{"id":"W2734262381","doi":"","title":"Some equalities for generalized inverses of matrix sums and block circulant matrices","year":2001,"lang":"en","type":"article","venue":"Czech digital mathematics library","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Circulant matrix; Mathematics; Inverse; Block (permutation group theory); Moore–Penrose pseudoinverse; Drazin inverse; Matrix (chemical analysis); Generalized inverse; Combinatorics; Block matrix; Pure mathematics; Algebra over a field; Eigenvalues and eigenvectors; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001494343,0.0001977437,0.0003531481,0.0001588336,0.00007524029,0.0005189726,0.0006203835,0.00007258374,0.00001300205],"category_scores_gemma":[0.00006019415,0.0001661969,0.0001216761,0.0002503342,0.00008361886,0.003170935,0.0003665715,0.00005600009,0.0000112924],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005393547,"about_ca_system_score_gemma":0.00004748454,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":9.06283e-7,"about_ca_topic_score_gemma":3.420639e-8,"domain_scores_codex":[0.9987843,0.00002331104,0.0004484614,0.0002647562,0.0002042224,0.0002749214],"domain_scores_gemma":[0.9987635,0.0004689315,0.0002125805,0.0004136115,0.00002790648,0.000113455],"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":[0.00001335018,0.000136347,0.0001413105,0.0008323301,0.00004352095,0.00001487159,0.0007588157,0.00001176868,0.0003029096,0.9946273,0.0007628846,0.002354583],"study_design_scores_gemma":[0.0006016102,0.000116001,0.00001748685,0.00012211,0.00002236671,0.0001210537,0.0003285971,0.02228221,0.006931819,0.9649143,0.004211274,0.0003311643],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8284327,0.005060601,0.157173,0.0008640915,0.000452872,0.00106239,0.0003401605,0.0008144037,0.00579973],"genre_scores_gemma":[0.6441914,0.001139465,0.3436561,0.0004045336,0.0005245905,0.00009183708,0.00006307254,0.0001009378,0.009828112],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1864831,"threshold_uncertainty_score":0.6777313,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02439548394324602,"score_gpt":0.2499608467588279,"score_spread":0.2255653628155819,"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."}}