{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:6d1cf432-5559-4e89-afa8-dad94bcb4ee2",
  "labels": {
    "zh-CN": "霍奇星算子",
    "en": "Hodge star operator"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "525e40fafecbc0c917ef2af32c7d4c2c8c6c2b71d48b85d5b542501d975a5783",
  "occurrences": [
    {
      "concept_id": "urn:uuid:6d1cf432-5559-4e89-afa8-dad94bcb4ee2",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-08/06-the-hodge-dual",
      "anchor": "first-21844d5d5be719368756-zh",
      "chapter": "8",
      "section": "8.6",
      "offset": 9268,
      "range": [
        15822,
        16067
      ],
      "source_revision": "3da4c782d2fe3d2cf6470b674253aa5a51c89adb3337c1279c4d0645e548df52",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "霍奇星算子(Hodge star operator)",
      "context": {
        "range": [
          15757,
          16132
        ],
        "quote": "一对一的映射$* : \\Lambda ^ { p } ( V ) \\to \\Lambda ^ { n - p } ( V )$称为<u class=\"concept-term\" data-concept-identity=\"urn:uuid:6d1cf432-5559-4e89-afa8-dad94bcb4ee2\" data-concept-route=\"/concept-identities#concept-6d1cf432-5559-4e89-afa8-dad94bcb4ee2\" id=\"first-21844d5d5be719368756-zh\">霍奇星算子(Hodge star operator)</u>；它将一个$( n - p )$-向量对应于每个$p$-向量，反之亦然。这种互反性之所以可能，仅仅是因为这两个向量空间的维数相同，",
        "quote_sha256": "e488d93ed42f2f18080b6dd3d0ac6c18fc8f154bf95c2aeb79d4bef2022f362b",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-08/06-the-hodge-dual",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-bb3c89824608016c0bfc5976"
    },
    {
      "concept_id": "urn:uuid:6d1cf432-5559-4e89-afa8-dad94bcb4ee2",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "en",
      "route": "en/chapter-08/06-the-hodge-dual",
      "anchor": "first-21844d5d5be719368756-en",
      "chapter": "8",
      "section": "8.6",
      "offset": 10692,
      "range": [
        16776,
        17014
      ],
      "source_revision": "cbe2eea55c48d493db23d7dc6921f75a2eaa8e650d9e0b5d685018b9d9c43751",
      "source_category": "original_transcription",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "Hodge star operator",
      "context": {
        "range": [
          16685,
          17184
        ],
        "quote": "The one-to-one map $* : \\Lambda ^ { p } ( V ) \\to \\Lambda ^ { n - p } ( V )$ is called the <u class=\"concept-term\" data-concept-identity=\"urn:uuid:6d1cf432-5559-4e89-afa8-dad94bcb4ee2\" data-concept-route=\"/concept-identities#concept-6d1cf432-5559-4e89-afa8-dad94bcb4ee2\" id=\"first-21844d5d5be719368756-en\">Hodge star operator</u>; it assigns an $( n - p )$ -vector to each $p$-vector, and vice versa. This reciprocity is only possible because the dimensions of these two vector spaces are identical,",
        "quote_sha256": "09ffc18784b4ef7d3f4149b5fb867fbafe4c6df5f3d474d3bc0ef7d1e7893400",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "zh/chapter-08/06-the-hodge-dual",
          "lang": "zh-CN",
          "source_category": "translation",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-3507092a3ce6edd2a1fb8648"
    }
  ],
  "registered_positions": [
    {
      "route": "en/chapter-08/06-the-hodge-dual",
      "lang": "en",
      "section": "8.6",
      "signal": "term-mark",
      "label": "Hodge star operator",
      "english": "Hodge star operator",
      "offset": 10479
    },
    {
      "route": "zh/chapter-08/06-the-hodge-dual",
      "lang": "zh-CN",
      "section": "8.6",
      "signal": "term-mark",
      "label": "霍奇星算子",
      "english": "Hodge star operator",
      "offset": 9055
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-bb3c89824608016c0bfc5976",
    "occ-3507092a3ce6edd2a1fb8648"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 2,
    "located_occurrences": 2,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "d057ca7556225e26b27f5f18e0d86a54ed50a8887b41f9be0f9bac85da173d8e",
  "optional_enrichments": []
}