{"id":"W2007890346","doi":"10.1080/03081080108818684","title":"Linear operators preserving decomposable numerical radii on orthonormal tensors","year":2001,"lang":"en","type":"article","venue":"Linear and Multilinear Algebra","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"University of Toronto","keywords":"Mathematics; Orthonormal basis; Matrix (chemical analysis); Degree (music); Combinatorics; Matrix function; Linear operators; Operator (biology); Pure mathematics; Orthonormality; Function (biology); Unitary state; Orthogonal matrix; Symmetric matrix; Mathematical analysis; Eigenvalues and eigenvectors; Orthogonal basis; Physics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001339161,0.0008013303,0.000420576,0.0009736244,0.0004879857,0.001267456,0.0006775131,0.0006200602,0.002830257],"category_scores_gemma":[0.003633975,0.0003065393,0.0004839175,0.0004847197,0.002051137,0.002671645,0.001698675,0.000856114,0.0005619162],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005344704,"about_ca_system_score_gemma":0.0003357374,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002730125,"about_ca_topic_score_gemma":0.0003087484,"domain_scores_codex":[0.9989504,0.0003346184,0.00005066365,0.0001967977,0.0002943732,0.0001732294],"domain_scores_gemma":[0.9977591,0.0006975374,0.0005908367,0.000302239,0.0002336333,0.0004166553],"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":[0.0001161241,0.00004619097,0.0005435841,0.00005825669,0.00001565346,0.0002803935,0.0005188729,0.01054075,0.02372219,0.9436466,0.0007898998,0.01972134],"study_design_scores_gemma":[0.00005489013,0.0002941177,0.001057302,0.00003106282,0.0000139394,0.0006870724,0.0004599055,0.1908974,0.01880756,0.7831032,0.004538507,0.00005510343],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5733182,0.0002927609,0.4120906,0.0002575056,0.0000572398,0.00006979546,0.0001106408,0.0003739013,0.01342939],"genre_scores_gemma":[0.9071932,0.0003380733,0.08021068,0.0001520489,0.0001222508,0.0001384146,0.0001515867,0.0001621292,0.01153168],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002830257,"threshold_uncertainty_score":0.009468198,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01410259040350412,"score_gpt":0.2630161250242409,"score_spread":0.2489135346207368,"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."}}