{"id":"https://openalex.org/W4413344833","doi":"https://doi.org/10.1515/spma-2025-0040","title":"Minimum trace norm of real symmetric and Hermitian matrices with zero diagonal","display_name":"Minimum trace norm of real symmetric and Hermitian matrices with zero diagonal","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4413344833","doi":"https://doi.org/10.1515/spma-2025-0040"},"language":"en","primary_location":{"id":"doi:10.1515/spma-2025-0040","doi":"https://doi.org/10.1515/spma-2025-0040","is_oa":true,"landing_page_url":"https://doi.org/10.1515/spma-2025-0040","pdf_url":null,"source":{"id":"https://openalex.org/S2737979056","display_name":"Special Matrices","issn_l":"2300-7451","issn":["2300-7451"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Special Matrices","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1515/spma-2025-0040","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091628990","display_name":"Mostafa Einollahzadeh","orcid":"https://orcid.org/0000-0002-8400-0280","observed_orcids":["https://orcid.org/0000-0002-8400-0280"]},"institutions":[{"id":"https://openalex.org/I170013655","display_name":"Isfahan University of Technology","ror":"https://ror.org/00af3sa43","country_code":"IR","type":"education","lineage":["https://openalex.org/I170013655"]},{"id":"https://openalex.org/I4210146419","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31","country_code":"IR","type":"facility","lineage":["https://openalex.org/I4210146419"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Mostafa Einollahzadeh","raw_affiliation_strings":["Department of Mathematical Sciences, Isfahan University of Technology , Isfahan , Iran","School of Mathematics, Institute for Research in Fundamental Sciences (IPM) , P.O. Box 19395-5746 , Tehran , Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Isfahan University of Technology , Isfahan , Iran","institution_ids":["https://openalex.org/I170013655"]},{"raw_affiliation_string":"School of Mathematics, Institute for Research in Fundamental Sciences (IPM) , P.O. Box 19395-5746 , Tehran , Iran","institution_ids":["https://openalex.org/I4210146419"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074466003","display_name":"Mohammad Ali Nematollahi","orcid":"https://orcid.org/0000-0003-0323-7305","observed_orcids":["https://orcid.org/0000-0003-0323-7305"]},"institutions":[{"id":"https://openalex.org/I4400600978","display_name":"Fasa University","ror":"https://ror.org/03a77cf20","country_code":"IR","type":"education","lineage":["https://openalex.org/I4400600978"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohammad Ali Nematollahi","raw_affiliation_strings":["Department of Computer Sciences, Fasa University , Fasa , Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, Fasa University , Fasa , Iran","institution_ids":["https://openalex.org/I4400600978"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5091628990"],"corresponding_institution_ids":["https://openalex.org/I170013655","https://openalex.org/I4210146419"],"apc_list":{"value":1050,"currency":"EUR","value_usd":1187},"apc_paid":{"value":1050,"currency":"EUR","value_usd":1187},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9907000064849854,"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":0.9907000064849854,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.006899999920278788,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/trace-norm","display_name":"trace norm","score":0.9240000247955322},{"id":"https://openalex.org/keywords/real-symmetric-matrices","display_name":"real symmetric matrices","score":0.9789999723434448},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrices","score":1.0},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.8240000009536743}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8074686527252197},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8030697703361511},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6871529221534729},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.6699768304824829},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6407260894775391},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5241793990135193},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.4701828062534332},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45564210414886475},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4011307656764984},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07749664783477783},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1515/spma-2025-0040","doi":"https://doi.org/10.1515/spma-2025-0040","is_oa":true,"landing_page_url":"https://doi.org/10.1515/spma-2025-0040","pdf_url":null,"source":{"id":"https://openalex.org/S2737979056","display_name":"Special Matrices","issn_l":"2300-7451","issn":["2300-7451"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Special Matrices","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2309.14958","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.14958","pdf_url":"https://arxiv.org/pdf/2309.14958","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:b140922856f94210acc3e8620260908b","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/b140922856f94210acc3e8620260908b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Special Matrices, Vol 13, Iss 1, Pp 103078-633 (2025)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2309.14958","doi":"https://doi.org/10.48550/arxiv.2309.14958","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2309.14958","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1515/spma-2025-0040","doi":"https://doi.org/10.1515/spma-2025-0040","is_oa":true,"landing_page_url":"https://doi.org/10.1515/spma-2025-0040","pdf_url":null,"source":{"id":"https://openalex.org/S2737979056","display_name":"Special Matrices","issn_l":"2300-7451","issn":["2300-7451"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Special Matrices","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4161997469","display_name":null,"funder_award_id":"1400050046","funder_id":"https://openalex.org/F4320323645","funder_display_name":"Institute for Research in Fundamental Sciences"}],"funders":[{"id":"https://openalex.org/F4320323627","display_name":"School of Mathematics, Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31"},{"id":"https://openalex.org/F4320323645","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4413344833.pdf","grobid_xml":"https://content.openalex.org/works/W4413344833.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W2114659717","https://openalex.org/W2167816765","https://openalex.org/W2253343217","https://openalex.org/W2725587699","https://openalex.org/W2911983998","https://openalex.org/W3122357668","https://openalex.org/W4229706427","https://openalex.org/W4248036694","https://openalex.org/W4255333822","https://openalex.org/W4396718543"],"related_works":["https://openalex.org/W7098329812","https://openalex.org/W2592555062","https://openalex.org/W7067522471","https://openalex.org/W2083739242","https://openalex.org/W1981554024","https://openalex.org/W2783595937","https://openalex.org/W2089691624","https://openalex.org/W7099064412","https://openalex.org/W1990695571","https://openalex.org/W2035565487"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"establish":[2],"tight":[3],"lower":[4],"bounds":[5,118],"for":[6,119,166],"the":[7,53,68,94,120,128,163],"trace":[8],"norm":[9,122,152],"(":[10,39,43,79],"\u2016":[11,13,40,42,72,74,76,78],"\u22c5":[12,41],"1":[14,36,44,75,80,144],")":[15,45,46,81],"\\left(\\Vert":[16,47],"\\cdot":[17,48],"{\\Vert":[18,49],"}_{1})":[19],"of":[20,32,55,60,130,154],"real":[21,57,136],"symmetric":[22,58,137],"and":[23,127],"Hermitian":[24,95,167],"matrices":[25,59,168],"with":[26,139],"zero":[27],"diagonal":[28,131,160],"entries":[29,141],"in":[30,145],"terms":[31],"their":[33],"entrywise":[34],"L":[35],"{L}^{1}":[37],"-norms":[38],"}_{\\left(1)})":[50],".":[51,92,110],"For":[52,133],"space":[54,129],"nonzero":[56],"order":[61],"n":[62,63,90,106,155],",":[64],"we":[65,114],"prove":[66],"that":[67],"minimum":[69,98],"possible":[70],"ratio":[71,99],"A":[73,77],"\\frac{\\Vert":[82],"A{\\Vert":[83,85],"}_{1}}{\\Vert":[84],"}_{\\left(1)}}":[86],"is":[87,100,169],"exactly":[88],"2":[89,105,156],"\\frac{2}{n}":[91],"In":[93],"case,":[96],"this":[97],"given":[101],"by":[102,143],"tan":[103],"\u03c0":[104],"\\tan":[107],"\\left(\\phantom{\\rule[-0.75em]{}{0ex}},\\frac{\\pi":[108],"}{2n}\\right)":[109],"Through":[111],"duality":[112],"arguments,":[113],"derive":[115],"sharp":[116],"upper":[117],"spectral":[121,151],"distance":[123,153],"between":[124],"a":[125,150,159],"matrix":[126,138],"matrices.":[132],"instance,":[134],"any":[135],"off-diagonal":[140],"bounded":[142],"absolute":[146],"value":[147],"lies":[148],"within":[149],"\\frac{n}{2}":[157],"from":[158],"matrix,":[161],"while":[162],"corresponding":[164],"bound":[165],"cot":[170],"<":[171]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2025-08-20T00:00:00"}