{"schema_version":"ocme-site-results-v1","locale":"zh-Hant","page_type":"derivations","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"q":"mko-dual-vector-space"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-dual-vector-space-01","title":{"zh-Hant":"雙基底與covector換基","en":"Dual basis and covector change"},"summary":{"zh-Hant":"對b₁=(1,1)、b₂=(1,−1)，φ₁=(x+y)/2、φ₂=(x−y)/2為雙基底。","en":"For b1=(1,1),b2=(1,-1), phi1=(x+y)/2,phi2=(x-y)/2 form the dual basis."},"mko_ids":["mko-dual-vector-space"]}],"title":"概念推導導讀"}