{"id":"W2963248211","doi":"10.4153/cmb-2015-049-4","title":"Factoring a Quadratic Operator as a Product of Two Positive Contractions","year":2015,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Multiplication operator; Operator (biology); Bounded operator; Quasinormal operator; Product (mathematics); Unitary operator; Shift operator; Compact operator; Factoring; Finite-rank operator; Pure mathematics; Bounded function; Hilbert space; Operator space; Quadratic equation; Algebra over a field; Mathematical analysis; Banach space","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":[0.001240833,0.0005380625,0.0004319476,0.0003839115,0.000564431,0.0009497549,0.0005233872,0.0005584951,0.007846054],"category_scores_gemma":[0.002196341,0.0002621273,0.0006212454,0.0003336857,0.001958387,0.002262231,0.001734977,0.001005542,0.0007449921],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002604657,"about_ca_system_score_gemma":0.0004173396,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002452539,"about_ca_topic_score_gemma":0.0002371439,"domain_scores_codex":[0.9990984,0.0002256016,0.00004852546,0.0001924296,0.0002814225,0.0001536522],"domain_scores_gemma":[0.9986321,0.0003852091,0.0001651265,0.000173685,0.0002969356,0.0003469877],"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":[0.0005799978,0.0001590257,0.001468662,0.0001698751,0.00004459397,0.001155347,0.0008302343,0.009312361,0.06901133,0.8813362,0.003875963,0.03205634],"study_design_scores_gemma":[0.0001369664,0.0008637005,0.001729721,0.00007887975,0.00004341029,0.001457129,0.0005886311,0.1998484,0.01966314,0.7570305,0.01846493,0.00009450352],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.340389,0.0002085932,0.636883,0.0006270809,0.0003331542,0.00008989226,0.00007169556,0.0003029001,0.02109467],"genre_scores_gemma":[0.9056419,0.0001108046,0.08005994,0.000281712,0.0002279975,0.0001013777,0.00009603635,0.0002103484,0.0132698],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007846054,"threshold_uncertainty_score":0.02624768,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02091534161772944,"score_gpt":0.2635711437668774,"score_spread":0.242655802149148,"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."}}