{"id":"https://openalex.org/W4361295207","doi":"https://doi.org/10.1155/2023/6235312","title":"Characterizations of the Generalized MPCEP Inverse of Rectangular Matrices","display_name":"Characterizations of the Generalized MPCEP Inverse of Rectangular Matrices","publication_year":2023,"publication_date":"2023-03-29","ids":{"openalex":"https://openalex.org/W4361295207","doi":"https://doi.org/10.1155/2023/6235312"},"language":"en","primary_location":{"id":"doi:10.1155/2023/6235312","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2023/6235312","pdf_url":"https://downloads.hindawi.com/journals/jam/2023/6235312.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2023/6235312.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033362612","display_name":"Jiaxuan Yao","orcid":"https://orcid.org/0009-0002-8616-8738"},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaxuan Yao","raw_affiliation_strings":["School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, China","institution_ids":["https://openalex.org/I145897649"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058546291","display_name":"Xiaoji Liu","orcid":"https://orcid.org/0000-0002-9249-5156"},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoji Liu","raw_affiliation_strings":["School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, China","institution_ids":["https://openalex.org/I145897649"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014521709","display_name":"Hongwei Jin","orcid":"https://orcid.org/0000-0001-9009-591X"},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongwei Jin","raw_affiliation_strings":["School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, China","institution_ids":["https://openalex.org/I145897649"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014521709"],"corresponding_institution_ids":["https://openalex.org/I145897649"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.5899,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69570556,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"2023","issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9990000128746033,"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":0.9990000128746033,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9710999727249146,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9682999849319458,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/inverse","display_name":"Inverse","score":0.8636354207992554},{"id":"https://openalex.org/keywords/generalized-inverse","display_name":"Generalized inverse","score":0.7374943494796753},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7274966239929199},{"id":"https://openalex.org/keywords/moore\u2013penrose-pseudoinverse","display_name":"Moore\u2013Penrose pseudoinverse","score":0.6318691968917847},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5641817450523376},{"id":"https://openalex.org/keywords/inverse-function","display_name":"Inverse function","score":0.5063701868057251},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4632400870323181},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4590005874633789},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4283655881881714},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34459078311920166},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3311106562614441},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29248952865600586},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06017795205116272},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.04250267148017883}],"concepts":[{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.8636354207992554},{"id":"https://openalex.org/C76134657","wikidata":"https://www.wikidata.org/wiki/Q370634","display_name":"Generalized inverse","level":3,"score":0.7374943494796753},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7274966239929199},{"id":"https://openalex.org/C21556879","wikidata":"https://www.wikidata.org/wiki/Q43219517","display_name":"Moore\u2013Penrose pseudoinverse","level":3,"score":0.6318691968917847},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5641817450523376},{"id":"https://openalex.org/C140528856","wikidata":"https://www.wikidata.org/wiki/Q191884","display_name":"Inverse function","level":3,"score":0.5063701868057251},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4632400870323181},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4590005874633789},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4283655881881714},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34459078311920166},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3311106562614441},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29248952865600586},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06017795205116272},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.04250267148017883},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2023/6235312","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2023/6235312","pdf_url":"https://downloads.hindawi.com/journals/jam/2023/6235312.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jnljam:6235312","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/jam/2023/6235312.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:86159596f5424c15bc19d578a73cfb5d","is_oa":true,"landing_page_url":"https://doaj.org/article/86159596f5424c15bc19d578a73cfb5d","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2023 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2023/6235312","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2023/6235312","pdf_url":"https://downloads.hindawi.com/journals/jam/2023/6235312.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2681324843","display_name":null,"funder_award_id":"2018 GXNSFDA281023","funder_id":"https://openalex.org/F4320322768","funder_display_name":"Natural Science Foundation of Guangxi Province"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4771591560","display_name":null,"funder_award_id":"12061015","funder_id":"https://openalex.org/F4320322768","funder_display_name":"Natural Science Foundation of Guangxi Province"},{"id":"https://openalex.org/G4899299961","display_name":null,"funder_award_id":"12061015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7608752429","display_name":null,"funder_award_id":"Talent","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7934048554","display_name":null,"funder_award_id":"GUIKE AD21220024","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8058745853","display_name":null,"funder_award_id":"2018 GXNSFDA281023","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8252601063","display_name":null,"funder_award_id":"GUIKE AD21220024","funder_id":"https://openalex.org/F4320322768","funder_display_name":"Natural Science Foundation of Guangxi Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322768","display_name":"Natural Science Foundation of Guangxi Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4361295207.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W2052197050","https://openalex.org/W2055576996","https://openalex.org/W2077639421","https://openalex.org/W2084265625","https://openalex.org/W2117133519","https://openalex.org/W2165942041","https://openalex.org/W2340966007","https://openalex.org/W2585829753","https://openalex.org/W2954696913","https://openalex.org/W2964125203","https://openalex.org/W3006793157","https://openalex.org/W3081577676","https://openalex.org/W3119821756","https://openalex.org/W3130389347","https://openalex.org/W6602615047"],"related_works":["https://openalex.org/W4385273312","https://openalex.org/W2350269050","https://openalex.org/W3081932876","https://openalex.org/W1797940506","https://openalex.org/W2349045512","https://openalex.org/W4225689497","https://openalex.org/W1644797008","https://openalex.org/W2369203135","https://openalex.org/W4361295207","https://openalex.org/W1859709464"],"abstract_inverted_index":{"In":[0],"this":[1,25],"paper,":[2],"we":[3],"introduce":[4],"a":[5,14,34],"new":[6,26],"generalized":[7],"inverse,":[8],"called":[9],"the":[10,31,49,53,59],"G-MPCEP":[11,54,60],"inverse":[12,55,61],"of":[13,24,33,68],"complex":[15],"matrix.":[16],"We":[17],"investigate":[18],"some":[19],"characterizations,":[20],"representations,":[21],"and":[22],"properties":[23],"inverse.":[27],"Cramer\u2019s":[28],"rule":[29],"for":[30,52],"solution":[32],"singular":[35],"equation":[36],"<a:math":[37],"xmlns:a=\"http://www.w3.org/1998/Math/MathML\"":[38],"id=\"M1\">":[39],"<a:mi>A</a:mi>":[40],"<a:mi>x</a:mi>":[41],"<a:mo>=</a:mo>":[42],"<a:mi>B</a:mi>":[43],"</a:math>":[44],"is":[45,71],"also":[46],"presented.":[47],"Moreover,":[48],"determinantal":[50],"representations":[51],"are":[56],"studied.":[57],"Finally,":[58],"being":[62],"used":[63],"in":[64],"solving":[65],"appropriate":[66],"systems":[67],"linear":[69],"equations":[70],"established.":[72]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
