{"id":"W148978679","doi":"10.1007/978-3-642-10473-2_6","title":"Rank of the Partitioned Matrix and the Matrix Product","year":2011,"lang":"en","type":"book-chapter","venue":"","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"","keywords":"Rank (graph theory); Matrix (chemical analysis); Mathematics; Product (mathematics); Combinatorics; Algebra over a field; Pure mathematics; Chemistry; 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":[0.0006496565,0.001250447,0.0008969012,0.001241544,0.0005415907,0.003139515,0.0007867556,0.0006928959,0.0225677],"category_scores_gemma":[0.00300594,0.0005582644,0.0005071157,0.002226815,0.001986011,0.00333365,0.0009127563,0.002358122,0.01146947],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005856273,"about_ca_system_score_gemma":0.0007778084,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007325833,"about_ca_topic_score_gemma":0.0009570194,"domain_scores_codex":[0.9994022,0.0001225455,0.00003111842,0.0001437886,0.0002627908,0.00003761629],"domain_scores_gemma":[0.9992177,0.0003342865,0.00005120186,0.0001697274,0.0001921316,0.00003484837],"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":[0.00004215729,0.00002384371,0.00009438954,0.000326865,0.00001981237,0.00009518022,0.0001738621,0.003698615,0.002190161,0.7569024,0.07802474,0.1584079],"study_design_scores_gemma":[0.00001051397,0.0000412354,0.0002080961,0.00008643876,0.00001553613,0.0004124416,0.00007646009,0.007779634,0.001653318,0.785831,0.2038509,0.00003438211],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0062233,0.03739742,0.6094288,0.00320014,0.004199097,0.00007737771,0.001129148,0.001330528,0.3370142],"genre_scores_gemma":[0.153219,0.0494387,0.3889963,0.002273898,0.007764944,0.0002632893,0.002327273,0.001960606,0.3937559],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.0225677,"threshold_uncertainty_score":0.07549644,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0143559567890163,"score_gpt":0.2220662342204691,"score_spread":0.2077102774314528,"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."}}