{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:1212910c-fd6e-468e-8315-db95c69ef22e", "labels": { "zh-CN": "对偶空间", "en": "dual space" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "61e73f6de076f6d6f67cf46cb72e7e3c6f61c8106d122e3c298b21003f957b27", "occurrences": [ { "concept_id": "urn:uuid:1212910c-fd6e-468e-8315-db95c69ef22e", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-03/07-dual-spaces", "anchor": "concept-3-dual-space", "chapter": "3", "section": "3.7", "offset": 4663, "range": [ 12002, 12228 ], "source_revision": "938dfcbbffde5cbdbd7e55327dc24b68109b332b4f17d94eeedfe4be90a42e74", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "对偶空间(dual space)", "context": { "range": [ 11941, 12578 ], "quote": "相对于这些运算，$V$ 上的线性泛函集合构成 $\\mathbb{K}$ 上的一个向量空间，称为 $V _ { ; }$ 的对偶空间(dual space)，通常记作 $V ^ { * }$。按照先前的约定，该空间的其他可能记号有 $L ( V , \\mathbb { K } )$ 或 $\\operatorname{Hom}(V,K)$。$V$ 上的线性泛函常被称为余向量(covector)，在后续章节中我们还有理由将其称为 1-形式。", "quote_sha256": "9c0c5a1ad7a3d64f52dfd5f8f28731b709687a5f48cd2f30f29a5c49d21b95fa", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-03/07-dual-spaces", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-36331021bc6aa96cfba943ae" }, { "concept_id": "urn:uuid:1212910c-fd6e-468e-8315-db95c69ef22e", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-04/index", "anchor": "first-e7062a6978544669061d-zh", "chapter": "4", "section": "4", "offset": 420, "range": [ 5889, 6184 ], "source_revision": "817da894ad55f033a62579af99ad92654dc5d97f7febfd4ec212c025ede48f81", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "对偶空间(dual space)", "context": { "range": [ 5824, 6650 ], "quote": "后续章节将假定读者具备扎实的线性代数基础，我们也会用到该学科中的若干具体结论。其中有些内容在常见的线性代数课程中并不受重视，例如[对偶空间(dual space)](../../../../../concepts/linear-algebra/dual-space)所起的作用，以及把不同类别的可逆矩阵作为群来研究。目前讨论的[向量空间(vector space)](../../../../../concepts/linear-algebra/vector-space)都是有限维的。后文还会涉及无限维状态空间及其引出的各种问题。", "quote_sha256": "ab7b0476aababc4785f465fec9fd339f6023bcd0316f3bfdc307cc2fcb73c842", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-04/index", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; 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