2026-07-22T22:19:44Z","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/10919/70494","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":["Chesley, Daniel Sprigg"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-04-21T15:34:48Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-04-21T15:34:48Z"]},{"key":"dc:date.issued","label":"Date","values":["1967"]},{"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/10919/70494"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Three different definitions for the determinant of a matrix over arbitrary lattices have been developed to determine which properties and relations were reminiscent of the determinant or permanent of elementary algebra. In each determinant there are properties concerning: the elements of the matrix in the expansion of its determinant; the determinant of a matrix and its transpose; a principle of duality for rows and columns; the interchange of rows and columns; the determinant of a matrix formed from another by a row or column meet of certain elements; and evaluations of certain special matrices. An expansion by row or column is given for one determinant and a lemma on inverses is proven in light of another. A preliminary section on Lattice Theory is also included."]},{"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":["Determinants of matrices over lattices"]}]}],"canonical_facts":{"dc:contributor.department":["Mathematics"],"dc:creator":["Chesley, Daniel Sprigg"],"dc:date.accessioned":["2016-04-21T15:34:48Z"],"dc:date.available":["2016-04-21T15:34:48Z"],"dc:date.issued":["1967"],"dc:description.abstract":["Three different definitions for the determinant of a matrix over arbitrary lattices have been developed to determine which properties and relations were reminiscent of the determinant or permanent of elementary algebra. In each determinant there are properties concerning: the elements of the matrix in the expansion of its determinant; the determinant of a matrix and its transpose; a principle of duality for rows and columns; the interchange of rows and columns; the determinant of a matrix formed from another by a row or column meet of certain elements; and evaluations of certain special matrices. An expansion by row or column is given for one determinant and a lemma on inverses is proven in light of another. A preliminary section on Lattice Theory is also included."],"dc:description.degree":["Master of Science"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/70494"],"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":["Determinants of matrices over lattices"],"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":"2026-07-22T22:19:44Z"}