"characteristic root" meaning in English

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        "3": "racine caractéristique"
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      "expansion": "Calque of French racine caractéristique",
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  "etymology_text": "Calque of French racine caractéristique, the term preferred by French mathematician Augustin-Louis Cauchy (1789–1857).",
  "forms": [
    {
      "form": "characteristic roots",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "args": {},
      "expansion": "characteristic root (plural characteristic roots)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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          "langcode": "en",
          "name": "Linear algebra",
          "orig": "en:Linear algebra",
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      "examples": [
        {
          "text": "1962 [Prentice Hall], Leonard E. Fuller, Basic Matrix Theory, 2017, Dover, page 217,\nThere is an important relationship between the characteristic roots of a symmetric matrix and the r and p of the associated quadratic form. It is true that the number of positive characteristic roots is p, whereas the number of nonzero characteristic roots is r."
        },
        {
          "ref": "1985, Takeshi Amemiya, Advanced Econometrics, Harvard University Press, page 459",
          "text": "The determinant of a matrix is the product of its characteristic roots.",
          "type": "quotation"
        },
        {
          "text": "2009, Babu Ram, Engineering Mathematics, Pearson Education India, page 13.56,\nTheorem 13.54. The characteristic roots of a Hermitian matrix are real."
        }
      ],
      "glosses": [
        "An eigenvalue."
      ],
      "id": "en-characteristic_root-en-noun-r8MdEZcz",
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        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "eigenvalue",
          "eigenvalue"
        ]
      ],
      "raw_glosses": [
        "(linear algebra) An eigenvalue."
      ],
      "related": [
        {
          "word": "characteristic polynomial"
        },
        {
          "word": "characteristic vector"
        }
      ],
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        "linear-algebra",
        "mathematics",
        "sciences"
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        "Augustin-Louis Cauchy"
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  "word": "characteristic root"
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      "name": "calque"
    }
  ],
  "etymology_text": "Calque of French racine caractéristique, the term preferred by French mathematician Augustin-Louis Cauchy (1789–1857).",
  "forms": [
    {
      "form": "characteristic roots",
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        "plural"
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  "head_templates": [
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      "expansion": "characteristic root (plural characteristic roots)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "characteristic polynomial"
    },
    {
      "word": "characteristic vector"
    }
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      "examples": [
        {
          "text": "1962 [Prentice Hall], Leonard E. Fuller, Basic Matrix Theory, 2017, Dover, page 217,\nThere is an important relationship between the characteristic roots of a symmetric matrix and the r and p of the associated quadratic form. It is true that the number of positive characteristic roots is p, whereas the number of nonzero characteristic roots is r."
        },
        {
          "ref": "1985, Takeshi Amemiya, Advanced Econometrics, Harvard University Press, page 459",
          "text": "The determinant of a matrix is the product of its characteristic roots.",
          "type": "quotation"
        },
        {
          "text": "2009, Babu Ram, Engineering Mathematics, Pearson Education India, page 13.56,\nTheorem 13.54. The characteristic roots of a Hermitian matrix are real."
        }
      ],
      "glosses": [
        "An eigenvalue."
      ],
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        "(linear algebra) An eigenvalue."
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  "word": "characteristic root"
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