{"id":"https://openalex.org/W2005155156","doi":"https://doi.org/10.1109/tac.2008.2008975","title":"Authors' Reply to \u201cComments on `A New Trace Bound for a General Square Matrix Product' \u201d","display_name":"Authors' Reply to \u201cComments on `A New Trace Bound for a General Square Matrix Product' \u201d","publication_year":2008,"publication_date":"2008-12-01","ids":{"openalex":"https://openalex.org/W2005155156","doi":"https://doi.org/10.1109/tac.2008.2008975","mag":"2005155156"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2008.2008975","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2008.2008975","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"letter","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/A5103207599","display_name":"Jianzhou Liu","orcid":"https://orcid.org/0000-0003-1056-0274"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianzhou Liu","raw_affiliation_strings":["Department of Mathematics, Xiangtan University, Xiangtan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Xiangtan University, Xiangtan, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056658384","display_name":"Lingli He","orcid":null},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lingli He","raw_affiliation_strings":["Department of Mathematics, Xiangtan University, Xiangtan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Xiangtan University, Xiangtan, China","institution_ids":["https://openalex.org/I4610292"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4610292"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"53","issue":"11","first_page":"2713","last_page":"2713"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9879999756813049,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.987500011920929,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.8470304012298584},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.7098086476325989},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.69892418384552},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6334376931190491},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.6028027534484863},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.53341144323349},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5318287014961243},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4521810710430145},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4184049367904663},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3753204643726349},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34368887543678284},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3379318118095398},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.32284992933273315},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.298162579536438},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.26838022470474243},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14607927203178406},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.08593353629112244},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0657530128955841},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.060872793197631836}],"concepts":[{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.8470304012298584},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.7098086476325989},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.69892418384552},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6334376931190491},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6028027534484863},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.53341144323349},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5318287014961243},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4521810710430145},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4184049367904663},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3753204643726349},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34368887543678284},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3379318118095398},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32284992933273315},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.298162579536438},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.26838022470474243},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14607927203178406},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.08593353629112244},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0657530128955841},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.060872793197631836},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2008.2008975","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2008.2008975","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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":0,"referenced_works":[],"related_works":["https://openalex.org/W2131958170","https://openalex.org/W2061122711","https://openalex.org/W2273754158","https://openalex.org/W4247954915","https://openalex.org/W2024189762","https://openalex.org/W2347961172","https://openalex.org/W3043065909","https://openalex.org/W2392643770","https://openalex.org/W1968988670","https://openalex.org/W2091414606"],"abstract_inverted_index":{"We":[0,46],"thank":[1],"Prof.":[2],"Robert":[3],"Schmid":[4],"for":[5,14,35,64],"comments":[6],"on":[7],"our":[8,52,79],"paper":[9,30,80],"\"a":[10,31],"new":[11,32],"trace":[12,33,62,99],"bound":[13,34],"a":[15,36,93],"general":[16,37],"square":[17,38,71],"matrix":[18,39],"product.\"":[19],"After":[20],"thorough":[21],"thought,":[22],"we":[23,54],"also":[24],"think":[25],"theorem":[26,89],"2":[27,90],"of":[28,67,78,96],"the":[29,57,61,65,74,97],"product\"":[40],"has":[41],"no":[42],"good":[43],"practical":[44],"value.":[45],"want":[47],"to":[48,85],"clarify":[49],"that":[50],"in":[51],"paper,":[53],"mainly":[55],"improve":[56],"recent":[58],"results":[59],"about":[60],"bounds":[63],"product":[66],"two":[68],"arbitrary":[69],"real":[70],"matrices.":[72],"Therefore,":[73],"title":[75],"and":[76],"abstract":[77],"do":[81],"not":[82],"explicitly":[83],"refer":[84],"Riccati":[86],"equations.":[87],"Hence,":[88],"is":[91],"only":[92],"simple":[94],"application":[95],"estimated":[98],"bounds.":[100]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
