{"id":"W2060293964","doi":"10.1016/j.jfa.2014.05.003","title":"Sums of orthogonal projections","year":2014,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":20,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Council","keywords":"Mathematics; Injective function; TRACE (psycholinguistics); Operator (biology); Hilbert space; Nuclear operator; Trace class; Uniqueness; Discrete mathematics; Closure (psychology); Norm (philosophy); Pure mathematics; Combinatorics; Integer (computer science); Banach space; Finite-rank operator; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001822452,0.001538994,0.001210557,0.002939467,0.001333836,0.004055322,0.001241776,0.001332382,0.01737234],"category_scores_gemma":[0.007961366,0.0009250618,0.001558818,0.001887223,0.002511097,0.004569544,0.004496797,0.002887049,0.00349958],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004815811,"about_ca_system_score_gemma":0.0008708614,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002984102,"about_ca_topic_score_gemma":0.000379754,"domain_scores_codex":[0.9975979,0.0007437271,0.0001681544,0.0004838929,0.0008289141,0.0001774412],"domain_scores_gemma":[0.9965791,0.001208813,0.0002568974,0.000553915,0.0009893617,0.000411901],"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":[0.00005090109,0.0000415695,0.0001902785,0.00007596843,0.0000503108,0.0000476739,0.0001047462,0.001930649,0.002947704,0.9575801,0.003319926,0.0336601],"study_design_scores_gemma":[0.0000106418,0.00003018817,0.0003695937,0.00003278552,0.00002789564,0.0003341348,0.00007571044,0.02992218,0.002059661,0.9581,0.008998953,0.0000382338],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04281065,0.001471422,0.8808674,0.0009326816,0.001360249,0.00008800821,0.000435832,0.0004772059,0.07155663],"genre_scores_gemma":[0.4749348,0.004279093,0.3709546,0.001192509,0.00235171,0.0004622597,0.001758049,0.001618719,0.1424482],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01737234,"threshold_uncertainty_score":0.05811626,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0107404054283522,"score_gpt":0.2223995426532241,"score_spread":0.2116591372248719,"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."}}