{"id":"https://openalex.org/W7167836527","doi":"https://doi.org/10.1145/3815436.3815468","title":"An Algorithm for Diagonalizing Matrices of Formal Power Series","display_name":"An Algorithm for Diagonalizing Matrices of Formal Power Series","publication_year":2026,"publication_date":"2026-07-09","ids":{"openalex":"https://openalex.org/W7167836527","doi":"https://doi.org/10.1145/3815436.3815468"},"language":null,"primary_location":{"id":"doi:10.1145/3815436.3815468","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3815436.3815468","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2026 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1145/3815436.3815468","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050963698","display_name":"Zhandong Dai","orcid":"https://orcid.org/0009-0000-3789-6320"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zihao Dai","raw_affiliation_strings":["State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0000-3789-6320","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104316163","display_name":"Hao Liang","orcid":"https://orcid.org/0009-0007-3284-1823"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Liang","raw_affiliation_strings":["State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0007-3284-1823","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072844990","display_name":"Jingyu Lu","orcid":"https://orcid.org/0009-0006-3125-3539"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jingyu Lu","raw_affiliation_strings":["University of Waterloo, Waterloo, ON, Canada"],"raw_orcid":"https://orcid.org/0009-0006-3125-3539","affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026679766","display_name":"Lihong Zhi","orcid":"https://orcid.org/0000-0001-9973-2217"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lihong Zhi","raw_affiliation_strings":["State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-9973-2217","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":null,"issue":null,"first_page":"142","last_page":"151"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.1882999986410141,"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":0.1882999986410141,"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/T11476","display_name":"Graph theory and applications","score":0.1014999970793724,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.07800000160932541,"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/series","display_name":"Series (stratigraphy)","score":0.5245000123977661},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.3822999894618988},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.3025999963283539},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.28209999203681946},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.2818000018596649},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.27239999175071716}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6662999987602234},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5245000123977661},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4862000048160553},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39399999380111694},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3822999894618988},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.25450000166893005},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3815436.3815468","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3815436.3815468","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2026 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3815436.3815468","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3815436.3815468","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2026 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W8416568","https://openalex.org/W1524052280","https://openalex.org/W1548944036","https://openalex.org/W1594278443","https://openalex.org/W1828084171","https://openalex.org/W1969780740","https://openalex.org/W1972632202","https://openalex.org/W1980267752","https://openalex.org/W1982581232","https://openalex.org/W1989957149","https://openalex.org/W1991005788","https://openalex.org/W2000368666","https://openalex.org/W2002276560","https://openalex.org/W2030403592","https://openalex.org/W2047200029","https://openalex.org/W2141040012","https://openalex.org/W2164690921","https://openalex.org/W2616294277","https://openalex.org/W2825602309","https://openalex.org/W2963080323","https://openalex.org/W2992264890","https://openalex.org/W3093164154","https://openalex.org/W4205630623","https://openalex.org/W4243098353","https://openalex.org/W4255359412","https://openalex.org/W4289684174","https://openalex.org/W4318562076","https://openalex.org/W4408074272"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,34,37,44,56,72,99],"unitary":[4,57],"diagonalization":[5],"of":[6,59,65,71,102],"matrices":[7,60],"over":[8,33,61,84],"formal":[9,86],"power":[10,87],"series":[11,88],"rings.":[12],"Our":[13],"main":[14],"result":[15],"shows":[16],"that":[17],"a":[18,75,81,85],"normal":[19],"matrix":[20],"is":[21,74],"unitarily":[22],"diagonalizable":[23],"if":[24,27],"and":[25,36,98],"only":[26],"its":[28],"minimal":[29],"polynomial":[30,82],"completely":[31],"splits":[32,83],"ring":[35],"associated":[38],"spectral":[39],"projections":[40],"have":[41],"entries":[42],"in":[43,105],"ring.":[45],"Building":[46],"on":[47],"this":[48,92],"characterization,":[49],"we":[50,90],"develop":[51],"an":[52],"algorithm":[53,73],"for":[54,78],"deciding":[55],"diagonalizability":[58],"regular":[62],"local":[63],"rings":[64],"algebraic":[66],"varieties.":[67],"A":[68],"central":[69],"ingredient":[70],"decision":[76],"procedure":[77],"determining":[79],"whether":[80],"ring;":[89],"establish":[91],"using":[93],"techniques":[94],"from":[95],"prime":[96],"decomposition":[97],"relative":[100],"smoothness":[101],"integral":[103],"closures":[104],"ramification":[106],"theory.":[107]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2026-07-10T00:00:00"}
