{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:151179b3-1206-4b6c-a3b9-d229f1f77314",
  "labels": {
    "zh-CN": "等距的",
    "en": "isometric"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "1855feea12efddd65591ac05b40b0fbc6aa6700c1b1f627dee084505ed2c7e10",
  "occurrences": [
    {
      "concept_id": "urn:uuid:151179b3-1206-4b6c-a3b9-d229f1f77314",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-13/04-bounded-linear-operators",
      "anchor": "concept-13-isometric",
      "chapter": "13",
      "section": "13.4",
      "offset": 16761,
      "range": [
        22639,
        22863
      ],
      "source_revision": "194ca7b68e093551807e302c52f29521e73d76a77f31f6fd5b10ca6c3ee642c4",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "等距的(isometric)",
      "context": {
        "range": [
          22302,
          22964
        ],
        "quote": "则称为<u id=\"concept-13-unitary\" class=\"concept-term\" data-concept-identity=\"urn:uuid:040e751e-8f47-4e5e-afb7-41c459e5d622\" data-concept-route=\"/concept-identities#concept-040e751e-8f47-4e5e-afb7-41c459e5d622\">酉的(unitary)</u>\n因为这暗示着 $\\left\\langle U^{*} U u \\mid v\\right\\rangle=\\langle u \\mid v\\rangle$, 算符$U$ 是酉的当且仅当 $U^{-1}=U^{*}$. 每个酉算符都是<u id=\"concept-13-isometric\" class=\"concept-term\" data-concept-identity=\"urn:uuid:151179b3-1206-4b6c-a3b9-d229f1f77314\" data-concept-route=\"/concept-identities#concept-151179b3-1206-4b6c-a3b9-d229f1f77314\">等距的(isometric)</u>, $\\|U u\\|=\\|u\\|$，对于所有 $u \\in \\mathcal{H}$-它保证两个向量间的距离 $d(u, v)=\\|u-v\\|$ 不变。反过来，每个等距算符都是酉的, 因为若$U$等距则",
        "quote_sha256": "7706ba67f186ff29e3b039568792e31188dcaafbfd985382859bed7c75576195",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-13/04-bounded-linear-operators",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-1d18f6534f1b08ca159c2852"
    },
    {
      "concept_id": "urn:uuid:151179b3-1206-4b6c-a3b9-d229f1f77314",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "en",
      "route": "en/chapter-13/04-bounded-linear-operators",
      "anchor": "first-4e0f8481f19555a6cfd3-en",
      "chapter": "13",
      "section": "13.4",
      "offset": 22418,
      "range": [
        27787,
        28015
      ],
      "source_revision": "eb0725f6ab7fc44fa4ee614b878f2ec644f55a6b84b31a4afac5555a1c5df299",
      "source_category": "original_transcription",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "isometric",
      "context": {
        "range": [
          27606,
          28236
        ],
        "quote": "Since this implies $\\langle U ^ { * } U u \\mid v \\rangle = \\langle u \\mid v \\rangle$ , an operator $U$ is unitary if and only if $U ^ { - 1 } = U ^ { * }$ Every unitary operator is <u class=\"concept-term\" data-concept-identity=\"urn:uuid:151179b3-1206-4b6c-a3b9-d229f1f77314\" data-concept-route=\"/concept-identities#concept-151179b3-1206-4b6c-a3b9-d229f1f77314\" id=\"first-4e0f8481f19555a6cfd3-en\">isometric</u>, $\\| U u \\| = \\| u \\|$ for all $u \\in \\mathcal { H } -$ it preserves the distance $d ( u , v ) = \\lVert u - v \\rVert$ between any two vectors. Conversely, every isometric operator is unitary, for if $U$ is isometric then",
        "quote_sha256": "bc22aaefeccfa8648ba9329d78daeb3a4e1da6d5041a9ab50ea22bb45f601af9",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "zh/chapter-13/04-bounded-linear-operators",
          "lang": "zh-CN",
          "source_category": "translation",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-2dc67b5a2e2f375f4deae5aa"
    }
  ],
  "registered_positions": [
    {
      "route": "en/chapter-13/04-bounded-linear-operators",
      "lang": "en",
      "section": "13.4",
      "signal": "term-mark",
      "label": "isometric",
      "english": "isometric",
      "offset": 20068
    },
    {
      "route": "zh/chapter-13/04-bounded-linear-operators",
      "lang": "zh-CN",
      "section": "13.4",
      "signal": "term-mark",
      "label": "等距的",
      "english": "isometric",
      "offset": 14917
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-1d18f6534f1b08ca159c2852",
    "occ-2dc67b5a2e2f375f4deae5aa"
  ],
  "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": "7f722ab8da4fc1176052fd5f5523b3c143f99e9a732dcd265f3b89d06e825cb4",
  "optional_enrichments": []
}