{"id":"W2027519704","doi":"10.1002/qua.10777","title":"Unitarily invariant decomposition of arbitrary Hermitian matrices of physical interest","year":2003,"lang":"en","type":"article","venue":"International Journal of Quantum Chemistry","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Ministerio de Ciencia y Tecnología","keywords":"Hermitian matrix; Invariant (physics); Mathematics; Decomposition; Pure mathematics; Quantum; Algebra over a field; Mathematical physics; Quantum mechanics; Physics; Chemistry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":false,"about_ca":true,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003457918,0.0001033801,0.0002206562,0.00009408415,0.00001810659,0.00003708431,0.0009845999,0.00004671753,0.00005609731],"category_scores_gemma":[0.00009590412,0.00009119428,0.0001767057,0.0001278323,0.00007053613,0.0003853395,0.00007686378,0.0002026319,0.000002194682],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003526648,"about_ca_system_score_gemma":0.0001440153,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004619906,"about_ca_topic_score_gemma":1.5413e-7,"domain_scores_codex":[0.9988084,0.00006395948,0.0005229666,0.0001125416,0.0003935103,0.00009865767],"domain_scores_gemma":[0.9984776,0.0001862331,0.0006934475,0.0001590546,0.0004115363,0.00007217847],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.0001376651,0.0009377545,0.0003381576,0.0001397494,0.0003388081,0.0002927498,0.0005846042,0.0002949266,0.575545,0.4181077,0.0001636335,0.003119175],"study_design_scores_gemma":[0.0006315296,0.0001301118,0.0002186681,0.0002896154,0.00002026943,0.000813923,0.0001213519,0.009341685,0.921701,0.0662516,0.0003544901,0.0001257995],"study_design_candidate":"bench_or_experimental","study_design_consensus":"bench_or_experimental","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.921612,0.0001826891,0.07459944,0.0002840316,0.0004197912,0.00002615876,0.00001275532,0.000009168006,0.002853999],"genre_scores_gemma":[0.9945713,0.00001958579,0.0051776,0.00003677939,0.0001641923,4.661596e-7,0.000002368799,0.000005327756,0.00002242968],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3518562,"threshold_uncertainty_score":0.3718795,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01575960976891935,"score_gpt":0.2825048663090287,"score_spread":0.2667452565401094,"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."}}