{"id":"W1414602992","doi":"10.1016/j.jmaa.2015.08.029","title":"Derivatives of compound matrix valued functions","year":2015,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"Western University","funders":"Office of Naval Research; California Institute of Technology; National Science Foundation","keywords":"Mathematics; Differentiable function; Multiplicative function; Matrix function; Generalization; Invariant (physics); Matrix (chemical analysis); Pure mathematics; Algebra over a field; Symmetric matrix; Mathematical analysis; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001333965,0.0007777446,0.0007083674,0.001939227,0.0006094484,0.002718511,0.0007902706,0.001294683,0.005636427],"category_scores_gemma":[0.006419839,0.0004219822,0.0004405846,0.001331548,0.002139526,0.004540974,0.00102903,0.001752396,0.0007895119],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001176063,"about_ca_system_score_gemma":0.0008341435,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009879491,"about_ca_topic_score_gemma":0.001133667,"domain_scores_codex":[0.9996188,0.0001287471,0.00002458771,0.000067667,0.0001181114,0.0000421385],"domain_scores_gemma":[0.9967657,0.001611341,0.0003988747,0.000240947,0.0006739486,0.0003091054],"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":[0.00004605424,0.0000214882,0.0002520535,0.00005981641,0.00001328223,0.0001270217,0.0001273477,0.00955594,0.002513313,0.9753219,0.001631537,0.01033031],"study_design_scores_gemma":[0.000009639246,0.00002940173,0.0004015962,0.00002534377,0.00001263754,0.0002321893,0.00006221491,0.1434335,0.001289837,0.8494678,0.005003048,0.00003290404],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1298747,0.003401916,0.8285868,0.001542944,0.0009096846,0.00003603133,0.0002646096,0.0003074793,0.03507595],"genre_scores_gemma":[0.8424404,0.003496602,0.1027984,0.0004978515,0.0007343148,0.00005724663,0.0002247275,0.0003697028,0.04938074],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005636427,"threshold_uncertainty_score":0.01885569,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02531476546837401,"score_gpt":0.2939239115119389,"score_spread":0.2686091460435649,"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."}}