"Sylvester's formula" meaning in English

{
  "etymology_text": "Named after James Joseph Sylvester.",
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      "glosses": [
        "A formula that expresses an analytic function f(A) of a matrix A as a polynomial in A, in terms of the eigenvalues and eigenvectors of A."
      ],
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          "mathematics",
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          "matrix",
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        [
          "polynomial",
          "polynomial"
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        [
          "eigenvalue",
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          "eigenvector",
          "eigenvector"
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      "raw_glosses": [
        "(mathematics) A formula that expresses an analytic function f(A) of a matrix A as a polynomial in A, in terms of the eigenvalues and eigenvectors of A."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
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          "name": "Geometry",
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      ],
      "glosses": [
        "A particular interpretation of the sum of three pairwise distinct vectors of equal length in the context of triangle geometry."
      ],
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      "raw_glosses": [
        "(geometry) A particular interpretation of the sum of three pairwise distinct vectors of equal length in the context of triangle geometry."
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "wikipedia": [
    "James Joseph Sylvester"
  ],
  "word": "Sylvester's formula"
}

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  "etymology_text": "Named after James Joseph Sylvester.",
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      ],
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          "mathematics",
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        "(mathematics) A formula that expresses an analytic function f(A) of a matrix A as a polynomial in A, in terms of the eigenvalues and eigenvectors of A."
      ],
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        "mathematics",
        "sciences"
      ]
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        "en:Geometry"
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      "glosses": [
        "A particular interpretation of the sum of three pairwise distinct vectors of equal length in the context of triangle geometry."
      ],
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        "(geometry) A particular interpretation of the sum of three pairwise distinct vectors of equal length in the context of triangle geometry."
      ],
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        "geometry",
        "mathematics",
        "sciences"
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    }
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}