"proper value" meaning in All languages combined

{
  "forms": [
    {
      "form": "proper values",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "proper value (plural proper values)",
      "name": "en-noun"
    }
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
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          "source": "w"
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          "source": "w"
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          "name": "Pages with entries",
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Linear algebra",
          "orig": "en:Linear algebra",
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            "Algebra",
            "Mathematics",
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          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "1961 [Oxford University Press], Sterling K. Berberian, Introduction to Hilbert Space, American Mathematical Society (AMS Chelsea), 1999, Reprint, page 178,\nIn this terminology, Theorem 1 asserts that every non-zero proper value of a CC-operator has finite multiplicity. This result is not always helpful, for there exist CC-operators having no proper values at all:"
        },
        {
          "ref": "1962, A. R. Amir-Moéz, A. L. Fass, Elements of Linear Space, Pergamon Press, page 134:",
          "text": "Thus any proper value of AA* is a proper value of A*A.",
          "type": "quote"
        },
        {
          "ref": "2010, F. Takens, A Vanderbauwhede, Local invariant manifolds and normal forms, H. Broer, F. Takens, B. Hasselblatt (editors), Handbook of Dynamical Systems, Volume 3, Elsevier (North-Holland), page 106, The proper values of this linear mapping are",
          "text": "– the proper values of L;\n– for each proper value α of L|Eᶜ and proper value β of L|Eᵘ, the proper value α/β — from the assumptions it follows that this latter collection of proper values consists of contracting proper values only."
        }
      ],
      "glosses": [
        "An eigenvalue."
      ],
      "id": "en-proper_value-en-noun-r8MdEZcz",
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "eigenvalue",
          "eigenvalue"
        ]
      ],
      "raw_glosses": [
        "(dated, linear algebra) An eigenvalue."
      ],
      "tags": [
        "dated"
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "proper value"
}

{
  "forms": [
    {
      "form": "proper values",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "args": {},
      "expansion": "proper value (plural proper values)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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        "English countable nouns",
        "English dated terms",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
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        "Pages with 1 entry",
        "Pages with entries",
        "en:Linear algebra"
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      "examples": [
        {
          "text": "1961 [Oxford University Press], Sterling K. Berberian, Introduction to Hilbert Space, American Mathematical Society (AMS Chelsea), 1999, Reprint, page 178,\nIn this terminology, Theorem 1 asserts that every non-zero proper value of a CC-operator has finite multiplicity. This result is not always helpful, for there exist CC-operators having no proper values at all:"
        },
        {
          "ref": "1962, A. R. Amir-Moéz, A. L. Fass, Elements of Linear Space, Pergamon Press, page 134:",
          "text": "Thus any proper value of AA* is a proper value of A*A.",
          "type": "quote"
        },
        {
          "ref": "2010, F. Takens, A Vanderbauwhede, Local invariant manifolds and normal forms, H. Broer, F. Takens, B. Hasselblatt (editors), Handbook of Dynamical Systems, Volume 3, Elsevier (North-Holland), page 106, The proper values of this linear mapping are",
          "text": "– the proper values of L;\n– for each proper value α of L|Eᶜ and proper value β of L|Eᵘ, the proper value α/β — from the assumptions it follows that this latter collection of proper values consists of contracting proper values only."
        }
      ],
      "glosses": [
        "An eigenvalue."
      ],
      "links": [
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          "linear algebra",
          "linear algebra"
        ],
        [
          "eigenvalue",
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        ]
      ],
      "raw_glosses": [
        "(dated, linear algebra) An eigenvalue."
      ],
      "tags": [
        "dated"
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      "topics": [
        "linear-algebra",
        "mathematics",
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  "word": "proper value"
}