{"id":"https://openalex.org/W1479785707","doi":"https://doi.org/10.1007/978-3-319-21398-9_19","title":"Evaluating Matrix Circuits","display_name":"Evaluating Matrix Circuits","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1479785707","doi":"https://doi.org/10.1007/978-3-319-21398-9_19","mag":"1479785707"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-21398-9_19","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-21398-9_19","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1502.03540","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090872841","display_name":"Daniel K\u00f6nig","orcid":null},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]},{"id":"https://openalex.org/I2800742272","display_name":"Folkwang University of the Arts","ror":"https://ror.org/03gf02c22","country_code":"DE","type":"education","lineage":["https://openalex.org/I2800742272"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Daniel K\u00f6nig","raw_affiliation_strings":["Universit\u00e4t Siegen, Siegen, Germany","UNIVERSITAT SIEGEN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Siegen, Siegen, Germany","institution_ids":["https://openalex.org/I206895457"]},{"raw_affiliation_string":"UNIVERSITAT SIEGEN","institution_ids":["https://openalex.org/I2800742272"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005500210","display_name":"Markus Lohrey","orcid":"https://orcid.org/0000-0002-4680-7198"},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]},{"id":"https://openalex.org/I2800742272","display_name":"Folkwang University of the Arts","ror":"https://ror.org/03gf02c22","country_code":"DE","type":"education","lineage":["https://openalex.org/I2800742272"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus Lohrey","raw_affiliation_strings":["Universit\u00e4t Siegen, Siegen, Germany","UNIVERSITAT SIEGEN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Siegen, Siegen, Germany","institution_ids":["https://openalex.org/I206895457"]},{"raw_affiliation_string":"UNIVERSITAT SIEGEN","institution_ids":["https://openalex.org/I2800742272"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"235","last_page":"248"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980000257492065,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980000257492065,"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/T11567","display_name":"semigroups and automata theory","score":0.9939000010490417,"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/T11130","display_name":"Coding theory and cryptography","score":0.987500011920929,"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":0.6862505674362183},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.6829593777656555},{"id":"https://openalex.org/keywords/identity-matrix","display_name":"Identity matrix","score":0.6232413649559021},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.603955090045929},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5573293566703796},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5355024337768555},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5158254504203796},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5122910737991333},{"id":"https://openalex.org/keywords/word-problem","display_name":"Word problem (mathematics education)","score":0.5015296936035156},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.48454299569129944},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48253366351127625},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.47319313883781433},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.46821001172065735},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.4399268627166748},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.4182812571525574},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.24909478425979614},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17139288783073425},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10163906216621399},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09307077527046204},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07207602262496948},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06456100940704346}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6862505674362183},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.6829593777656555},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.6232413649559021},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.603955090045929},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5573293566703796},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5355024337768555},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5158254504203796},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5122910737991333},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.5015296936035156},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.48454299569129944},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48253366351127625},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47319313883781433},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.46821001172065735},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.4399268627166748},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.4182812571525574},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.24909478425979614},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17139288783073425},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10163906216621399},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09307077527046204},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07207602262496948},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06456100940704346},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-3-319-21398-9_19","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-21398-9_19","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:arXiv.org:1502.03540","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1502.03540","pdf_url":"https://arxiv.org/pdf/1502.03540","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:1479785707","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1502.03540","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1502.03540","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1502.03540","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1502.03540","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1502.03540","pdf_url":"https://arxiv.org/pdf/1502.03540","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W41330591","https://openalex.org/W70771486","https://openalex.org/W85552082","https://openalex.org/W636399398","https://openalex.org/W1587860830","https://openalex.org/W1963661988","https://openalex.org/W1984509356","https://openalex.org/W1995503643","https://openalex.org/W2009571139","https://openalex.org/W2011758726","https://openalex.org/W2015676876","https://openalex.org/W2017205387","https://openalex.org/W2021736779","https://openalex.org/W2024091095","https://openalex.org/W2024522546","https://openalex.org/W2026036943","https://openalex.org/W2040034546","https://openalex.org/W2040721698","https://openalex.org/W2041755862","https://openalex.org/W2043641704","https://openalex.org/W2043667326","https://openalex.org/W2052653988","https://openalex.org/W2052788392","https://openalex.org/W2085012646","https://openalex.org/W2104952158","https://openalex.org/W2120798401","https://openalex.org/W2123466414","https://openalex.org/W2128810420","https://openalex.org/W2171197316","https://openalex.org/W2261858229","https://openalex.org/W2313272764","https://openalex.org/W2962914768","https://openalex.org/W4230191592"],"related_works":["https://openalex.org/W2962914768","https://openalex.org/W3013848491","https://openalex.org/W2949123768","https://openalex.org/W1986593186","https://openalex.org/W3045417474","https://openalex.org/W2749098850","https://openalex.org/W2950833134","https://openalex.org/W2403541957","https://openalex.org/W2016929319","https://openalex.org/W2137828924","https://openalex.org/W2963570027","https://openalex.org/W1997198079","https://openalex.org/W2162763810","https://openalex.org/W1559446374","https://openalex.org/W3110487089","https://openalex.org/W2951444808","https://openalex.org/W2113226559","https://openalex.org/W1503555929","https://openalex.org/W2138554486","https://openalex.org/W1969557621"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
