{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:9395d494-7be0-4d0f-8429-30b4f311266c",
  "labels": {
    "zh-CN": "初等因子",
    "en": "elementary divisor"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "058219dbf0fa298255c3d2f1ffa9002196e3355cb3e25bc8ee402a857068824c",
  "occurrences": [
    {
      "concept_id": "urn:uuid:9395d494-7be0-4d0f-8429-30b4f311266c",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-04/01-eigenspaces-and-characteristic-equations",
      "anchor": "concept-4-elementary-divisor",
      "chapter": "4",
      "section": "4.1",
      "offset": 19519,
      "range": [
        26304,
        26546
      ],
      "source_revision": "514384cf6693578d8563cf69e52e982af6896549d7df962809d1431d495e387a",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "初等因子(elementary divisor)",
      "context": {
        "range": [
          26155,
          26666
        ],
        "quote": "其中 $\\lambda _ { 1 } , \\lambda _ { 2 } , \\ldots , \\lambda _ { m }$ 取遍 $S$ 的所有互异特征值。各个因子 $\\left( z - \\lambda _ { i } \\right) ^ { k _ { i } }$ 称为 $S$ 的 <u id=\"concept-4-elementary-divisor\" class=\"concept-term\" data-concept-identity=\"urn:uuid:9395d494-7be0-4d0f-8429-30b4f311266c\" data-concept-route=\"/concept-identities#concept-9395d494-7be0-4d0f-8429-30b4f311266c\">初等因子(elementary divisor)</u>。以下定理表明，特征多项式总能被最小零化多项式整除；也就是说，对每个 $i = 1 , 2 , \\ldots , m$，系数 $k _ { i } \\leq p _ { i }$，其中 $p _ { i }$ 是第 $i$ 个特征值的重数。",
        "quote_sha256": "9e926178e383cc670df2dfbbab1470e0c654c2a43406e399d422705470726868",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-04/01-eigenspaces-and-characteristic-equations",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-6d198fca527ed22707dfe3d5"
    }
  ],
  "registered_positions": [
    {
      "route": "zh/chapter-04/01-eigenspaces-and-characteristic-equations",
      "lang": "zh-CN",
      "section": "4.1",
      "signal": "term-mark",
      "label": "初等因子",
      "english": "elementary divisor",
      "offset": 18129
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-6d198fca527ed22707dfe3d5"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 1,
    "located_occurrences": 1,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "fd2774d74938039f6489d5ecf9bff798d0f3cdb114e85cd1d3fbd3dde6e67875",
  "optional_enrichments": []
}
