{"id":"W1994239841","doi":"10.1016/j.laa.2005.11.016","title":"On the nullspace, the rangespace and the characteristic polynomial of Euclidean distance matrices","year":2006,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Digital Image Processing Techniques","field":"Computer Science","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Windsor","funders":"","keywords":"Mathematics; Characterization (materials science); Euclidean distance; Polynomial; Matrix (chemical analysis); Euclidean distance matrix; Combinatorics; Realization (probability); Euclidean geometry; Subspace topology; Characteristic polynomial; Algebra over a field; Pure mathematics; Euclidean space; Mathematical analysis; Geometry","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":[0.001564735,0.001001627,0.0009517572,0.002230409,0.0009884264,0.003366211,0.001375558,0.001258148,0.003838241],"category_scores_gemma":[0.01034775,0.000457585,0.0006422605,0.002517253,0.005852007,0.01017881,0.002696244,0.003890269,0.0008148561],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001073639,"about_ca_system_score_gemma":0.0009728256,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001491841,"about_ca_topic_score_gemma":0.0008884417,"domain_scores_codex":[0.9988595,0.0003946461,0.00005191184,0.0002474503,0.0002996791,0.0001467285],"domain_scores_gemma":[0.9946412,0.003364636,0.0007046408,0.000355964,0.0005221436,0.000411306],"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":[0.00005308696,0.00002038151,0.000207987,0.00004846409,0.000006510211,0.00004184313,0.0001823134,0.0043703,0.0005577328,0.9831024,0.00115685,0.01025213],"study_design_scores_gemma":[0.000007081896,0.00001857332,0.0001498749,0.00001293106,0.000002998223,0.00006206905,0.0000493763,0.01207971,0.0001251335,0.986352,0.0011259,0.00001434619],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2435327,0.007094574,0.6943358,0.005762155,0.0004897792,0.00004972866,0.000647266,0.0001658957,0.04792211],"genre_scores_gemma":[0.9155344,0.007940884,0.05294463,0.0007992079,0.001783498,0.0001118097,0.0006605723,0.0001647885,0.02006016],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003838241,"threshold_uncertainty_score":0.01284021,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005901363129197902,"score_gpt":0.2212384894735892,"score_spread":0.2153371263443913,"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."}}