{"id":"W4299680605","doi":"","title":"Condition number of a square matrix with i.i.d. columns drawn from a convex body","year":2013,"lang":"en","type":"article","venue":"","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Square (algebra); Regular polygon; Mathematics; Combinatorics; Matrix (chemical analysis); Square matrix; Convex body; Geometry; Materials science; Convex hull; Composite material; Physics; 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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0001025805,0.000134348,0.0003189379,0.00007354672,0.00006247742,0.00008788778,0.0001139697,0.00008000333,0.01754917],"category_scores_gemma":[0.0001542413,0.00009841428,0.00005388665,0.0003015175,0.00009848455,0.0002545704,0.00003408306,0.00007898005,0.0004001488],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001920591,"about_ca_system_score_gemma":0.00006911445,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002902277,"about_ca_topic_score_gemma":0.00009980362,"domain_scores_codex":[0.9989902,0.00002816705,0.000336607,0.000162548,0.0002826833,0.0001998248],"domain_scores_gemma":[0.9987102,0.0004704677,0.0001878541,0.0002399984,0.0003287068,0.00006278996],"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":[0.0001178051,0.0008601574,0.03344749,0.00180366,0.0006751169,0.00001746563,0.005688456,0.0000027588,0.00120826,0.8673709,0.08820976,0.0005981427],"study_design_scores_gemma":[0.002642965,0.000413523,0.005701291,0.0003142822,0.0001980112,0.0000382582,0.01088687,0.0008265934,0.01104853,0.9630891,0.004193482,0.0006470616],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9626001,0.00003451389,0.01128985,0.0002112217,0.00004135281,0.0003591503,0.0001047057,0.0000972183,0.02526185],"genre_scores_gemma":[0.9804437,0.00000461162,0.01066567,0.0001014785,0.00005030342,0.00006652188,0.00004200096,0.00002028268,0.008605448],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0957182,"threshold_uncertainty_score":0.9833489,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01982661621928501,"score_gpt":0.3185033047469114,"score_spread":0.2986766885276264,"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."}}