{"id":"https://openalex.org/W4323656813","doi":"https://doi.org/10.1137/22m1471535","title":"Primitivity and Hurwitz Primitivity of Nonnegative Matrix Tuples: A Unified Approach","display_name":"Primitivity and Hurwitz Primitivity of Nonnegative Matrix Tuples: A Unified Approach","publication_year":2023,"publication_date":"2023-03-09","ids":{"openalex":"https://openalex.org/W4323656813","doi":"https://doi.org/10.1137/22m1471535"},"language":"en","primary_location":{"id":"doi:10.1137/22m1471535","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1471535","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","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/A5010329446","display_name":"Yaokun Wu","orcid":"https://orcid.org/0000-0002-6811-7067"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yaokun Wu","raw_affiliation_strings":["School of Mathematical Sciences and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China"],"raw_orcid":"https://orcid.org/0000-0002-6811-7067","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018728190","display_name":"Yinfeng Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yinfeng Zhu","raw_affiliation_strings":["School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China, and Department of Mathematics, Imperial College London, 180 Queen\u2019s Gate, London SW7 2AZ, UK","School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China, and Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK"],"raw_orcid":"https://orcid.org/0000-0003-1724-5250","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China, and Department of Mathematics, Imperial College London, 180 Queen\u2019s Gate, London SW7 2AZ, UK","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China, and Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010329446"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":0.388,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61733271,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"44","issue":"1","first_page":"196","last_page":"211"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9984999895095825,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9973999857902527,"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/mathematics","display_name":"Mathematics","score":0.8431960344314575},{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.6357446908950806},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.6065833568572998},{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.5875431299209595},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5623656511306763},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5277177691459656},{"id":"https://openalex.org/keywords/hurwitz-matrix","display_name":"Hurwitz matrix","score":0.5251510143280029},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5161955952644348},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4690176844596863},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42280134558677673},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3973264694213867},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3368990421295166}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8431960344314575},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.6357446908950806},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.6065833568572998},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.5875431299209595},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5623656511306763},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5277177691459656},{"id":"https://openalex.org/C198931094","wikidata":"https://www.wikidata.org/wiki/Q2610096","display_name":"Hurwitz matrix","level":3,"score":0.5251510143280029},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5161955952644348},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4690176844596863},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42280134558677673},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3973264694213867},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3368990421295166},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1471535","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1471535","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2154040637","display_name":null,"funder_award_id":"11971305","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W630797071","https://openalex.org/W1275173217","https://openalex.org/W1540360878","https://openalex.org/W1794931121","https://openalex.org/W1972887674","https://openalex.org/W1985459513","https://openalex.org/W1985762288","https://openalex.org/W1987579414","https://openalex.org/W1991980356","https://openalex.org/W1999883305","https://openalex.org/W2006924088","https://openalex.org/W2015970678","https://openalex.org/W2032418100","https://openalex.org/W2034962669","https://openalex.org/W2051638203","https://openalex.org/W2055037223","https://openalex.org/W2078426390","https://openalex.org/W2079961436","https://openalex.org/W2084186311","https://openalex.org/W2102353107","https://openalex.org/W2102787657","https://openalex.org/W2108151339","https://openalex.org/W2118382442","https://openalex.org/W2122803069","https://openalex.org/W2131370775","https://openalex.org/W2137688090","https://openalex.org/W2140147014","https://openalex.org/W2140195055","https://openalex.org/W2165469059","https://openalex.org/W2173819663","https://openalex.org/W2267387057","https://openalex.org/W2284475030","https://openalex.org/W2314937304","https://openalex.org/W2411579325","https://openalex.org/W2743964443","https://openalex.org/W2887301084","https://openalex.org/W2953557426","https://openalex.org/W2971604437","https://openalex.org/W3104052932","https://openalex.org/W3134505533","https://openalex.org/W4205848555","https://openalex.org/W4210686978","https://openalex.org/W4213217062","https://openalex.org/W4239117818","https://openalex.org/W4240899876","https://openalex.org/W4243154068","https://openalex.org/W4246219036","https://openalex.org/W4299687166","https://openalex.org/W4302097244"],"related_works":["https://openalex.org/W1972942382","https://openalex.org/W2009962825","https://openalex.org/W1722744795","https://openalex.org/W124275629","https://openalex.org/W2136727990","https://openalex.org/W2950014027","https://openalex.org/W2952991236","https://openalex.org/W964575223","https://openalex.org/W4296948412","https://openalex.org/W2358718285"],"abstract_inverted_index":{".For":[0],"an":[1,116,124],"\\(m\\)":[2],"-tuple":[3],"of":[4,19,45,60,78,81,94,98,135],"nonnegative":[5],"\\(n{\\times":[6],"}n\\)":[7],"matrices":[8,82,99],"\\(":[9],"(A_1,":[10],"\\ldots,":[11],"A_m)\\)":[12],",":[13,52],"primitivity/Hurwitz":[14],"primitivity":[15,122],"means":[16,57],"the":[17,43,58,61,74,90,112],"existence":[18,59],"a":[20,35,65,70,105,130],"positive":[21,66],"product/Hurwitz":[22],"product,":[23],"respectively":[24],"(all":[25],"products":[26,47],"are":[27],"with":[28,34,48,64,107],"repetitions":[29],"permitted).":[30],"The":[31],"Hurwitz":[32,95,131,146],"product":[33,63],"Parikh":[36],"vector":[37,133],"\\(\\alpha":[38],"=(\\alpha_1,\\ldots,\\alpha_m)\\in":[39],"\\mathbb{Z}_{\\ge":[40],"0}^m\\)":[41],"is":[42],"sum":[44],"all":[46],"\\(\\alpha_i\\)":[49],"multipliers":[50],"\\(A_i\\)":[51],"\\(i=1,\\ldots,m\\)":[53],".":[54,138],"Ergodicity/Hurwitz":[55],"ergodicity":[56],"corresponding":[62],"row.":[67],"We":[68,139],"give":[69],"unified":[71],"proof":[72],"for":[73,89],"Protasov\u2013Vonyov":[75],"characterization":[76,92],"(2012)":[77],"primitive":[79,96,132],"tuples":[80,97],"without":[83,100],"zero":[84,101],"rows":[85],"and":[86,88,123,145],"columns":[87],"Protasov":[91],"(2013)":[93],"rows.":[102],"By":[103],"establishing":[104],"connection":[106],"synchronizing":[108],"automata,":[109],"we,":[110],"under":[111],"aforementioned":[113],"conditions,":[114],"find":[115],"\\(O(n^2m)\\)":[117],"-time":[118,126],"algorithm":[119,127],"to":[120,128],"decide":[121],"\\(O(n^3m^2)\\)":[125],"construct":[129],"\\(\\alpha\\)":[134],"weight":[136],"\\(\\sum_{i=1}^m\\alpha_i=O(n^3)\\)":[137],"also":[140],"report":[141],"results":[142],"on":[143],"ergodic":[144,147],"matrix":[148],"tuples.Keywordsautomaton\u010cern\u00fd":[149],"functionergodic":[150],"exponentHamiltonian":[151],"walkprimitive":[152],"exponentstable":[153],"relationMSC":[154],"codes15B4847D0368Q1968Q45":[155]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2025-12-24T23:09:58.560324","created_date":"2025-10-10T00:00:00"}