{"id":"https://openalex.org/W1975494153","doi":"https://doi.org/10.1137/s089547980342204x","title":"Eigenvalues and Condition Numbers of Complex Random Matrices","display_name":"Eigenvalues and Condition Numbers of Complex Random Matrices","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1975494153","doi":"https://doi.org/10.1137/s089547980342204x","mag":"1975494153"},"language":"en","primary_location":{"id":"doi:10.1137/s089547980342204x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s089547980342204x","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/A5091847007","display_name":"Tharmalingam Ratnarajah","orcid":"https://orcid.org/0000-0002-7636-1246"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. Ratnarajah","raw_affiliation_strings":["Institute of Electrical and Electronics Engineers"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Electrical and Electronics Engineers","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109371455","display_name":"R\u00e9mi Vaillancourt","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. Vaillancourt","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081603363","display_name":"Mayer Alvo","orcid":"https://orcid.org/0000-0002-9999-4185"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Alvo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0949,"has_fulltext":false,"cited_by_count":114,"citation_normalized_percentile":{"value":0.94314303,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"2","first_page":"441","last_page":"456"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.8928053975105286},{"id":"https://openalex.org/keywords/wishart-distribution","display_name":"Wishart distribution","score":0.849509596824646},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.7403821349143982},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6731920838356018},{"id":"https://openalex.org/keywords/hypergeometric-function","display_name":"Hypergeometric function","score":0.6451345682144165},{"id":"https://openalex.org/keywords/complex-normal-distribution","display_name":"Complex normal distribution","score":0.6375979781150818},{"id":"https://openalex.org/keywords/hypergeometric-distribution","display_name":"Hypergeometric distribution","score":0.5251184105873108},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4679637849330902},{"id":"https://openalex.org/keywords/matrix-analysis","display_name":"Matrix analysis","score":0.4474216401576996},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4260510802268982},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.4150787591934204},{"id":"https://openalex.org/keywords/random-variate","display_name":"Random variate","score":0.4129006862640381},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38307252526283264},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3301387429237366},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.16254284977912903},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10314524173736572},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.09602954983711243}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8928053975105286},{"id":"https://openalex.org/C33962027","wikidata":"https://www.wikidata.org/wiki/Q1930697","display_name":"Wishart distribution","level":3,"score":0.849509596824646},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.7403821349143982},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6731920838356018},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.6451345682144165},{"id":"https://openalex.org/C201080289","wikidata":"https://www.wikidata.org/wiki/Q5156587","display_name":"Complex normal distribution","level":3,"score":0.6375979781150818},{"id":"https://openalex.org/C176671685","wikidata":"https://www.wikidata.org/wiki/Q730600","display_name":"Hypergeometric distribution","level":2,"score":0.5251184105873108},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4679637849330902},{"id":"https://openalex.org/C149488123","wikidata":"https://www.wikidata.org/wiki/Q17098730","display_name":"Matrix analysis","level":3,"score":0.4474216401576996},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4260510802268982},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.4150787591934204},{"id":"https://openalex.org/C141547133","wikidata":"https://www.wikidata.org/wiki/Q7291996","display_name":"Random variate","level":3,"score":0.4129006862640381},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38307252526283264},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3301387429237366},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.16254284977912903},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10314524173736572},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.09602954983711243},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s089547980342204x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s089547980342204x","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:CiteSeerX.psu:10.1.1.84.8669","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.84.8669","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.crm.umontreal.ca/pub/Rapports/3000-3099/3022.pdf","raw_type":"text"},{"id":"pmh:oai:pure.qub.ac.uk/portal:publications/8d9d8183-b764-4048-9b27-e0055304796f","is_oa":false,"landing_page_url":"https://pure.qub.ac.uk/en/publications/8d9d8183-b764-4048-9b27-e0055304796f","pdf_url":null,"source":{"id":"https://openalex.org/S4306402319","display_name":"Research Portal (Queen's University Belfast)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126231945","host_organization_name":"Queen's University Belfast","host_organization_lineage":["https://openalex.org/I126231945"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ratnarajah , T , Valliancourt , R &amp; Alvo , M 2005 , ' Eigenvalues and Condition Numbers of Complex Random Matrices ' , SIAM Journal on Matrix Analysis and Applications , vol. 26(2) , no. 2 , pp. 441-456 . https://doi.org/10.1137/S089547980342204X","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1520752838","https://openalex.org/W1974637548","https://openalex.org/W1974755392","https://openalex.org/W1986844693","https://openalex.org/W1992225165","https://openalex.org/W1993875036","https://openalex.org/W1999057764","https://openalex.org/W1999273581","https://openalex.org/W2004432340","https://openalex.org/W2032869812","https://openalex.org/W2037738514","https://openalex.org/W2052645364","https://openalex.org/W2055317087","https://openalex.org/W2120350343","https://openalex.org/W2124818311","https://openalex.org/W2134984950","https://openalex.org/W2157560371","https://openalex.org/W2162826883","https://openalex.org/W2949940291","https://openalex.org/W3099086814","https://openalex.org/W4235941905","https://openalex.org/W4293005804","https://openalex.org/W4362230038"],"related_works":["https://openalex.org/W345496474","https://openalex.org/W1995792624","https://openalex.org/W2131668296","https://openalex.org/W3016315862","https://openalex.org/W4249479935","https://openalex.org/W2154515045","https://openalex.org/W4300812695","https://openalex.org/W46201091","https://openalex.org/W1997856184","https://openalex.org/W2130988783"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,6,16],"distributions":[4,27,70],"of":[5,11,19,34,43,68],"largest":[7],"and":[8,15,55,59,74],"smallest":[9],"eigenvalues":[10],"complex":[12,20,31,44,52,56],"Wishart":[13],"matrices":[14,23],"condition":[17],"number":[18],"Gaussian":[21],"random":[22],"are":[24,28,49,60,78],"derived.":[25],"These":[26],"represented":[29],"by":[30],"hypergeometric":[32,53],"functions":[33,54],"matrix":[35],"arguments,":[36],"which":[37],"can":[38],"be":[39],"expressed":[40],"in":[41,71],"terms":[42],"zonal":[45,57],"polynomials.":[46],"Several":[47],"results":[48],"derived":[50],"on":[51],"polynomials":[58],"used":[61],"to":[62],"evaluate":[63],"these":[64,69],"distributions.":[65],"Finally,":[66],"applications":[67],"numerical":[72],"analysis":[73],"statistical":[75],"hypothesis":[76],"testing":[77],"mentioned.":[79]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
