{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001010237,0.0004070082,0.0004308809,0.001581438,0.0006786353,0.001497307,0.0008969145,0.0006022856,0.003986897],"category_scores_gemma":[0.003268231,0.000182847,0.0004269766,0.001649897,0.002161463,0.002419356,0.0009202838,0.001068322,0.0005661829],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009350699,"about_ca_system_score_gemma":0.0006182852,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001627615,"about_ca_topic_score_gemma":0.001106757,"domain_scores_codex":[0.99942,0.0001921306,0.0000194475,0.00007482312,0.0002180672,0.00007559083],"domain_scores_gemma":[0.9991376,0.0003302867,0.0001338622,0.00009418648,0.0002203897,0.00008365345],"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":[0.000003890355,0.000005403504,0.00003044138,0.00001411642,0.000001390272,0.00003228588,0.0000340335,0.001647379,0.0001931179,0.9945893,0.0003913461,0.003057268],"study_design_scores_gemma":[0.000004693929,0.00001544308,0.0001356859,0.00001679624,0.000002570065,0.0001078074,0.00004754922,0.05119401,0.0002395095,0.9435547,0.004668202,0.00001310209],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.203012,0.007528332,0.635962,0.003144324,0.001116635,0.00005759931,0.0001850455,0.0001875803,0.1488064],"genre_scores_gemma":[0.9061037,0.004087844,0.06783511,0.0005421906,0.002032268,0.00005065659,0.00008114688,0.00007850883,0.01918855],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003986897,"threshold_uncertainty_score":0.01333749,"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."}}