{"id":"https://openalex.org/W7225112197","doi":"https://doi.org/10.5281/zenodo.23885983","title":"Resolving User3's orthogonal absolute-product question: minimum and minimizers","display_name":"Resolving User3's orthogonal absolute-product question: minimum and minimizers","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225112197","doi":"https://doi.org/10.5281/zenodo.23885983"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23885983","doi":"https://doi.org/10.5281/zenodo.23885983","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23885983","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23885983","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140197743","display_name":"Haobo Ma","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ma, Haobo","raw_affiliation_strings":["ChronoAI Pte Ltd, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ChronoAI Pte Ltd, Singapore","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5118983640","display_name":"Wenlin Zhang","orcid":"https://orcid.org/0009-0005-2414-7968","observed_orcids":["https://orcid.org/0009-0005-2414-7968"]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Zhang, Wenlin","raw_affiliation_strings":["National University of Singapore; ChronoAI Pte Ltd, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Singapore; ChronoAI Pte Ltd, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/triangularization","display_name":"triangularization","score":0.7739999890327454},{"id":"https://openalex.org/keywords/row-and-column-permutations","display_name":"row and column permutations","score":0.8610000014305115},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.9620000123977661},{"id":"https://openalex.org/keywords/special-orthogonal-group","display_name":"special orthogonal group","score":0.8140000104904175},{"id":"https://openalex.org/keywords/minimizers","display_name":"minimizers","score":0.48899999260902405}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8518999814987183},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7712000012397766},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.5669999718666077},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.541700005531311},{"id":"https://openalex.org/C2776285698","wikidata":"https://www.wikidata.org/wiki/Q2642214","display_name":"Exposition (narrative)","level":2,"score":0.5164999961853027},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.49950000643730164},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4909000098705292},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.4878999888896942},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.39660000801086426},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3831999897956848},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.3716000020503998},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2847000062465668},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2540000081062317},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23885983","doi":"https://doi.org/10.5281/zenodo.23885983","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23885983","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23885984","doi":"https://doi.org/10.5281/zenodo.23885984","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23885984","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23885983","doi":"https://doi.org/10.5281/zenodo.23885983","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23885983","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2913384800","https://openalex.org/W2773064159","https://openalex.org/W4399974263","https://openalex.org/W2086623440","https://openalex.org/W7096217457","https://openalex.org/W4403045263","https://openalex.org/W3175541615","https://openalex.org/W1980874769","https://openalex.org/W7058408488","https://openalex.org/W4376891368"],"abstract_inverted_index":{"We":[0,44],"resolve":[1],"User3's":[2],"question":[3,103],"(question":[4],"515549,":[5],"revision":[6],"1,":[7],"September":[8],"25,":[9],"2026):":[10],"for":[11,40],"every":[12,60],"nonsingular":[13],"real":[14],"square":[15],"matrix":[16],"of":[17,23,49,76],"positive":[18],"size,":[19],"the":[20,32,50,54,74,94,99,106],"orthogonal":[21,96],"minimum":[22,91],"rho(|PQ||Q^T":[24],"P^{-1}|)":[25],"is":[26,78],"attained":[27],"and":[28,65,80],"equals":[29],"one.":[30],"Thus":[31],"proposed":[33],"strict":[34],"uniform":[35],"lower":[36],"bound":[37],"cannot":[38],"hold":[39],"any":[41],"such":[42],"matrix.":[43],"give":[45],"a":[46],"self-contained":[47],"exposition":[48],"triangularization":[51],"proof":[52],"in":[53],"pinned":[55],"formal":[56],"source,":[57],"then":[58],"characterize":[59],"minimizer":[61],"by":[62],"independent":[63],"row":[64],"column":[66],"permutations":[67],"to":[68],"triangular":[69],"form.":[70],"For":[71],"fixed":[72],"P,":[73],"set":[75],"minimizers":[77],"finite":[79],"has":[81],"an":[82],"explicit":[83],"description":[84],"using":[85],"row-permuted":[86],"QR":[87],"factorizations.":[88],"The":[89],"same":[90],"holds":[92],"over":[93],"special":[95],"group.":[97],"Finally,":[98],"companion":[100],"absolute-row-sum":[101],"balancing":[102],"follows":[104],"from":[105],"Yamabe-Yujobo":[107],"theorem.":[108]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-11-03T00:00:00"}