{"id":"https://openalex.org/W2050032130","doi":"https://doi.org/10.1109/isit.2007.4557458","title":"Shannon Transform of Certain Matrix Products","display_name":"Shannon Transform of Certain Matrix Products","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2050032130","doi":"https://doi.org/10.1109/isit.2007.4557458","mag":"2050032130"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2007.4557458","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2007.4557458","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},"type":"conference-paper","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/A5029714738","display_name":"Nick Letzepis","orcid":"https://orcid.org/0000-0003-0374-2109"},"institutions":[{"id":"https://openalex.org/I170239107","display_name":"University of South Australia","ror":"https://ror.org/01p93h210","country_code":"AU","type":"education","lineage":["https://openalex.org/I170239107"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Nick Letzepis","raw_affiliation_strings":["Institute for Telecommunications Research, University of South Australia, Australia","#N#University of South Australia, Adelaide#N#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Telecommunications Research, University of South Australia, Australia","institution_ids":["https://openalex.org/I170239107"]},{"raw_affiliation_string":"#N#University of South Australia, Adelaide#N#","institution_ids":["https://openalex.org/I170239107"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072485708","display_name":"Alex Grant","orcid":"https://orcid.org/0000-0002-5345-7771"},"institutions":[{"id":"https://openalex.org/I170239107","display_name":"University of South Australia","ror":"https://ror.org/01p93h210","country_code":"AU","type":"education","lineage":["https://openalex.org/I170239107"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Alex Grant","raw_affiliation_strings":["Institute for Telecommunications Research, University of South Australia, Australia","#N#University of South Australia, Adelaide#N#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Telecommunications Research, University of South Australia, Australia","institution_ids":["https://openalex.org/I170239107"]},{"raw_affiliation_string":"#N#University of South Australia, Adelaide#N#","institution_ids":["https://openalex.org/I170239107"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I170239107"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"66","issue":null,"first_page":"1646","last_page":"1650"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9983000159263611,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9883000254631042,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.6319921016693115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5668452978134155},{"id":"https://openalex.org/keywords/hypergeometric-function","display_name":"Hypergeometric function","score":0.4995455741882324},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4946450889110565},{"id":"https://openalex.org/keywords/unitary-matrix","display_name":"Unitary matrix","score":0.4638984203338623},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.45615354180336},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.44484901428222656},{"id":"https://openalex.org/keywords/closed-form-expression","display_name":"Closed-form expression","score":0.44025516510009766},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4386785924434662},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.4380779564380646},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.39541321992874146},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.353624165058136},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27321237325668335},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2556840181350708},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13947510719299316},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09107667207717896}],"concepts":[{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.6319921016693115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5668452978134155},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.4995455741882324},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4946450889110565},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.4638984203338623},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.45615354180336},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.44484901428222656},{"id":"https://openalex.org/C4530962","wikidata":"https://www.wikidata.org/wiki/Q777407","display_name":"Closed-form expression","level":2,"score":0.44025516510009766},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4386785924434662},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4380779564380646},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.39541321992874146},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.353624165058136},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27321237325668335},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2556840181350708},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13947510719299316},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09107667207717896},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2007.4557458","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2007.4557458","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310369","display_name":"National ICT Australia","ror":"https://ror.org/03q397159"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1572777589","https://openalex.org/W1822870367","https://openalex.org/W2060581589","https://openalex.org/W2068224164","https://openalex.org/W2068728923","https://openalex.org/W2076291223","https://openalex.org/W2078582032","https://openalex.org/W2086351984","https://openalex.org/W2099111195","https://openalex.org/W2115692375","https://openalex.org/W2120339991","https://openalex.org/W2129741794","https://openalex.org/W2129755576","https://openalex.org/W2130509920","https://openalex.org/W2168492199","https://openalex.org/W2169693117","https://openalex.org/W2181292907","https://openalex.org/W2953226370","https://openalex.org/W3179903767","https://openalex.org/W4229746864","https://openalex.org/W4232758566","https://openalex.org/W4253567193","https://openalex.org/W4301253858","https://openalex.org/W6679280877"],"related_works":["https://openalex.org/W1999313313","https://openalex.org/W2111789608","https://openalex.org/W2499716529","https://openalex.org/W2963658971","https://openalex.org/W2034442087","https://openalex.org/W2386636239","https://openalex.org/W2059686565","https://openalex.org/W1568150511","https://openalex.org/W4293832529","https://openalex.org/W2018613836"],"abstract_inverted_index":{"We":[0],"derive":[1],"a":[2,62],"closed":[3],"form":[4],"expression":[5],"for":[6,70],"the":[7,11,25],"Shannon":[8],"transform":[9],"of":[10,13,24,44],"product":[12],"two":[14],"arbitrary":[15],"positive":[16],"semidefinite":[17],"random":[18],"matrices,":[19],"where":[20],"at":[21],"least":[22],"one":[23],"matrices":[26,73],"is":[27,68],"unitary":[28],"invariant.":[29],"In":[30],"principle,":[31],"S-transforms":[32],"could":[33],"be":[34],"directly":[35],"applied":[36],"in":[37,41],"this":[38,46],"scenario,":[39],"however":[40],"many":[42],"cases":[43],"interest":[45],"approach":[47],"leads":[48,60],"to":[49,61],"an":[50],"intractable":[51],"expression.":[52,65],"Our":[53],"alternative":[54],"approach,":[55],"based":[56],"on":[57],"hypergeometric":[58],"functions,":[59],"tractable":[63],"asymptotic":[64],"This":[66],"result":[67],"validated":[69],"finite":[71],"size":[72],"using":[74],"Monte":[75],"Carlo":[76],"simulations.":[77]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
