{"id":"W2106204743","doi":"10.1016/s0024-3795(01)00415-3","title":"Quadratic expansions of spectral functions","year":2002,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":16,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Hessian matrix; Eigenvalues and eigenvectors; Hessian equation; Positive-definite matrix; Pure mathematics; Invariant (physics); Quadratic equation; Mathematical analysis; Quadratic form (statistics); Function (biology); Symmetric matrix; Quadratic function; Combinatorics; Applied mathematics; Mathematical physics; Geometry","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":[0.00006779721,0.00007654106,0.0001011879,0.00006339692,0.0001834394,0.00002540012,0.0002467398,0.00003442018,0.0001917015],"category_scores_gemma":[0.00001352705,0.00006864917,0.00004041486,0.0003750483,0.0000386633,0.000181002,0.00006317364,0.0000785571,0.0002052814],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000003898802,"about_ca_system_score_gemma":0.000009249233,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001674418,"about_ca_topic_score_gemma":0.000001110945,"domain_scores_codex":[0.9993852,0.00002202035,0.0001770985,0.0002008363,0.00008981875,0.0001249739],"domain_scores_gemma":[0.999402,0.00008470751,0.00005294452,0.0003327496,0.00004556806,0.00008197171],"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":[5.925559e-7,0.0001436373,0.00002274212,0.00001705541,0.00001201295,4.704716e-7,0.0003669967,0.00002477348,0.002247432,0.9815566,0.00055817,0.0150495],"study_design_scores_gemma":[0.000992057,0.0003047409,0.001499497,0.00004401561,0.00008646179,0.00009535258,0.0003430397,0.7307715,0.02122591,0.115866,0.1280013,0.0007700092],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02861722,0.001129167,0.9588164,0.001924501,0.00009371479,0.0004023934,0.00002365166,0.0001801083,0.008812821],"genre_scores_gemma":[0.9797107,0.0001476142,0.01649404,0.0001344955,0.0001397086,0.00009613593,0.000005230698,0.000007267036,0.003264819],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9510935,"threshold_uncertainty_score":0.2799432,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01589457871349883,"score_gpt":0.2319566486574005,"score_spread":0.2160620699439016,"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."}}