{"id":"W2085120770","doi":"10.1016/j.laa.2012.05.035","title":"Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute","year":2012,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Matrix (chemical analysis); Involutory matrix; Block (permutation group theory); Matrix analysis; Algebra over a field; Combinatorics; Pure mathematics; Square matrix; Symmetric matrix; Eigenvalues and eigenvectors","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":[0.0004936498,0.0001327065,0.0002411757,0.0001537195,0.0001503401,0.00002178138,0.0003537778,0.00006485922,0.00001038047],"category_scores_gemma":[0.00002252266,0.0001189124,0.00005388622,0.0003947729,0.00008568054,0.000452018,0.0002060671,0.0001099302,0.000009235678],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000008579355,"about_ca_system_score_gemma":0.00003197564,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001695532,"about_ca_topic_score_gemma":0.000001011538,"domain_scores_codex":[0.9989775,0.00008322624,0.0003477013,0.0002061662,0.0001962229,0.0001892285],"domain_scores_gemma":[0.9989448,0.0001881138,0.000265867,0.0003575852,0.000119298,0.0001243224],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00001286683,0.000428361,0.0008539589,0.000212507,0.0000416257,4.188551e-7,0.001609654,0.00001265964,0.003345434,0.9662383,0.00005293591,0.02719124],"study_design_scores_gemma":[0.01295278,0.001529014,0.03075743,0.0004205125,0.0007037672,0.0003701775,0.001594287,0.5332794,0.139288,0.2187413,0.05777362,0.002589673],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5063984,0.01566811,0.4751318,0.0006581311,0.0001475414,0.001129398,0.00006209832,0.0001371954,0.000667344],"genre_scores_gemma":[0.9701058,0.0007693326,0.02869722,0.00005330569,0.00009381844,0.0000593218,0.00001147894,0.00001003375,0.0001997528],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.747497,"threshold_uncertainty_score":0.4849105,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0179595651600082,"score_gpt":0.2747893100120989,"score_spread":0.2568297448520907,"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."}}