{"id":"W1973642390","doi":"10.1016/j.laa.2011.12.010","title":"Every invertible matrix is diagonally equivalent to a matrix with distinct eigenvalues","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 Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Invertible matrix; Diagonally dominant matrix; Eigenvalues and eigenvectors; Matrix (chemical analysis); Pure mathematics; Conjecture; Diagonal; Combinatorics; Eigendecomposition of a matrix; Diagonal matrix; Geometry; Physics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0006489172,0.0009377716,0.0006182277,0.001404374,0.001346566,0.002589787,0.0007572121,0.001236992,0.01317208],"category_scores_gemma":[0.003447188,0.0004499639,0.000669945,0.001248259,0.003553946,0.002524974,0.002113086,0.002084968,0.003307383],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003206493,"about_ca_system_score_gemma":0.0006856253,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002538283,"about_ca_topic_score_gemma":0.0003315358,"domain_scores_codex":[0.9983591,0.0002532579,0.00009554896,0.0005407732,0.000495381,0.000255912],"domain_scores_gemma":[0.9976249,0.0008197774,0.0003232563,0.0004861819,0.0005776726,0.0001682335],"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":[0.0001079881,0.0001758341,0.0003938889,0.0001286447,0.00004643243,0.0002065202,0.000328295,0.001216806,0.01482453,0.9339302,0.004416751,0.0442241],"study_design_scores_gemma":[0.00004287257,0.0001161061,0.00060507,0.00002797684,0.00002136317,0.0003966776,0.0002611951,0.005086473,0.007376715,0.9746551,0.01136237,0.00004812121],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1997349,0.0004670804,0.6510484,0.001905838,0.002036753,0.0002167414,0.0007182169,0.001390473,0.1424817],"genre_scores_gemma":[0.8476235,0.0007193559,0.1141914,0.001666954,0.001140809,0.0003137492,0.0007324492,0.0004589416,0.03315285],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01317208,"threshold_uncertainty_score":0.04406494,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01626442222791432,"score_gpt":0.2825331558781582,"score_spread":0.2662687336502439,"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."}}