{"id":"https://openalex.org/W3012029385","doi":"https://doi.org/10.1109/cdc40024.2019.9030103","title":"Karpelevich Theorem and the positive realization of matrices","display_name":"Karpelevich Theorem and the positive realization of matrices","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W3012029385","doi":"https://doi.org/10.1109/cdc40024.2019.9030103","mag":"3012029385"},"language":"en","primary_location":{"id":"doi:10.1109/cdc40024.2019.9030103","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030103","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5007661526","display_name":"Filippo Cacace","orcid":"https://orcid.org/0000-0003-1060-744X"},"institutions":[{"id":"https://openalex.org/I155125353","display_name":"Universit\u00e0 Campus Bio-Medico","ror":"https://ror.org/04gqx4x78","country_code":"IT","type":"education","lineage":["https://openalex.org/I155125353"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"F. Cacace","raw_affiliation_strings":["Universit\u00e0 Campus Bio-medico di Roma, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 Campus Bio-medico di Roma, Italy","institution_ids":["https://openalex.org/I155125353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042421338","display_name":"Alfredo Germani","orcid":"https://orcid.org/0000-0003-4457-8800"},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"A. Germani","raw_affiliation_strings":["Dipartimento di Ingegneria e Scienze dell\u2019Informazione e Matematica, Universit\u00e0 dell\u2019Aquila, Italy","Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Universit\u00e0 dell'Aquila, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria e Scienze dell\u2019Informazione e Matematica, Universit\u00e0 dell\u2019Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]},{"raw_affiliation_string":"Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Universit\u00e0 dell'Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031215647","display_name":"Costanzo Manes","orcid":"https://orcid.org/0000-0002-0771-7413"},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"C. Manes","raw_affiliation_strings":["Dipartimento di Ingegneria e Scienze dell\u2019Informazione e Matematica, Universit\u00e0 dell\u2019Aquila, Italy","Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Universit\u00e0 dell'Aquila, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria e Scienze dell\u2019Informazione e Matematica, Universit\u00e0 dell\u2019Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]},{"raw_affiliation_string":"Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Universit\u00e0 dell'Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":null,"first_page":"6074","last_page":"6079"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.996399998664856,"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":0.996399998664856,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9894999861717224,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9595999717712402,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.8413193821907043},{"id":"https://openalex.org/keywords/diagonalizable-matrix","display_name":"Diagonalizable matrix","score":0.8123456835746765},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7533208131790161},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6633322834968567},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.599711537361145},{"id":"https://openalex.org/keywords/matrix-representation","display_name":"Matrix representation","score":0.5390832424163818},{"id":"https://openalex.org/keywords/representation-theorem","display_name":"Representation theorem","score":0.4778549373149872},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4557386040687561},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4337146580219269},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4107394516468048},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37135547399520874},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34747159481048584},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.3289979100227356},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07310712337493896},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.06035727262496948},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05208668112754822}],"concepts":[{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.8413193821907043},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.8123456835746765},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7533208131790161},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6633322834968567},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.599711537361145},{"id":"https://openalex.org/C103275481","wikidata":"https://www.wikidata.org/wiki/Q6787889","display_name":"Matrix representation","level":3,"score":0.5390832424163818},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.4778549373149872},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4557386040687561},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4337146580219269},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4107394516468048},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37135547399520874},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34747159481048584},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3289979100227356},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07310712337493896},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.06035727262496948},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05208668112754822},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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:10.1109/cdc40024.2019.9030103","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030103","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W2003546335","https://openalex.org/W2004231187","https://openalex.org/W2011635872","https://openalex.org/W2028739770","https://openalex.org/W2033494182","https://openalex.org/W2074210988","https://openalex.org/W2074706500","https://openalex.org/W2095189861","https://openalex.org/W2900845500","https://openalex.org/W2946965658","https://openalex.org/W4205615190","https://openalex.org/W4230651879","https://openalex.org/W6806110348","https://openalex.org/W6812580718","https://openalex.org/W6983188761"],"related_works":["https://openalex.org/W2041405663","https://openalex.org/W2366095940","https://openalex.org/W2978783905","https://openalex.org/W1980417461","https://openalex.org/W2353317030","https://openalex.org/W40680864","https://openalex.org/W370913997","https://openalex.org/W2086251549","https://openalex.org/W1977519779","https://openalex.org/W2036364068"],"abstract_inverted_index":{"This":[0,34],"paper":[1],"describes":[2],"a":[3,9],"generalized":[4,42],"internally":[5,43],"positive":[6,44],"representation":[7,45],"of":[8,40,46],"diagonalizable":[10],"matrix":[11],"and":[12],"proves":[13],"that":[14,22],"its":[15,23],"stability":[16],"is":[17],"equivalent":[18],"to":[19,26],"the":[20,27,31,38,41],"fact":[21],"eigenvalues":[24],"belong":[25],"zone":[28],"described":[29],"by":[30],"Karpelevich":[32],"Theorem.":[33],"in":[35],"turn":[36],"implies":[37],"minimality":[39],"complex":[47],"numbers.":[48]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}