{"id":"W3168607775","doi":"10.1016/j.laa.2023.01.026","title":"Restricted Riemannian geometry for positive semidefinite matrices","year":2023,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Morphological variations and asymmetry","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Positive-definite matrix; Submanifold; Geodesic; Manifold (fluid mechanics); Rank (graph theory); Riemannian manifold; Exponential map (Riemannian geometry); Cholesky decomposition; Combinatorics; Riemannian geometry; Logarithm; Pure mathematics; Eigenvalues and eigenvectors; Geometry; Sectional curvature; Mathematical analysis; Scalar curvature; Curvature","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":[0.000982518,0.001381594,0.0009991551,0.002340713,0.001243042,0.00263996,0.001251795,0.001307667,0.006462464],"category_scores_gemma":[0.003122303,0.0005343634,0.0008028292,0.001308639,0.003620307,0.004352768,0.001948503,0.002672266,0.001027601],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001474915,"about_ca_system_score_gemma":0.0006302933,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00193495,"about_ca_topic_score_gemma":0.00166285,"domain_scores_codex":[0.9992911,0.0002816892,0.00003373805,0.0001650627,0.0001660381,0.00006236334],"domain_scores_gemma":[0.9981151,0.0006885258,0.0004175251,0.0001546046,0.0003125978,0.0003117888],"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":[0.000009116485,0.000008159986,0.00007297818,0.00001969061,0.000005270524,0.00003978319,0.00009308032,0.0009074741,0.0004904888,0.9958075,0.0007460351,0.001800377],"study_design_scores_gemma":[0.000004848783,0.00001188797,0.0001451549,0.000005237338,0.00000303659,0.00006708979,0.00003316216,0.006886436,0.0001232681,0.990884,0.001825643,0.000010287],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3705552,0.005977033,0.4896229,0.007597043,0.0008740778,0.00007137516,0.0008903667,0.0004399681,0.1239722],"genre_scores_gemma":[0.920024,0.002770076,0.03715204,0.0008638161,0.001364224,0.00009662091,0.0004635743,0.0002101305,0.03705553],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006462464,"threshold_uncertainty_score":0.02161908,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04263587865802931,"score_gpt":0.3186822227165739,"score_spread":0.2760463440585446,"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."}}