{"id":"W3195954217","doi":"10.5539/jmr.v13n5p1","title":"Lower Bounds of the Smallest Singular Value of Matrices","year":2021,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Singular value; Hermitian matrix; TRACE (psycholinguistics); Upper and lower bounds; Matrix norm; Combinatorics; Value (mathematics); Matrix (chemical analysis); Euclidean geometry; Norm (philosophy); Complex matrix; Pure mathematics; Eigenvalues and eigenvectors; Mathematical analysis; Geometry; Statistics; Law","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004961565,0.00007279365,0.0002831628,0.0001825838,0.0001030441,0.00009873634,0.001574773,0.00005276962,0.00007279029],"category_scores_gemma":[0.000951596,0.00004500984,0.0002057759,0.0008547012,0.0001707824,0.0001478645,0.0005469197,0.0003962077,0.000004835454],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002992137,"about_ca_system_score_gemma":0.0004764644,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000301557,"about_ca_topic_score_gemma":8.347226e-7,"domain_scores_codex":[0.9972836,0.0003658132,0.0006297455,0.00009601293,0.001415213,0.0002095934],"domain_scores_gemma":[0.9967119,0.0009063401,0.0004710959,0.00060049,0.001239975,0.00007018918],"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":[0.0000259564,0.001611156,0.0003118306,0.001224461,0.0002052369,0.0002684092,0.004752425,0.0003606863,0.051599,0.9339955,0.001350898,0.004294389],"study_design_scores_gemma":[0.0008978609,0.0005641623,0.0005995649,0.001506733,0.00004644495,0.001053224,0.001752242,0.04022482,0.2307879,0.7194833,0.00287405,0.0002096782],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8109276,0.002179678,0.1781789,0.002033746,0.0006859925,0.0001609466,0.000003573679,0.000007277031,0.005822293],"genre_scores_gemma":[0.8525592,0.0001686763,0.1460889,0.00001813817,0.0001156767,7.61572e-7,7.277976e-8,0.00001008991,0.001038482],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2145123,"threshold_uncertainty_score":0.2926347,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05446158766527369,"score_gpt":0.3519074992135249,"score_spread":0.2974459115482512,"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."}}