{"id":"W2045010435","doi":"10.1007/bf01217534","title":"Repeated eigenvectors and the numerical range of self-adjoint quadratic operator polynomials","year":2002,"lang":"en","type":"article","venue":"Integral Equations and Operator Theory","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Mathematics; Eigenvalues and eigenvectors; Hilbert space; Operator (biology); Self-adjoint operator; Polynomial; Numerical range; Quadratic equation; Pure mathematics; Quadratic function; 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":[0.002183923,0.0004975003,0.0004721117,0.001258615,0.0006224064,0.002148733,0.001119131,0.0009527993,0.003770207],"category_scores_gemma":[0.01669766,0.0004006751,0.000276837,0.0006087993,0.002427278,0.003266215,0.002064273,0.001762968,0.0005761904],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004722463,"about_ca_system_score_gemma":0.0004082692,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003152713,"about_ca_topic_score_gemma":0.0003351136,"domain_scores_codex":[0.998828,0.0005368785,0.00004151751,0.0001142059,0.0003842682,0.00009517938],"domain_scores_gemma":[0.9952317,0.003157097,0.0003320182,0.0004254406,0.0005364339,0.0003172645],"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":[0.0001444276,0.00008580163,0.0006760306,0.0000891137,0.00001741396,0.0001776759,0.0003848349,0.03534986,0.0104983,0.9283078,0.001055914,0.02321285],"study_design_scores_gemma":[0.00002926396,0.00003759979,0.0003163662,0.00003992717,0.000006562115,0.0001785309,0.00008004194,0.309289,0.005029737,0.6832915,0.001666148,0.00003533697],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3631342,0.001851217,0.586584,0.001879439,0.0002681665,0.00004433671,0.00006428629,0.00116401,0.0450103],"genre_scores_gemma":[0.954468,0.0003117714,0.03979893,0.0001546435,0.0001067547,0.00003496397,0.00004057525,0.0002311636,0.004853268],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003770207,"threshold_uncertainty_score":0.01261258,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01244586385731611,"score_gpt":0.2201443527513429,"score_spread":0.2076984888940268,"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."}}