{"id":"W1893802408","doi":"","title":"A note on LU decomposition of the Discrete Fourier Transform matrix","year":2015,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"","keywords":"Mathematics; Toeplitz matrix; Vandermonde matrix; Matrix (chemical analysis); Inverse; Matrix decomposition; Triangular matrix; Transpose; Combinatorics; Decomposition; Discrete Fourier transform (general); DFT matrix; LU decomposition; Pure mathematics; Fourier transform; Symmetric matrix; Mathematical analysis; Square matrix; Physics; Fourier analysis; Eigenvalues and eigenvectors; Fractional Fourier transform; Geometry; Invertible matrix; Quantum mechanics","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":[0.0003948958,0.0002441286,0.0002728665,0.0002129642,0.000129336,0.00005483217,0.002003583,0.0002069683,0.00001712063],"category_scores_gemma":[0.00001225699,0.0001995385,0.0003155271,0.0005992714,0.0001189385,0.0002361182,0.0008343582,0.0004791099,0.00003186019],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000108933,"about_ca_system_score_gemma":0.0001564428,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004446795,"about_ca_topic_score_gemma":0.00001202142,"domain_scores_codex":[0.9986351,0.0001931609,0.00019202,0.0005913097,0.0001523877,0.0002359803],"domain_scores_gemma":[0.9982009,0.00008725738,0.0002363486,0.001239715,0.0001175362,0.0001182627],"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":[0.0001945607,0.0001727757,0.0001353114,0.0001682899,0.0001122436,0.0001122975,0.000940602,0.1978474,0.00009874246,0.795476,0.0006484499,0.004093406],"study_design_scores_gemma":[0.0006474632,0.0001130785,0.0001605226,0.0002003186,0.0000870041,0.000007014485,0.00004398826,0.6055837,0.001945082,0.389941,0.0008885537,0.0003822798],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1133069,0.00003132191,0.8748381,0.0004897031,0.0009422273,0.0004398624,0.00005562681,0.0001162853,0.009779996],"genre_scores_gemma":[0.9960524,0.00004384376,0.00232153,0.00005753106,0.00006940672,7.24105e-7,0.00000627146,0.00001172513,0.001436501],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8827456,"threshold_uncertainty_score":0.8136945,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03514681147008313,"score_gpt":0.2185232277862718,"score_spread":0.1833764163161887,"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."}}