{"id":"https://openalex.org/W4390143542","doi":"https://doi.org/10.1007/978-3-031-50078-7_31","title":"On Singular Value Decomposition and\u00a0Polar Decomposition in\u00a0Geometric Algebras","display_name":"On Singular Value Decomposition and\u00a0Polar Decomposition in\u00a0Geometric Algebras","publication_year":2023,"publication_date":"2023-12-23","ids":{"openalex":"https://openalex.org/W4390143542","doi":"https://doi.org/10.1007/978-3-031-50078-7_31"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-50078-7_31","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-50078-7_31","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090590071","display_name":"Dmitry Shirokov","orcid":"https://orcid.org/0000-0002-2407-9601"},"institutions":[{"id":"https://openalex.org/I118501908","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516","country_code":"RU","type":"education","lineage":["https://openalex.org/I118501908"]},{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210097085","https://openalex.org/I4210107660"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Dmitry Shirokov","raw_affiliation_strings":["HSE University, 101000, Moscow, Russia","Institute for Information Transmission Problems of the Russian Academy of Sciences, 127051, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"HSE University, 101000, Moscow, Russia","institution_ids":["https://openalex.org/I118501908"]},{"raw_affiliation_string":"Institute for Information Transmission Problems of the Russian Academy of Sciences, 127051, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090590071"],"corresponding_institution_ids":["https://openalex.org/I118501908","https://openalex.org/I4210107660"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":4.6678,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.95571956,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"391","last_page":"401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9702000021934509,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/geometric-algebra","display_name":"Geometric algebra","score":0.8660551905632019},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8218556642532349},{"id":"https://openalex.org/keywords/multivector","display_name":"Multivector","score":0.6747419834136963},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5963089466094971},{"id":"https://openalex.org/keywords/clifford-algebra","display_name":"Clifford algebra","score":0.5618764758110046},{"id":"https://openalex.org/keywords/polar-decomposition","display_name":"Polar decomposition","score":0.5542320013046265},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4740833044052124},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4709737300872803},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.46676796674728394},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4330374002456665},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4125560522079468},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35018089413642883},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3267357647418976},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2701864242553711},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19670924544334412},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.1933123767375946},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.1826038360595703},{"id":"https://openalex.org/keywords/jordan-algebra","display_name":"Jordan algebra","score":0.17299231886863708},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09153598546981812}],"concepts":[{"id":"https://openalex.org/C180671464","wikidata":"https://www.wikidata.org/wiki/Q1186649","display_name":"Geometric algebra","level":4,"score":0.8660551905632019},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8218556642532349},{"id":"https://openalex.org/C26238338","wikidata":"https://www.wikidata.org/wiki/Q2377336","display_name":"Multivector","level":5,"score":0.6747419834136963},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5963089466094971},{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.5618764758110046},{"id":"https://openalex.org/C130956294","wikidata":"https://www.wikidata.org/wiki/Q2101158","display_name":"Polar decomposition","level":3,"score":0.5542320013046265},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4740833044052124},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4709737300872803},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.46676796674728394},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4330374002456665},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4125560522079468},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35018089413642883},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3267357647418976},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2701864242553711},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19670924544334412},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.1933123767375946},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.1826038360595703},{"id":"https://openalex.org/C100376341","wikidata":"https://www.wikidata.org/wiki/Q649977","display_name":"Jordan algebra","level":4,"score":0.17299231886863708},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09153598546981812},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-50078-7_31","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-50078-7_31","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W122875470","https://openalex.org/W1595823061","https://openalex.org/W1930799948","https://openalex.org/W1958349209","https://openalex.org/W1964262399","https://openalex.org/W1998046655","https://openalex.org/W2033772417","https://openalex.org/W2151252442","https://openalex.org/W2511615556","https://openalex.org/W2616421582","https://openalex.org/W2785139474","https://openalex.org/W2941296300","https://openalex.org/W3095097816","https://openalex.org/W3104260428","https://openalex.org/W3105114451","https://openalex.org/W3161039615","https://openalex.org/W3174119315","https://openalex.org/W3200241202","https://openalex.org/W3205470081","https://openalex.org/W4281689616","https://openalex.org/W4327955856","https://openalex.org/W4367147840"],"related_works":["https://openalex.org/W2099345067","https://openalex.org/W1515695641","https://openalex.org/W2157610680","https://openalex.org/W2069039005","https://openalex.org/W2294799822","https://openalex.org/W2361911558","https://openalex.org/W2014430590","https://openalex.org/W2145907930","https://openalex.org/W4235793957","https://openalex.org/W3006042754"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-01-24T23:23:39.755997","created_date":"2025-10-10T00:00:00"}