{"id":"W2886678902","doi":"10.1007/978-0-387-79428-0_4","title":"Matrix Inverses, Matrix Groups and the $${ LPDU}$$ Decomposition","year":2017,"lang":"en","type":"book-chapter","venue":"","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Invertible matrix; Permutation matrix; Mathematics; Matrix (chemical analysis); Combinatorics; Triangular matrix; Group (periodic table); Block matrix; Diagonal matrix; Inverse; Involutory matrix; Pure mathematics; Diagonal; Symmetric matrix; Nonnegative matrix; Physics; 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":[0.0004154849,0.001014202,0.0005853268,0.001305479,0.001110209,0.003567531,0.000657727,0.0008156298,0.01281653],"category_scores_gemma":[0.0009658713,0.0003890562,0.0005560276,0.001363594,0.002910679,0.003467964,0.001106354,0.003981752,0.006007749],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009642118,"about_ca_system_score_gemma":0.0005939648,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008872392,"about_ca_topic_score_gemma":0.0009094207,"domain_scores_codex":[0.9997305,0.00007665468,0.00001230224,0.00005482617,0.0000953772,0.00003033199],"domain_scores_gemma":[0.9998192,0.00005918553,0.00002108428,0.00002843116,0.00004984886,0.00002223695],"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":[0.000003788312,0.000005562684,0.00001031158,0.00002828409,0.000001606304,0.000007659281,0.00006507559,0.000132341,0.0002128842,0.9824867,0.007812789,0.009233128],"study_design_scores_gemma":[0.00000219147,0.000005397917,0.00003300434,0.00001657821,0.00000155728,0.00004221082,0.00003239569,0.0005290048,0.000136382,0.9642917,0.03490479,0.000004769573],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.01547221,0.02652121,0.1836968,0.007340886,0.00579123,0.00004127543,0.0003909652,0.0005031217,0.7602424],"genre_scores_gemma":[0.3064269,0.03188308,0.1300397,0.005122961,0.0114412,0.0002574435,0.001062071,0.001160724,0.512606],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.01281653,"threshold_uncertainty_score":0.04287553,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03582251030799639,"score_gpt":0.34513358795154,"score_spread":0.3093110776435437,"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."}}