{"id":"W2064891073","doi":"10.1016/j.laa.2003.08.012","title":"The simplest proof of Burnside's theorem on matrix algebras","year":2003,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":55,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Algebraically closed field; Invariant subspace; Pure mathematics; Invariant (physics); Simple (philosophy); Elementary proof; Algebra over a field; Matrix (chemical analysis); Subspace topology; Discrete mathematics; Linear subspace; Mathematical analysis; Mathematical physics","routes":{"ca_aff":true,"ca_fund":false,"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":[0.001403369,0.00122412,0.0009928808,0.00174552,0.001987463,0.002417744,0.001760535,0.001442305,0.01420796],"category_scores_gemma":[0.003675461,0.0004487259,0.001171397,0.001269675,0.003254404,0.006642969,0.00372943,0.004340181,0.002765979],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001121135,"about_ca_system_score_gemma":0.001022696,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005574612,"about_ca_topic_score_gemma":0.0005384445,"domain_scores_codex":[0.9993099,0.000121001,0.00003548925,0.0001317231,0.000298653,0.0001031977],"domain_scores_gemma":[0.9988809,0.0003787283,0.00007157152,0.0002313916,0.0003090686,0.0001282466],"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":[0.0000367905,0.00002433746,0.00008132029,0.0001404038,0.00001559526,0.00006141246,0.0001442592,0.0002224226,0.001331745,0.9754826,0.008791838,0.01366732],"study_design_scores_gemma":[0.00001380421,0.00001208505,0.00008142266,0.00002212876,0.00001131107,0.0001129701,0.00002534565,0.000609827,0.001222077,0.9841354,0.01374035,0.00001333119],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0627822,0.006042907,0.5175859,0.02151594,0.007500332,0.0001515769,0.0007732151,0.001544091,0.3821039],"genre_scores_gemma":[0.7225066,0.005322861,0.1380892,0.009430224,0.005309606,0.0002762346,0.0006334414,0.0007989989,0.1176328],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01420796,"threshold_uncertainty_score":0.04753035,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02937311205438796,"score_gpt":0.3314041468443836,"score_spread":0.3020310347899957,"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."}}