{"id":"W2024312265","doi":"10.1016/j.laa.2013.03.019","title":"An identity of degree 2 n − 3 for the n × n skews, n even, and corollaries for standard identities","year":2013,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"John Abbott College","funders":"","keywords":"Mathematics; Identity (music); Combinatorics; Integer (computer science); Transpose; Degree (music); Involution (esoterism); Skew; Discrete mathematics; Eigenvalues and eigenvectors","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":[0.0001813611,0.0001070028,0.0001851735,0.00003138369,0.0003265502,0.00007662135,0.0001859736,0.0000604843,0.00002661505],"category_scores_gemma":[0.0002427223,0.00008117998,0.00004255455,0.00007776618,0.0001406566,0.0003711102,0.00005494167,0.00005943442,0.000002243193],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00000864842,"about_ca_system_score_gemma":0.00002414499,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006583169,"about_ca_topic_score_gemma":0.00003621945,"domain_scores_codex":[0.9992876,0.00001204126,0.0002617427,0.0001825724,0.0001160505,0.0001400019],"domain_scores_gemma":[0.9983771,0.0008264851,0.0001366286,0.0003142039,0.0002933349,0.00005226953],"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":[0.00001030622,0.00002963491,0.000154855,0.0001785557,0.00003526673,1.451477e-8,0.0002502979,0.000001159887,0.0005105635,0.9938294,0.0006253987,0.004374504],"study_design_scores_gemma":[0.0003763059,0.00008281373,0.0007067227,0.0000100304,0.00008200188,0.000002215937,0.0003959163,0.001283875,0.002814302,0.9862926,0.007851731,0.0001014788],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1844257,0.001427477,0.8100961,0.0006831922,0.00005388092,0.002837339,0.0003199931,0.00005308918,0.0001031917],"genre_scores_gemma":[0.8358727,0.0007212334,0.1584818,0.0001617935,0.0003374668,0.003227893,0.000040826,0.00005291247,0.001103318],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6516143,"threshold_uncertainty_score":0.3310424,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06015457558956999,"score_gpt":0.3599721825334498,"score_spread":0.2998176069438798,"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."}}