{"id":"W2609527018","doi":"10.1142/s100538671700013x","title":"A System of Matrix Equations over the Quaternion Algebra with Applications","year":2017,"lang":"en","type":"article","venue":"Algebra Colloquium","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":21,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"","keywords":"Quaternion; Mathematics; Algebra over a field; Representation (politics); Matrix (chemical analysis); Consistency (knowledge bases); Matrix representation; Expression (computer science); Quaternion algebra; System of linear equations; Current (fluid); Applied mathematics; Pure mathematics; Algebra representation; Mathematical analysis; Discrete mathematics; Division algebra; Geometry; Computer science; Law; Group (periodic table)","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005423429,0.0001539517,0.0001982366,0.00007091766,0.0009211602,0.0003693997,0.002111778,0.00005725168,0.00002017759],"category_scores_gemma":[0.00003252242,0.0001000043,0.00008305021,0.0002481331,0.0001895644,0.0005407627,0.0003499497,0.0001144145,0.00009322959],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003562081,"about_ca_system_score_gemma":0.0001148071,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001139415,"about_ca_topic_score_gemma":0.00003007887,"domain_scores_codex":[0.9987006,0.00009878832,0.0002785816,0.0003248867,0.0003529101,0.0002442202],"domain_scores_gemma":[0.997168,0.0002134462,0.0004185355,0.001990701,0.0001332554,0.00007606067],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000009182301,0.00004224513,0.0003479955,0.00004343652,0.00003690169,0.000003241527,0.0002456328,0.00003887448,0.0002333133,0.9963281,0.0001738359,0.002497212],"study_design_scores_gemma":[0.01072953,0.001844006,0.07547329,0.001280271,0.0008108654,0.0004872271,0.002809661,0.499395,0.03697397,0.2767264,0.08932561,0.004144153],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02719579,0.0001195431,0.9655433,0.00141399,0.0002798904,0.000800763,0.00001848894,0.0001709809,0.004457239],"genre_scores_gemma":[0.9921974,0.000005333373,0.006402108,0.00006030343,0.0001279313,0.0002355562,0.000003300477,0.00001308373,0.0009550175],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9650016,"threshold_uncertainty_score":0.7084913,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01101486769092788,"score_gpt":0.2563539428283959,"score_spread":0.245339075137468,"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."}}