{"id":"https://openalex.org/W7161732372","doi":"https://doi.org/10.48550/arxiv.2605.16954","title":"Block Krylov subspaces and orthogonal matrix polynomials: a structural correspondence with applications to unitary matrices","display_name":"Block Krylov subspaces and orthogonal matrix polynomials: a structural correspondence with applications to unitary matrices","publication_year":2026,"publication_date":"2026-05-16","ids":{"openalex":"https://openalex.org/W7161732372","doi":"https://doi.org/10.48550/arxiv.2605.16954"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.16954","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.16954","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.16954","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090990730","display_name":"Michele Rinelli","orcid":"https://orcid.org/0000-0003-2405-7442"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rinelli, Michele","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039999347","display_name":"Raf Vandebril","orcid":"https://orcid.org/0000-0003-2119-8696"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vandebril, Raf","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"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":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":0.929099977016449,"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":0.929099977016449,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.014299999922513962,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.01360000018030405,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.647599995136261},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.6200000047683716},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.605400025844574},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.5266000032424927},{"id":"https://openalex.org/keywords/orthogonal-matrix","display_name":"Orthogonal matrix","score":0.4943000078201294},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4853000044822693},{"id":"https://openalex.org/keywords/laurent-polynomial","display_name":"Laurent polynomial","score":0.46239998936653137},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45719999074935913},{"id":"https://openalex.org/keywords/unitary-matrix","display_name":"Unitary matrix","score":0.45570001006126404},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.41920000314712524}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8356999754905701},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.647599995136261},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.6200000047683716},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.605400025844574},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.5266000032424927},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.4943000078201294},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4853000044822693},{"id":"https://openalex.org/C106639798","wikidata":"https://www.wikidata.org/wiki/Q1701125","display_name":"Laurent polynomial","level":2,"score":0.46239998936653137},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45719999074935913},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.45570001006126404},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43790000677108765},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.41920000314712524},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.4077000021934509},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.38199999928474426},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.3573000133037567},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.3357999920845032},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.3319000005722046},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3156999945640564},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.31310001015663147},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.30970001220703125},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3043999969959259},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30250000953674316},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.2980000078678131},{"id":"https://openalex.org/C54940322","wikidata":"https://www.wikidata.org/wiki/Q3997740","display_name":"Orthogonal transformation","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.29089999198913574},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.26440000534057617},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.25769999623298645},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.251800000667572}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.16954","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.16954","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.16954","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.16954","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,39,64,76,84,107,111,116,125,133,141,149],"connection":[3,120],"between":[4],"block":[5,20,55,142,155],"Krylov":[6,21,56,66,143,156],"subspaces":[7,22,57],"and":[8,41,46,58,62,132,153],"matrix":[9,29,73,77,97,130,138],"orthogonal":[10,129],"functions.":[11],"Under":[12],"a":[13,35,89,94,100],"no-deflation":[14],"assumption,":[15],"we":[16,81],"show":[17],"that":[18,83],"polynomial":[19,152],"are":[23],"isometrically":[24],"isomorphic":[25],"to":[26,71,123,140],"spaces":[27],"of":[28,31,43,93,151],"polynomials":[30,131,139],"bounded":[32],"degree,":[33],"providing":[34],"unified":[36],"framework":[37,135],"for":[38,53,103,128,136,148],"analysis":[40],"construction":[42],"orthonormal":[44],"bases":[45],"recurrence":[47,127],"relations.":[48],"The":[49],"same":[50],"correspondence":[51],"holds":[52],"rational":[54,60],"matrix-valued":[59],"functions,":[61],"in":[63,91],"extended":[65,154],"setting":[67],"this":[68,119],"leads":[69],"naturally":[70],"Laurent":[72,137],"polynomials.":[74],"When":[75],"$A$":[78],"is":[79,113],"normal,":[80],"prove":[82],"induced":[85],"inner":[86],"product":[87],"admits":[88],"representation":[90],"terms":[92],"discrete":[95],"spectral":[96],"measure,":[98],"extending":[99],"classical":[101],"result":[102],"Hermitian":[104],"matrices.":[105],"In":[106],"unitary":[108],"case,":[109],"where":[110],"measure":[112],"supported":[114],"on":[115],"unit":[117],"circle,":[118],"allows":[121],"us":[122],"transfer":[124],"Szeg\u0151":[126],"CMV":[134],"setting,":[144],"yielding":[145],"efficient":[146],"procedures":[147],"orthogonalization":[150],"subspaces.":[157]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-20T00:00:00"}
