{"id":"W2399407323","doi":"10.4169/amer.math.monthly.121.02.150","title":"An Eigenvalue Theorem for Systems of Polynomial Equations","year":2014,"lang":"en","type":"article","venue":"American Mathematical Monthly","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Eigenvalues and eigenvectors; Mathematics; Polynomial; Matrix polynomial; Applied mathematics; Pure mathematics; Mathematical analysis; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005917241,0.0002144626,0.0007183522,0.00008724519,0.0001156562,0.00004227363,0.0002946043,0.00006848123,0.00003263821],"category_scores_gemma":[0.001924264,0.0001686757,0.0001837685,0.000202744,0.0003098379,0.0001137721,0.00003042636,0.00008235664,0.00001869651],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004317513,"about_ca_system_score_gemma":0.00002802394,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000948403,"about_ca_topic_score_gemma":0.00001552331,"domain_scores_codex":[0.9980588,0.0002015033,0.000797281,0.0002927367,0.0003200574,0.0003296178],"domain_scores_gemma":[0.9953465,0.003178967,0.000478463,0.0006379394,0.000165577,0.0001925884],"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":[0.0000325744,0.0003600268,0.0000255499,0.0001867459,0.00003933167,1.228928e-7,0.000295785,0.0007905854,0.0009766171,0.9954261,0.00008327797,0.001783298],"study_design_scores_gemma":[0.0003323386,0.0004388782,0.00003811456,0.00006015255,0.00007317642,8.842422e-7,0.0005685585,0.3954119,0.0001308299,0.602625,0.0001377364,0.0001824477],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04539597,0.00001120022,0.9457858,0.00005471915,0.0001073215,0.0008031591,0.00008384496,0.0001134739,0.007644561],"genre_scores_gemma":[0.9023913,4.559314e-7,0.09699973,0.00002183803,0.0001727177,0.0002180844,0.00002271991,0.00004759896,0.0001255163],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8569953,"threshold_uncertainty_score":0.6878397,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02788848698142395,"score_gpt":0.3205464975578446,"score_spread":0.2926580105764207,"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."}}