{"id":"https://openalex.org/W2007192575","doi":"https://doi.org/10.1137/040613585","title":"Some Properties of Generalized Positive Subdefinite Matrices","display_name":"Some Properties of Generalized Positive Subdefinite Matrices","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2007192575","doi":"https://doi.org/10.1137/040613585","mag":"2007192575"},"language":"en","primary_location":{"id":"doi:10.1137/040613585","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040613585","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/A5007628003","display_name":"Sarmistha Neogy","orcid":"https://orcid.org/0000-0003-1497-671X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. K. Neogy","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5069144965","display_name":"Ashok Kumar Das","orcid":"https://orcid.org/0000-0003-2508-7563"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. K. Das","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007628003"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.09709189,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"27","issue":"4","first_page":"988","last_page":"995"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9988999962806702,"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":0.9988999962806702,"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":0.9930999875068665,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9646999835968018,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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":0.8578605055809021},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.6723726391792297},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6470354199409485},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5798379778862},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5508168935775757},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5185770988464355},{"id":"https://openalex.org/keywords/subclass","display_name":"Subclass","score":0.47582486271858215},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.4658753573894501},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.45800137519836426},{"id":"https://openalex.org/keywords/matrix-splitting","display_name":"Matrix splitting","score":0.4325731694698334},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.4303179979324341},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.3944266736507416},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36814412474632263},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3439812660217285},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34384459257125854},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.19915100932121277},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11353260278701782},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.06423860788345337}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8578605055809021},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.6723726391792297},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6470354199409485},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5798379778862},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5508168935775757},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5185770988464355},{"id":"https://openalex.org/C2776194381","wikidata":"https://www.wikidata.org/wiki/Q3965271","display_name":"Subclass","level":3,"score":0.47582486271858215},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.4658753573894501},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45800137519836426},{"id":"https://openalex.org/C133589720","wikidata":"https://www.wikidata.org/wiki/Q6787891","display_name":"Matrix splitting","level":5,"score":0.4325731694698334},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.4303179979324341},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3944266736507416},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36814412474632263},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3439812660217285},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34384459257125854},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.19915100932121277},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11353260278701782},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.06423860788345337},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C159654299","wikidata":"https://www.wikidata.org/wiki/Q79460","display_name":"Antibody","level":2,"score":0.0},{"id":"https://openalex.org/C203014093","wikidata":"https://www.wikidata.org/wiki/Q101929","display_name":"Immunology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040613585","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040613585","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W64450559","https://openalex.org/W584634945","https://openalex.org/W1500921805","https://openalex.org/W1966636125","https://openalex.org/W1967897811","https://openalex.org/W1970000960","https://openalex.org/W1981752806","https://openalex.org/W1982002079","https://openalex.org/W1987635542","https://openalex.org/W1990995401","https://openalex.org/W2000151369","https://openalex.org/W2033766167","https://openalex.org/W2047118504","https://openalex.org/W2063971955","https://openalex.org/W2064608549","https://openalex.org/W2948315098","https://openalex.org/W4253868373"],"related_works":["https://openalex.org/W2030388112","https://openalex.org/W2000061193","https://openalex.org/W2050814432","https://openalex.org/W2381582030","https://openalex.org/W2169778792","https://openalex.org/W1982337446","https://openalex.org/W3195796569","https://openalex.org/W2000798143","https://openalex.org/W2791640097","https://openalex.org/W2007192575"],"abstract_inverted_index":{"The":[0,23],"class":[1,12,61],"of":[2,35,62,87,93,103,106,144,175,181],"generalized":[3,49],"positive":[4,50],"subdefinite":[5,51],"(GPSBD)":[6],"matrices":[7,43,65],"is":[8,81,98],"an":[9,150],"interesting":[10],"matrix":[11,53,123,136,148,156],"introduced":[13,66],"by":[14,67],"Crouzeix":[15],"and":[16,46,70,153,157,178],"Koml\u00f3si":[17],"[Appl.":[18],"Optim.":[19],"59,":[20],"Kluwer,":[21],"Dordrecht,":[22],"Netherlands,":[24],"2001,":[25],"pp.":[26,77],"45-63].":[27],"In":[28],"this":[29],"paper,":[30],"we":[31,131],"obtain":[32],"some":[33,55],"properties":[34],"GPSBD":[36,42,88,122],"matrices.":[37],"We":[38,112],"show":[39,118,132],"that":[40,83,119,133],"copositive":[41,121,155],"are":[44],"$P_{0}$":[45],"a":[47,85,94,114,120,135,142,145,154,161,179],"merely":[48],"(MGPSBD)":[52],"with":[54,149],"additional":[56,151],"conditions":[57],"belongs":[58],"to":[59,117],"the":[60,90,101,107,173],"row":[63],"sufficient":[64,127],"Cottle,":[68],"Pang,":[69],"Venkateswarn":[71],"[Linear":[72],"Algebra":[73],"Appl.,":[74],"114/115":[75],"(1989),":[76],"231-249].":[78],"Further,":[79],"it":[80,159],"shown":[82],"for":[84],"subclass":[86],"matrices,":[89],"solution":[91],"set":[92,102],"linear":[95],"complementarity":[96],"problem":[97],"same":[99],"as":[100,141],"Karush--Kuhn--Tucker-stationary":[104],"points":[105],"corresponding":[108],"quadratic":[109],"programming":[110],"problem.":[111],"provide":[113],"counter":[115],"example":[116],"need":[124],"not":[125],"be":[126,139],"in":[128],"general.":[129],"Finally,":[130],"if":[134,158],"A":[137],"can":[138,167],"written":[140],"sum":[143],"copositive-plus":[146],"MGPSBD":[147],"condition":[152],"satisfies":[160],"feasibility":[162],"condition,":[163],"then":[164],"Lemke's":[165,176],"algorithm":[166,177],"solve":[168],"LCP$(q,A).$":[169],"This":[170],"further":[171],"extends":[172],"applicability":[174],"result":[180],"Evers.":[182]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}