{"id":"W1989515285","doi":"10.1016/j.laa.2011.11.014","title":"On irreducible algebras spanned by triangularizable matrices","year":2011,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Algebraically closed field; Mathematics; Semigroup; Subalgebra; Field (mathematics); Pure mathematics; Zero (linguistics); Linear map; Basis (linear algebra); Discrete mathematics; Algebra over a field","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001641501,0.0002284023,0.0002600921,0.0001037778,0.0002529565,0.00003171162,0.0002963272,0.0001416119,0.0004871131],"category_scores_gemma":[0.0001704734,0.0002113277,0.00006372559,0.00035451,0.00006483008,0.0001688086,0.00008535628,0.0002173727,0.0003353363],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002236133,"about_ca_system_score_gemma":0.00002436574,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007003881,"about_ca_topic_score_gemma":0.00000200355,"domain_scores_codex":[0.9986293,0.00003299128,0.0003551741,0.0004697765,0.0001962321,0.0003165384],"domain_scores_gemma":[0.9987199,0.0003013526,0.0001635066,0.0005742771,0.00007768873,0.0001632758],"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":[0.00001764928,0.0002709776,0.00001930295,0.00004436827,0.0000306597,9.68073e-7,0.0002267714,3.057168e-7,0.00114255,0.9909025,0.005367484,0.001976432],"study_design_scores_gemma":[0.0004954425,0.0000957856,0.00004294817,0.0000225772,0.00005819732,0.000007318974,0.00008153069,0.0001615096,0.01890851,0.9520798,0.02776287,0.0002834976],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5832527,0.00640545,0.2602763,0.002433022,0.0005326046,0.006159228,0.0004710824,0.001830761,0.1386388],"genre_scores_gemma":[0.800769,0.0008685144,0.1708623,0.001204624,0.0007100089,0.00155881,0.0001616063,0.0002499345,0.02361521],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2175162,"threshold_uncertainty_score":0.8617694,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04913492660136495,"score_gpt":0.307485929687885,"score_spread":0.2583510030865201,"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."}}