{"id":"W2102134292","doi":"10.4153/cmb-2009-012-3","title":"Matrix Valued Orthogonal Polynomials on the Unit Circle: Some Extensions of the Classical Theory","year":2009,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Orthogonal polynomials; Classical orthogonal polynomials; Christoffel symbols; Discrete orthogonal polynomials; Unit circle; Wilson polynomials; Hahn polynomials; Pascal matrix; Algebra over a field; Matrix (chemical analysis); Gegenbauer polynomials; Pure mathematics; Orthogonal matrix; Polynomial matrix; Representation (politics); Difference polynomials; Symmetric matrix; Square matrix; Mathematical analysis; Matrix polynomial; Polynomial; Orthogonal basis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.00147679,0.000193102,0.0002852038,0.00009895463,0.0003779209,0.00009720815,0.001635669,0.0001178924,0.002646579],"category_scores_gemma":[0.0009892272,0.0001121137,0.000209872,0.0003410933,0.0002885353,0.00004834626,0.0001126928,0.0003817601,0.00195467],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005083346,"about_ca_system_score_gemma":0.0003382727,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002357151,"about_ca_topic_score_gemma":0.00002120393,"domain_scores_codex":[0.9978606,0.0005573009,0.0003990011,0.0003071153,0.0003843795,0.0004916653],"domain_scores_gemma":[0.9969811,0.001303488,0.0001194693,0.001138163,0.00006674127,0.0003910094],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000006106388,0.0000551144,0.000001032847,0.000007794151,0.00001081983,0.00001457738,0.0001126535,0.00001053723,0.0001187972,0.9886218,0.007909734,0.00313103],"study_design_scores_gemma":[0.0002067318,0.00008826284,0.0008415241,0.0001190613,0.00002126886,0.00005201252,0.00005706477,0.002011588,0.0007792045,0.9773971,0.0182128,0.00021334],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"commentary","genre_gemma":"empirical","genre_scores_codex":[0.2304922,0.0004749177,0.07714728,0.6001561,0.001269215,0.002655427,0.000158549,0.0003699302,0.08727632],"genre_scores_gemma":[0.9806834,0.000002267153,0.002184462,0.01075932,0.0001774474,0.00001485816,0.000001167331,0.00001659825,0.0061605],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7501912,"threshold_uncertainty_score":0.9988225,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01616429111016382,"score_gpt":0.238416967674949,"score_spread":0.2222526765647851,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}