{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:040e751e-8f47-4e5e-afb7-41c459e5d622",
  "labels": {
    "zh-CN": "Hilbert空间的酉算符",
    "en": "unitary operator on a Hilbert space"
  },
  "alternative_labels": [
    {
      "lang": "en",
      "value": "unitary"
    },
    {
      "lang": "zh-CN",
      "value": "酉的"
    }
  ],
  "scope_note": "§13.4 considers bounded Hilbert-space operators and the two-sided unitary condition.",
  "identity_status": "active",
  "identity_revision": "8a0aa11e81522df6d6ef8709f2a6c2d75e1ad56db717c66c30656990e28b872a",
  "occurrences": [
    {
      "concept_id": "urn:uuid:040e751e-8f47-4e5e-afb7-41c459e5d622",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-13/04-bounded-linear-operators",
      "anchor": "concept-13-unitary",
      "chapter": "13",
      "section": "13.4",
      "offset": 16427,
      "range": [
        22305,
        22524
      ],
      "source_revision": "194ca7b68e093551807e302c52f29521e73d76a77f31f6fd5b10ca6c3ee642c4",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "酉的(unitary)",
      "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-b542449f02c1c1f5673f33be"
    },
    {
      "concept_id": "urn:uuid:040e751e-8f47-4e5e-afb7-41c459e5d622",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "en",
      "route": "en/chapter-13/04-bounded-linear-operators",
      "anchor": "first-d2b31bf1671157421fee-en",
      "chapter": "13",
      "section": "13.4",
      "offset": 21890,
      "range": [
        27259,
        27485
      ],
      "source_revision": "eb0725f6ab7fc44fa4ee614b878f2ec644f55a6b84b31a4afac5555a1c5df299",
      "source_category": "original_transcription",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "unitary",
      "context": {
        "range": [
          27197,
          27488
        ],
        "quote": "An operator $U : \\mathcal { H } \\to \\mathcal { H }$ is called <u class=\"concept-term\" data-concept-identity=\"urn:uuid:040e751e-8f47-4e5e-afb7-41c459e5d622\" data-concept-route=\"/concept-identities#concept-040e751e-8f47-4e5e-afb7-41c459e5d622\" id=\"first-d2b31bf1671157421fee-en\">unitary</u> if",
        "quote_sha256": "8a40ee92ebb0e4cf5ff40b06d6f4f3fa68ec29939bdb97269de2afce0194bd5e",
        "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-d5788f6df6b0fd63e934448b"
    }
  ],
  "registered_positions": [
    {
      "route": "en/chapter-13/04-bounded-linear-operators",
      "lang": "en",
      "section": "13.4",
      "signal": "term-mark",
      "label": "unitary",
      "english": "unitary",
      "offset": 19731
    },
    {
      "route": "zh/chapter-13/04-bounded-linear-operators",
      "lang": "zh-CN",
      "section": "13.4",
      "signal": "term-mark",
      "label": "酉的",
      "english": "unitary",
      "offset": 14739
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-b542449f02c1c1f5673f33be",
    "occ-d5788f6df6b0fd63e934448b"
  ],
  "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": "777b0a2eda6f7f78fc854063edffc976a849a0881a42a6de25c2b165b583eb18",
  "optional_enrichments": []
}