{"id":"https://openalex.org/W2078128104","doi":"https://doi.org/10.1137/s0895479898335465","title":"An Algebraic Approach to the Construction of Polyhedral Invariant Cones","display_name":"An Algebraic Approach to the Construction of Polyhedral Invariant Cones","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2078128104","doi":"https://doi.org/10.1137/s0895479898335465","mag":"2078128104"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479898335465","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479898335465","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/A5064493313","display_name":"Maria Elena Valcher","orcid":"https://orcid.org/0000-0002-7595-3688"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maria Elena Valcher","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5074179530","display_name":"Lorenzo Farina","orcid":"https://orcid.org/0000-0001-8314-6029"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lorenzo Farina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3487,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.88661011,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"2","first_page":"453","last_page":"471"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","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/T10792","display_name":"Matrix Theory and Algorithms","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/T11673","display_name":"Advanced Topics in Algebra","score":0.9969000220298767,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9929999709129333,"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/mathematics","display_name":"Mathematics","score":0.8472816944122314},{"id":"https://openalex.org/keywords/irreducibility","display_name":"Irreducibility","score":0.784184455871582},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6713108420372009},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5984176397323608},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5733084678649902},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.5503411889076233},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5095574855804443},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.4515123665332794},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.45010632276535034},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4482635259628296},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3734785318374634},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3210058808326721},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20160835981369019},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07337453961372375},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.068823903799057},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.057961076498031616}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8472816944122314},{"id":"https://openalex.org/C2776823524","wikidata":"https://www.wikidata.org/wiki/Q6073561","display_name":"Irreducibility","level":2,"score":0.784184455871582},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6713108420372009},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5984176397323608},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5733084678649902},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.5503411889076233},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5095574855804443},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.4515123665332794},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.45010632276535034},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4482635259628296},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3734785318374634},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3210058808326721},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20160835981369019},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07337453961372375},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.068823903799057},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.057961076498031616},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479898335465","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479898335465","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"},{"id":"pmh:oai:iris.uniroma1.it:11573/47080","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/47080","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"info:eu-repo/semantics/article"}],"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/W1500921805","https://openalex.org/W1529274881","https://openalex.org/W1547644141","https://openalex.org/W1568175246","https://openalex.org/W1965838222","https://openalex.org/W1972435218","https://openalex.org/W1987932119","https://openalex.org/W1998319923","https://openalex.org/W1999878649","https://openalex.org/W2005226933","https://openalex.org/W2007823335","https://openalex.org/W2020150158","https://openalex.org/W2021317570","https://openalex.org/W2023010641","https://openalex.org/W2082907458","https://openalex.org/W2089857791","https://openalex.org/W2220716464","https://openalex.org/W2275045947","https://openalex.org/W2326792270","https://openalex.org/W2584404844","https://openalex.org/W2798813531","https://openalex.org/W4299798129"],"related_works":["https://openalex.org/W2954167023","https://openalex.org/W2064351239","https://openalex.org/W2949665548","https://openalex.org/W2114983089","https://openalex.org/W1586747893","https://openalex.org/W2950188642","https://openalex.org/W2028676759","https://openalex.org/W2257471395","https://openalex.org/W1589204344","https://openalex.org/W1968663039"],"abstract_inverted_index":{"In":[0,80],"this":[1],"paper,":[2],"based":[3],"on":[4,76],"algebraic":[5],"arguments,":[6],"a":[7,20,39],"new":[8,66],"proof":[9,37],"of":[10,14],"the":[11,55,72,77],"spectral":[12,57],"characterization":[13],"those":[15],"real":[16],"matrices":[17],"that":[18],"leave":[19],"proper":[21,61],"polyhedral":[22,62],"cone":[23,63,78],"invariant":[24],"[":[25],"Trans.":[26],"Amer.":[27],"Math.":[28],"Soc.,":[29],"343":[30],"(1994),":[31],"pp.":[32],"479--524]":[33],"is":[34,38],"given.":[35],"The":[36],"constructive":[40],"one,":[41],"as":[42],"it":[43],"allows":[44],"us":[45],"to":[46],"explicitly":[47],"obtain":[48],"for":[49],"every":[50],"matrix":[51],"A,":[52],"which":[53],"satisfies":[54],"aforementioned":[56],"requirements,":[58],"an":[59],"A-invariant":[60],"$\\mathcal{K}$.":[64,79],"Some":[65],"results":[67],"are":[68,86],"also":[69],"presented,":[70],"concerning":[71],"way":[73],"A":[74],"acts":[75],"particular,":[81],"$\\mathcal{K}$-irreducibility,":[82],"$\\mathcal{K}$-primitivity,":[83],"and":[84],"$\\mathcal{K}$-positivity":[85],"fully":[87],"characterized.":[88]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}