{"id":"https://openalex.org/W3130450312","doi":"https://doi.org/10.1093/imamci/dnab001","title":"On the algebraic structure of the Moore\u2013Penrose inverse of a polynomial matrix","display_name":"On the algebraic structure of the Moore\u2013Penrose inverse of a polynomial matrix","publication_year":2021,"publication_date":"2021-01-06","ids":{"openalex":"https://openalex.org/W3130450312","doi":"https://doi.org/10.1093/imamci/dnab001","mag":"3130450312"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dnab001","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnab001","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","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/A5075118848","display_name":"Ioannis Kafetzis","orcid":"https://orcid.org/0000-0002-3533-2246"},"institutions":[{"id":"https://openalex.org/I21370196","display_name":"Aristotle University of Thessaloniki","ror":"https://ror.org/02j61yw88","country_code":"GR","type":"education","lineage":["https://openalex.org/I21370196"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Ioannis S Kafetzis","raw_affiliation_strings":["School of Mathematics , Aristotle University of Thessaloniki, Thessaloniki 54124, Greece"],"affiliations":[{"raw_affiliation_string":"School of Mathematics , Aristotle University of Thessaloniki, Thessaloniki 54124, Greece","institution_ids":["https://openalex.org/I21370196"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066594965","display_name":"Nicholas P. Karampetakis","orcid":"https://orcid.org/0000-0002-4578-5521"},"institutions":[{"id":"https://openalex.org/I21370196","display_name":"Aristotle University of Thessaloniki","ror":"https://ror.org/02j61yw88","country_code":"GR","type":"education","lineage":["https://openalex.org/I21370196"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Nicholas P Karampetakis","raw_affiliation_strings":["School of Mathematics , Aristotle University of Thessaloniki, Thessaloniki 54124, Greece"],"affiliations":[{"raw_affiliation_string":"School of Mathematics , Aristotle University of Thessaloniki, Thessaloniki 54124, Greece","institution_ids":["https://openalex.org/I21370196"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5075118848"],"corresponding_institution_ids":["https://openalex.org/I21370196"],"apc_list":{"value":2582,"currency":"GBP","value_usd":3167},"apc_paid":null,"fwci":0.5919,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7006465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"39","issue":"2","first_page":"443","last_page":"459"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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/T10232","display_name":"Optical Network Technologies","score":0.9851999878883362,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9811999797821045,"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":0.8136827945709229},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6882380247116089},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6240402460098267},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.5785905122756958},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.5663527846336365},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.549323558807373},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5464285016059875},{"id":"https://openalex.org/keywords/minimal-polynomial","display_name":"Minimal polynomial (linear algebra)","score":0.47597140073776245},{"id":"https://openalex.org/keywords/companion-matrix","display_name":"Companion matrix","score":0.45115363597869873},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.44736456871032715},{"id":"https://openalex.org/keywords/characteristic-polynomial","display_name":"Characteristic polynomial","score":0.41770613193511963},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4100257158279419},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32949769496917725},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11957579851150513}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8136827945709229},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6882380247116089},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6240402460098267},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.5785905122756958},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.5663527846336365},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.549323558807373},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5464285016059875},{"id":"https://openalex.org/C30597210","wikidata":"https://www.wikidata.org/wiki/Q1163608","display_name":"Minimal polynomial (linear algebra)","level":5,"score":0.47597140073776245},{"id":"https://openalex.org/C141495983","wikidata":"https://www.wikidata.org/wiki/Q814361","display_name":"Companion matrix","level":5,"score":0.45115363597869873},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.44736456871032715},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.41770613193511963},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4100257158279419},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32949769496917725},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11957579851150513},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/imamci/dnab001","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnab001","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W63662626","https://openalex.org/W1516379708","https://openalex.org/W1594851591","https://openalex.org/W1970606629","https://openalex.org/W1975179215","https://openalex.org/W1975778770","https://openalex.org/W1977688320","https://openalex.org/W1979255254","https://openalex.org/W1980151054","https://openalex.org/W1994146628","https://openalex.org/W1996248405","https://openalex.org/W1997661387","https://openalex.org/W2033079945","https://openalex.org/W2051295637","https://openalex.org/W2055576996","https://openalex.org/W2059962345","https://openalex.org/W2066807205","https://openalex.org/W2067805107","https://openalex.org/W2070395439","https://openalex.org/W2075066642","https://openalex.org/W2080549201","https://openalex.org/W2085849252","https://openalex.org/W2086242700","https://openalex.org/W2086742230","https://openalex.org/W2121836583","https://openalex.org/W2130970793","https://openalex.org/W2142777436","https://openalex.org/W2157508176","https://openalex.org/W2170444563","https://openalex.org/W2265466360","https://openalex.org/W2406624004","https://openalex.org/W2477745194","https://openalex.org/W2533849559","https://openalex.org/W2535631930","https://openalex.org/W2558581641","https://openalex.org/W2604446226","https://openalex.org/W2788629066","https://openalex.org/W2972270818","https://openalex.org/W4238324407","https://openalex.org/W4242045505","https://openalex.org/W7015426794"],"related_works":["https://openalex.org/W1981843820","https://openalex.org/W1543706171","https://openalex.org/W2364793762","https://openalex.org/W2062371205","https://openalex.org/W2391577669","https://openalex.org/W170171843","https://openalex.org/W2004329086","https://openalex.org/W2150665371","https://openalex.org/W1993248888","https://openalex.org/W3130450312"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"work":[2],"establishes":[3],"the":[4,7,25,30,42,62,68,90,94],"connection":[5],"between":[6,67],"finite":[8,52,56],"and":[9,17,54,77],"infinite":[10,69],"algebraic":[11],"structure":[12,71],"of":[13,24,45,64,72,93],"singular":[14,47,74],"polynomial":[15,48,75],"matrices":[16,97],"their":[18],"Moore\u2013Penrose":[19],"(MP)":[20],"inverse.":[21],"The":[22],"uniqueness":[23],"MP":[26,43,79],"inverse":[27,44,80],"leads":[28],"to":[29,83],"assumption":[31],"that":[32,41,89],"such":[33],"a":[34,46,65],"relation":[35],"must":[36],"exist.":[37,84],"It":[38],"is":[39,81,87],"proved":[40,82],"matrix":[49,76],"has":[50],"no":[51],"zeros":[53],"its":[55,78],"poles":[57],"are":[58,98],"fully":[59],"determined.":[60],"Furthermore,":[61],"existence":[63],"correspondence":[66],"pole/zero":[70],"any":[73],"Finally,":[85],"it":[86],"shown":[88],"minimal":[91],"indices":[92],"two":[95],"aforementioned":[96],"connected":[99],"as":[100],"well.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
