{"id":"https://openalex.org/W2392556599","doi":null,"title":"The Polynonomial of Diagonalizable Linear Transformation","display_name":"The Polynonomial of Diagonalizable Linear Transformation","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2392556599","mag":"2392556599"},"language":"en","primary_location":{"id":"mag:2392556599","doi":null,"is_oa":false,"landing_page_url":"http://en.cnki.com.cn/Article_en/CJFDTOTAL-SRSX200206001.htm","pdf_url":null,"source":{"id":"https://openalex.org/S2765078294","display_name":"Journal of Shangrao Normal University","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":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Journal of Shangrao Teachers College","raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5081729072","display_name":"Aiping Li","orcid":"https://orcid.org/0000-0001-6174-0991","observed_orcids":["https://orcid.org/0000-0001-6174-0991"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Aiping Li","raw_affiliation_strings":["1,ZHU Hong-xiang  2"],"raw_orcid":"https://orcid.org/0000-0001-6174-0991","affiliations":[{"raw_affiliation_string":"1,ZHU Hong-xiang  2","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5081729072"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"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":null,"issue":null,"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":0.9916999936103821,"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":0.9916999936103821,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.004399999976158142,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11476","display_name":"Graph theory and applications","score":0.0007999999797903001,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/minimal-polynomial","display_name":"minimal polynomial","score":0.7910000085830688},{"id":"https://openalex.org/keywords/necessary-and-sufficient-conditions","display_name":"necessary and sufficient conditions","score":0.8980000019073486},{"id":"https://openalex.org/keywords/polynomial-properties","display_name":"polynomial properties","score":0.335999995470047}],"concepts":[{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.9721931219100952},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.7093455791473389},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.5809521079063416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5662586092948914},{"id":"https://openalex.org/C165443888","wikidata":"https://www.wikidata.org/wiki/Q1482183","display_name":"Transformation matrix","level":3,"score":0.5556516051292419},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46590858697891235},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45950621366500854},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3715754747390747},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3346705436706543},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.204382985830307},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07682886719703674},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.06781479716300964},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.06622245907783508},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0600227415561676},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.057524532079696655},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2392556599","doi":null,"is_oa":false,"landing_page_url":"http://en.cnki.com.cn/Article_en/CJFDTOTAL-SRSX200206001.htm","pdf_url":null,"source":{"id":"https://openalex.org/S2765078294","display_name":"Journal of Shangrao Normal University","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":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Journal of Shangrao Teachers College","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2372107181","https://openalex.org/W7095219219","https://openalex.org/W2350959548","https://openalex.org/W2384046643","https://openalex.org/W2360316590","https://openalex.org/W7099504743","https://openalex.org/W2365913682","https://openalex.org/W2371029490","https://openalex.org/W2362323554","https://openalex.org/W2388213378"],"abstract_inverted_index":{"This":[0],"paper":[1,29],"studies":[2],"some":[3,26],"properties":[4],"of":[5,8,28],"the":[6],"polynonomial":[7],"diagonalizable":[9],"linear":[10],"transformation.":[11],"We":[12],"describle":[13],"a":[14],"necessary":[15],"and":[16],"sufficient":[17],"conditions":[18],"for":[19],"n-th":[20],"order":[21],"diagonalization":[22],"matrix,":[23],"thus,":[24],"generalized":[25],"resuit":[27],"??.":[30]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2016-06-24T00:00:00"}