{"id":"W2963641145","doi":"10.2140/ant.2008.2.979","title":"The number of 2×2 integer matrices having a prescribed integer eigenvalue","year":2008,"lang":"en","type":"article","venue":"Algebra & Number Theory","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Integer (computer science); Mathematics; Integer matrix; Eigenvalues and eigenvectors; Divide-and-conquer eigenvalue algorithm; Integer points in convex polyhedra; Matrix (chemical analysis); Random matrix; Probability distribution; Combinatorics; Interval (graph theory); Discrete mathematics; Integer programming; Symmetric matrix; Branch and price; Nonnegative matrix; Mathematical optimization; Statistics; Computer science","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":[0.003592539,0.0006374615,0.001100606,0.001514553,0.00147198,0.003958732,0.001848251,0.001554682,0.006906605],"category_scores_gemma":[0.03317385,0.0005075113,0.0006198384,0.001359538,0.003624827,0.006685745,0.001742173,0.00157276,0.000912905],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009183511,"about_ca_system_score_gemma":0.0005687363,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003387015,"about_ca_topic_score_gemma":0.0002832983,"domain_scores_codex":[0.9970093,0.001022955,0.0001883224,0.0007619907,0.0006590466,0.0003582682],"domain_scores_gemma":[0.9704517,0.02079195,0.002984957,0.00239703,0.001787664,0.001586682],"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":[0.0005728636,0.0001020004,0.008522885,0.0003542431,0.00008975694,0.0003047078,0.0006771205,0.0212319,0.009736336,0.9148092,0.004712906,0.03888613],"study_design_scores_gemma":[0.0001117357,0.0002477902,0.007179307,0.0001510893,0.00007849296,0.001370667,0.0005843767,0.1463368,0.01435128,0.8184184,0.01094999,0.0002200856],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6160333,0.001824227,0.3281717,0.005755087,0.0005893124,0.0001759071,0.001739754,0.0007056166,0.04500503],"genre_scores_gemma":[0.9641018,0.001043391,0.02224561,0.0004238278,0.0004535688,0.0002719281,0.0006821456,0.0001530814,0.0106248],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006906605,"threshold_uncertainty_score":0.02310485,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02768472433392679,"score_gpt":0.3101371751155966,"score_spread":0.2824524507816699,"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."}}