{"id":"W2129405000","doi":"10.1016/s0024-3795(00)00237-8","title":"A criterion for the existence of common invariant subspaces of matrices","year":2001,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":20,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Regina","funders":"","keywords":"Mathematics; Linear subspace; Invertible matrix; Invariant (physics); Eigenvalues and eigenvectors; Invariant subspace; Subspace topology; Grassmannian; Pure mathematics; Scalar (mathematics); Dimension (graph theory); Combinatorics; Mathematical analysis; Mathematical 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":[0.0002053652,0.00005500815,0.0001026056,0.00003392074,0.0001203974,0.00002245423,0.0003954127,0.00002474906,0.000005978179],"category_scores_gemma":[0.000015446,0.00003748066,0.00003294406,0.0002708177,0.00004980166,0.0001240556,0.00007795325,0.00003445138,0.000002321364],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000001747516,"about_ca_system_score_gemma":0.00001357456,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001306109,"about_ca_topic_score_gemma":0.000003953398,"domain_scores_codex":[0.9995276,0.00001908675,0.0001708869,0.0001286324,0.0000730449,0.00008074802],"domain_scores_gemma":[0.9991852,0.0003317759,0.0001127842,0.0002687873,0.00007467925,0.00002674047],"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":[0.000007514359,0.00006535815,0.00007034796,0.00006118902,0.0000106421,1.530112e-7,0.0004060487,0.00001268745,0.002178118,0.9770821,0.00003899609,0.02006686],"study_design_scores_gemma":[0.001072392,0.0004432385,0.00448485,0.0001135942,0.0001216158,0.00007064574,0.0006419833,0.5850528,0.06095841,0.2406441,0.1059204,0.000475908],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06628323,0.002926454,0.927373,0.002114861,0.00004174498,0.0006793344,0.00002762922,0.00003691619,0.0005168264],"genre_scores_gemma":[0.9782978,0.0008638473,0.02034057,0.00009157715,0.0000693976,0.0001408198,0.0000034846,0.00000442463,0.0001880831],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9120145,"threshold_uncertainty_score":0.1528417,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02188721000028494,"score_gpt":0.2794851996961133,"score_spread":0.2575979896958284,"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."}}