{"id":"https://openalex.org/W2050802534","doi":"https://doi.org/10.1137/s0895479893253616","title":"Trace and Eigenvalue Inequalities for Ordinary and Hadamard Products of Positive Semidefinite Hermitian Matrices","display_name":"Trace and Eigenvalue Inequalities for Ordinary and Hadamard Products of Positive Semidefinite Hermitian Matrices","publication_year":1995,"publication_date":"1995-10-01","ids":{"openalex":"https://openalex.org/W2050802534","doi":"https://doi.org/10.1137/s0895479893253616","mag":"2050802534"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479893253616","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893253616","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/A5023612858","display_name":"Bo-Ying Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bo-Ying Wang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090138238","display_name":"Fuzhen Zhang","orcid":"https://orcid.org/0000-0002-3414-2037"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fuzhen Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023612858"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0746,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.84604368,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"4","first_page":"1173","last_page":"1183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/combinatorics","display_name":"Combinatorics","score":0.7174168825149536},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6861944794654846},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6771196722984314},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.6650437116622925},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5146597027778625},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4932798743247986},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.4339022934436798},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2191186249256134},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1262698471546173},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.060879409313201904}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7174168825149536},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6861944794654846},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6771196722984314},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.6650437116622925},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5146597027778625},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4932798743247986},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.4339022934436798},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2191186249256134},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1262698471546173},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.060879409313201904},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479893253616","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893253616","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:nsuworks.nova.edu:math_facarticles-1129","is_oa":false,"landing_page_url":"https://nsuworks.nova.edu/math_facarticles/130","pdf_url":null,"source":{"id":"https://openalex.org/S4377196410","display_name":"NSUWorks (Nova Southeastern University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I203088144","host_organization_name":"Nova Southeastern University","host_organization_lineage":["https://openalex.org/I203088144"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Faculty Articles","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":14,"referenced_works":["https://openalex.org/W225487592","https://openalex.org/W1488435683","https://openalex.org/W1552202016","https://openalex.org/W1967792697","https://openalex.org/W1976033737","https://openalex.org/W1983051686","https://openalex.org/W2005875914","https://openalex.org/W2006309149","https://openalex.org/W2023267838","https://openalex.org/W2039859942","https://openalex.org/W2046609171","https://openalex.org/W2166243171","https://openalex.org/W2328512290","https://openalex.org/W4300694379"],"related_works":["https://openalex.org/W2367027423","https://openalex.org/W4206234077","https://openalex.org/W2121030460","https://openalex.org/W2950761947","https://openalex.org/W2009320932","https://openalex.org/W2951116071","https://openalex.org/W2371640884","https://openalex.org/W3185648916","https://openalex.org/W2073904121","https://openalex.org/W1993806324"],"abstract_inverted_index":{"Let":[0],"A":[1],"and":[2,15,31,47,131,147],"B":[3],"be":[4,18],"$n":[5],"\\times":[6,38],"n$":[7],"positive":[8],"semidefinite":[9],"Hermitian":[10],"matrices,":[11,30],"let":[12,21,32],"$\\alpha":[13],"$":[14,17,22,24,34],"$\\beta":[16],"real":[19],"numbers,":[20],"\\circ":[23,54,58,69,73,86,94],"denote":[25,35],"the":[26,128,132],"Hadamard":[27],"product":[28],"of":[29,42],"$A_k":[33],"any":[36],"$k":[37],"k$":[39],"principal":[40],"submatrix":[41],"A.":[43],"The":[44,124],"following":[45],"trace":[46],"eigenvalue":[48],"inequalities":[49,129,134],"are":[50,160,165],"shown:":[51],"\\[":[52,135,148],"\\operatorname{tr}(A":[53,68],"B)^\\alpha":[55,70],"\\leq":[56,61,77,79,89,97,110,117,137,157],"\\operatorname{tr}(A^\\alpha":[57,72,138,151],"B^\\alpha":[59,74,87,139,152],"),\\quad\\alpha":[60,96],"0\\,{\\text{":[62],"or":[63],"}}\\,\\alpha":[64],"\\geq":[65,71,144,150],"1,":[66,80,145],"\\]\\[":[67,81,103],"),\\quad":[75,140,153],"0":[76],"\\alpha":[78,83,142,155],"\\lambda^{1/":[82],"}":[84,92,106,113],"(A^\\alpha":[85],")":[88],"\\lambda":[90,104,111],"^{1/\\beta":[91,112],"(A^\\beta":[93],"B^\\beta":[95],"\\beta":[98,100,118,120],",\\alpha":[99,119],"\\ne":[101,121],"0,":[102],"^{1/\\alpha":[105],"[(A^\\alpha":[107],")_k":[108,115],"]":[109],"[(A^\\beta":[114],"],\\quad\\alpha":[116],"0.":[122],"\\]":[123,146,159],"equalities":[125],"corresponding":[126],"to":[127],"above":[130],"known":[133],"\\operatorname{tr}(AB)^\\alpha":[136,149],"|":[141,143,154,156],"1":[158],"thoroughly":[161],"discussed.":[162],"Some":[163],"applications":[164],"given.":[166]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}