{"id":"W2170477486","doi":"10.1016/j.laa.2003.12.038","title":"Tridiagonal normal forms for orthogonal similarity classes of symmetric matrices","year":2004,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"Wilfrid Laurier University; University of Waterloo","funders":"","keywords":"Tridiagonal matrix; Mathematics; Combinatorics; Orthogonal matrix; Transpose; Identity matrix; Matrix (chemical analysis); Similarity (geometry); Pure mathematics; Algebraically closed field; Band matrix; Symmetric group; Symmetric matrix; Square matrix; Orthogonal basis; Image (mathematics); Eigenvalues and eigenvectors; Chemistry","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":[0.0001600227,0.0001508502,0.0002508895,0.00014439,0.0001713786,0.00001601522,0.0001914107,0.0001120728,0.00002297985],"category_scores_gemma":[0.0002799667,0.0001340392,0.0000968606,0.0004622735,0.000066591,0.0001765584,0.0000692781,0.0001372197,0.00000863909],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002634245,"about_ca_system_score_gemma":0.00008042176,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000177927,"about_ca_topic_score_gemma":0.000008018415,"domain_scores_codex":[0.9989191,0.000008529995,0.0004099052,0.000251684,0.0001883059,0.0002224622],"domain_scores_gemma":[0.9987544,0.0005129583,0.0002090701,0.0002430746,0.0001891416,0.00009133252],"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":[0.00001455334,0.0001836452,0.0000834721,0.0002051594,0.00002973454,2.065211e-7,0.00004686751,0.00001409203,0.0003385405,0.9960147,0.00003883773,0.003030219],"study_design_scores_gemma":[0.0008385466,0.00008770899,0.0004507655,0.00001744539,0.00007274723,0.000009136173,0.00004486043,0.0003479687,0.009458453,0.9796912,0.008807749,0.0001734364],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5078229,0.001162286,0.4861709,0.0009403093,0.0000638186,0.001716113,0.0003933194,0.0001321516,0.001598159],"genre_scores_gemma":[0.857942,0.0002965741,0.140603,0.0001148601,0.000275018,0.0004815141,0.00006016345,0.0000358754,0.0001910039],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3501191,"threshold_uncertainty_score":0.5465961,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0380040935599548,"score_gpt":0.3311265068808308,"score_spread":0.293122413320876,"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."}}