{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:b66bf048-7f86-4318-8350-fbb64491a8b4",
  "labels": {
    "zh-CN": "基变换",
    "en": "change of basis"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "ab211a2c165e30f6e352d008b7fe86df85f08b101e6503c7a66c4cf6e157c3ab",
  "occurrences": [
    {
      "concept_id": "urn:uuid:b66bf048-7f86-4318-8350-fbb64491a8b4",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-04/03-change-of-basis",
      "anchor": "first-fdef6b203b0a71d6f29d-zh",
      "chapter": "4",
      "section": "4.3",
      "offset": 1056,
      "range": [
        7295,
        7609
      ],
      "source_revision": "bec696b6f936752cf0758c469855e6cc4fc2c00529b2390e1c917724951f8b42",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "基变换(change of basis)",
      "context": {
        "range": [
          6894,
          7619
        ],
        "quote": "[<u class=\"concept-term\" data-concept-reference=\"concepts/linear-algebra/linear-map\" data-concept-identity=\"urn:uuid:9d1874b8-6c8c-465e-849a-f2ddc348d3d0\" data-concept-route=\"/concept-identities#concept-9d1874b8-6c8c-465e-849a-f2ddc348d3d0\">线性变换(linear transformation)</u>](../../../../../concepts/linear-algebra/linear-map) $L$ 的矩阵在这项[<span id=\"concept-4-change-of-basis\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-id=\"concept-4-change-of-basis\" data-concept-role=\"definition\" data-concept-identity=\"urn:uuid:b66bf048-7f86-4318-8350-fbb64491a8b4\" data-concept-route=\"/concept-identities#concept-b66bf048-7f86-4318-8350-fbb64491a8b4\" id=\"first-fdef6b203b0a71d6f29d-zh\">基变换(change of basis)</u>]下按以下规则变换：",
        "quote_sha256": "db62b9c6afadcbc596510dacb7df2f8304d60ca012a06b1ecf51e84035a656f9",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-04/03-change-of-basis",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-507990f1428ca06c31529c56"
    },
    {
      "concept_id": "urn:uuid:b66bf048-7f86-4318-8350-fbb64491a8b4",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-04/06-orthogonal-and-unitary-transformations",
      "anchor": "source-block-148",
      "chapter": "4",
      "section": "4.6",
      "offset": 925,
      "range": [
        9799,
        10054
      ],
      "source_revision": "275772d36042626ed5283276e9f16090689e690c0c3bf42b24860f610c397103",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "基变换(change of basis)",
      "context": {
        "range": [
          9439,
          10102
        ],
        "quote": "对所有 $v,w\\in V$ 都成立。此类变换把[<u class=\"concept-term\" data-concept-reference=\"concepts/linear-algebra/basis\" data-concept-identity=\"urn:uuid:dabe32db-8d84-4c17-9eeb-583f0609a265\" data-concept-route=\"/concept-identities#concept-dabe32db-8d84-4c17-9eeb-583f0609a265\">正交标准基(orthonormal basis)</u>](../../../../../concepts/linear-algebra/basis)映为正交标准基，因此也可用作两组正交标准基之间的[<u class=\"concept-term\" data-concept-reference=\"concept-4-change-of-basis\" data-concept-identity=\"urn:uuid:b66bf048-7f86-4318-8350-fbb64491a8b4\" data-concept-route=\"/concept-identities#concept-b66bf048-7f86-4318-8350-fbb64491a8b4\">基变换(change of basis)</u>](03-change-of-basis#concept-4-change-of-basis)。",
        "quote_sha256": "716928bd9140026c08f2ccff7312d61909e538125dbd379d40e3bb8a51182ec7",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-04/06-orthogonal-and-unitary-transformations",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-f49eed6253acc5f2ac1d6f23"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-04/03-change-of-basis",
      "lang": "zh-CN",
      "section": "4.3",
      "signal": "term-mark",
      "label": "基变换",
      "english": "change of basis",
      "offset": 835
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-04/06-orthogonal-and-unitary-transformations",
      "lang": "zh-CN",
      "section": "4.6",
      "signal": "term-mark",
      "label": "基变换",
      "english": "change of basis",
      "offset": 769
    }
  ],
  "statements": [],
  "resolved_references": [
    {
      "raw": "[<u class=\"concept-term\" data-concept-reference=\"concept-4-change-of-basis\" data-concept-identity=\"urn:uuid:b66bf048-7f86-4318-8350-fbb64491a8b4\" data-concept-route=\"/concept-identities#concept-b66bf048-7f86-4318-8350-fbb64491a8b4\">基变换(change of basis)</u>](03-change-of-basis#concept-4-change-of-basis)",
      "href": "03-change-of-basis#concept-4-change-of-basis",
      "range": [
        9798,
        10101
      ],
      "relation": "references",
      "target_route": "books/woit-qtgr/2025-10-20/zh/chapter-04/03-change-of-basis",
      "target_anchor": "concept-4-change-of-basis",
      "resolved": true,
      "reason": null,
      "source_revision": "275772d36042626ed5283276e9f16090689e690c0c3bf42b24860f610c397103",
      "source_route": "books/woit-qtgr/2025-10-20/zh/chapter-04/06-orthogonal-and-unitary-transformations",
      "occurrence_id": "occ-f49eed6253acc5f2ac1d6f23"
    }
  ],
  "reading_order": [
    "occ-507990f1428ca06c31529c56",
    "occ-f49eed6253acc5f2ac1d6f23"
  ],
  "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": "7f7163b313da99a91297312a6a63c4283824608d9c020f687b81f32f4fcae102",
  "optional_enrichments": []
}