{"id":"W32449668","doi":"10.20344/amp.14155","title":"HUA'S MATRIX EQUALITY AND SCHUR COMPLEMENTS","year":2008,"lang":"en","type":"article","venue":"","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Schur complement; Mathematical proof; Mathematics; Schur product theorem; Schur's theorem; Generalization; Schur decomposition; Algebra over a field; Matrix (chemical analysis); Complement (music); Pure mathematics; Combinatorics; Eigenvalues and eigenvectors; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001764272,0.0006913834,0.0006901004,0.001917001,0.001358714,0.001921823,0.0009264982,0.0006446658,0.0120272],"category_scores_gemma":[0.004517313,0.0002844621,0.0007649041,0.001762136,0.004452565,0.005247997,0.002195961,0.002373496,0.001555979],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001273174,"about_ca_system_score_gemma":0.001209048,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002928036,"about_ca_topic_score_gemma":0.002412917,"domain_scores_codex":[0.9987716,0.0002898935,0.0000562969,0.0002105947,0.0004442031,0.0002273921],"domain_scores_gemma":[0.9975546,0.001167848,0.0001519592,0.0002105504,0.0007829972,0.0001321052],"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":[0.000009942877,0.00000684275,0.00005277005,0.00003157626,0.000004521764,0.00004898408,0.00008825564,0.0004318553,0.0004802279,0.9890209,0.001072408,0.008751841],"study_design_scores_gemma":[0.000007059743,0.00003892049,0.000209351,0.00002585595,0.0000085265,0.00009394176,0.00008478857,0.006230407,0.001812727,0.9779044,0.01356636,0.00001758088],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04380086,0.002924285,0.7135633,0.002733542,0.0008205831,0.0000912918,0.0002832538,0.0002737792,0.2355091],"genre_scores_gemma":[0.8153391,0.004321798,0.1280356,0.002152132,0.001569237,0.0002044871,0.0002958169,0.0001701537,0.04791169],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0120272,"threshold_uncertainty_score":0.04023498,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.3050936514228589,"score_gpt":0.4434791705364389,"score_spread":0.1383855191135799,"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."}}