{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006988978,0.0007363605,0.000490889,0.001083055,0.000502998,0.001567896,0.0004567768,0.0005946417,0.005563951],"category_scores_gemma":[0.003525487,0.0002622418,0.0004655531,0.001122125,0.001173744,0.001781278,0.0007702245,0.001735873,0.00249511],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004677653,"about_ca_system_score_gemma":0.0003623204,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009662989,"about_ca_topic_score_gemma":0.0006928616,"domain_scores_codex":[0.9995277,0.0001501143,0.00002310146,0.00006830449,0.0001707739,0.00006002993],"domain_scores_gemma":[0.9991519,0.0004003569,0.00007541051,0.0001048588,0.0001951988,0.00007218245],"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":[0.00005066481,0.00004137627,0.0003164061,0.0000929942,0.000008331357,0.0003484892,0.0003831364,0.009507678,0.01097468,0.9312522,0.008076337,0.03894771],"study_design_scores_gemma":[0.00001455866,0.0001366469,0.0004471092,0.00006613781,0.00001057439,0.0005866917,0.0001528801,0.182592,0.009024394,0.7737023,0.03320438,0.00006226727],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.03988093,0.003319236,0.8988096,0.001232683,0.0008617835,0.00004517593,0.0003312047,0.0004496555,0.05506982],"genre_scores_gemma":[0.6274712,0.004743782,0.3277514,0.001569363,0.002380683,0.0002380271,0.0007649822,0.0008364657,0.03424411],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.005563951,"threshold_uncertainty_score":0.01861322,"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."}}