{"id":"https://openalex.org/W1996965151","doi":"https://doi.org/10.1137/100783315","title":"On the Kronecker Canonical Form of Mixed Matrix Pencils","display_name":"On the Kronecker Canonical Form of Mixed Matrix Pencils","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1996965151","doi":"https://doi.org/10.1137/100783315","mag":"1996965151"},"language":"en","primary_location":{"id":"doi:10.1137/100783315","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100783315","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/A5040460257","display_name":"Satoru Iwata","orcid":"https://orcid.org/0000-0002-6467-1335"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Satoru Iwata","raw_affiliation_strings":["iwata@kurims.kyoto-u.ac.jp#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"iwata@kurims.kyoto-u.ac.jp#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075575637","display_name":"Mizuyo Takamatsu","orcid":"https://orcid.org/0000-0002-8048-6439"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mizuyo Takamatsu","raw_affiliation_strings":["takamatsu@ise.chuo-u.ac.jp#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"takamatsu@ise.chuo-u.ac.jp#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3045,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79269186,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"32","issue":"1","first_page":"44","last_page":"71"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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":0.9993000030517578,"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/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.9836999773979187,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9836999773979187,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.8425508141517639},{"id":"https://openalex.org/keywords/kronecker-product","display_name":"Kronecker product","score":0.7935545444488525},{"id":"https://openalex.org/keywords/matrix-pencil","display_name":"Matrix pencil","score":0.7513625025749207},{"id":"https://openalex.org/keywords/canonical-form","display_name":"Canonical form","score":0.6993978023529053},{"id":"https://openalex.org/keywords/pencil","display_name":"Pencil (optics)","score":0.6912215948104858},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.6211574077606201},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.576714277267456},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.5625501275062561},{"id":"https://openalex.org/keywords/skew-symmetric-matrix","display_name":"Skew-symmetric matrix","score":0.48997965455055237},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.45477885007858276},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.450141042470932},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.43253523111343384},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4318453073501587},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3937050402164459},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3311704397201538},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.13141033053398132}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8425508141517639},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.7935545444488525},{"id":"https://openalex.org/C1576492","wikidata":"https://www.wikidata.org/wiki/Q3739929","display_name":"Matrix pencil","level":3,"score":0.7513625025749207},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.6993978023529053},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.6912215948104858},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.6211574077606201},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.576714277267456},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.5625501275062561},{"id":"https://openalex.org/C41106240","wikidata":"https://www.wikidata.org/wiki/Q526790","display_name":"Skew-symmetric matrix","level":5,"score":0.48997965455055237},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.45477885007858276},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.450141042470932},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.43253523111343384},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4318453073501587},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3937050402164459},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3311704397201538},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.13141033053398132},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100783315","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100783315","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:CiteSeerX.psu:10.1.1.608.7098","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.608.7098","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.keisu.t.u-tokyo.ac.jp/research/techrep/data/2010/METR10-01.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.75}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W637320825","https://openalex.org/W1514375184","https://openalex.org/W1533712308","https://openalex.org/W1978376980","https://openalex.org/W1984452258","https://openalex.org/W1985910458","https://openalex.org/W2002297246","https://openalex.org/W2008256634","https://openalex.org/W2013474260","https://openalex.org/W2018158936","https://openalex.org/W2019609727","https://openalex.org/W2020927880","https://openalex.org/W2023810039","https://openalex.org/W2034698420","https://openalex.org/W2043765006","https://openalex.org/W2061647611","https://openalex.org/W2066944191","https://openalex.org/W2068200970","https://openalex.org/W2068844468","https://openalex.org/W2074709117","https://openalex.org/W2090223047","https://openalex.org/W2094372481","https://openalex.org/W2097178696","https://openalex.org/W2153132823","https://openalex.org/W3217072053","https://openalex.org/W4210391498"],"related_works":["https://openalex.org/W2050609748","https://openalex.org/W2617451319","https://openalex.org/W590681473","https://openalex.org/W4293488901","https://openalex.org/W2280235975","https://openalex.org/W2120296059","https://openalex.org/W2963109527","https://openalex.org/W4365800530","https://openalex.org/W1996965151","https://openalex.org/W2043539212"],"abstract_inverted_index":{"A":[0],"mixed":[1,42,69],"matrix":[2,6,43],"pencil":[3,7,44],"is":[4],"a":[5,41,52,63,67],"with":[8],"two":[9],"kinds":[10],"of":[11,33,35,49,62,66],"nonzero":[12],"coefficients:":[13],"fixed":[14],"constants":[15],"that":[16,24],"account":[17],"for":[18,40,58],"conservation":[19],"laws":[20],"and":[21],"independent":[22],"parameters":[23],"represent":[25],"physical":[26],"characteristics.":[27],"In":[28],"this":[29,54],"paper,":[30],"the":[31,36,60],"indices":[32],"nilpotency":[34],"Kronecker":[37],"canonical":[38],"form":[39],"are":[45],"characterized":[46],"in":[47],"terms":[48],"matroids.":[50],"As":[51],"byproduct,":[53],"provides":[55],"an":[56],"algorithm":[57],"computing":[59],"rank":[61],"power":[64],"product":[65],"square":[68],"matrix.":[70]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}