{"id":"W3203646126","doi":"10.13001/ela.2021.4991","title":"Generalized Commutators and the Moore-Penrose Inverse","year":2021,"lang":"en","type":"article","venue":"Electronic Journal of Linear Algebra","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"Division of Mathematical Sciences; Fields Institute for Research in Mathematical Sciences","keywords":"Mathematics; Commutator; Combinatorics; Inverse; Kernel (algebra); Conjecture; Rank (graph theory); Matrix (chemical analysis); Operator (biology); TRACE (psycholinguistics); Algebra over a field; Pure mathematics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001506521,0.0001101614,0.0002530743,0.00005581855,0.0001701745,0.0001171251,0.0005967534,0.00003904099,0.00004122245],"category_scores_gemma":[0.0001258288,0.00006989327,0.000137582,0.0002970109,0.0001216211,0.0002967225,0.0001706083,0.0005104429,0.0000101352],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003996669,"about_ca_system_score_gemma":0.000448708,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004640064,"about_ca_topic_score_gemma":0.000007264468,"domain_scores_codex":[0.9985466,0.0004196982,0.000334539,0.0001275934,0.0002426605,0.0003289149],"domain_scores_gemma":[0.9990171,0.0002154738,0.0002236269,0.0003045104,0.0001500754,0.00008925558],"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":[0.00006684508,0.00004481999,0.00005629774,0.000006312135,0.0001179038,0.00009912896,0.0008198395,0.00008124602,0.0004662807,0.9916214,0.0004682883,0.006151675],"study_design_scores_gemma":[0.01153298,0.0004610505,0.0001795463,0.00005911236,0.0001261534,0.00571174,0.0004009447,0.05781499,0.02664155,0.8550621,0.04156038,0.0004495147],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7618983,0.01889098,0.2043597,0.0133649,0.0006939883,0.0001466011,0.000001400923,0.00004599919,0.0005981404],"genre_scores_gemma":[0.9794846,0.001620551,0.01581712,0.001938578,0.0004270746,0.000001700429,0.000001021909,0.00001471006,0.0006946057],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2175863,"threshold_uncertainty_score":0.2850165,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006631096575086481,"score_gpt":0.230134476426218,"score_spread":0.2235033798511315,"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."}}