"Sylvester's criterion" meaning in English

{
  "etymology_text": "Named after James Joseph Sylvester.",
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  "lang_code": "en",
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      "glosses": [
        "A necessary and sufficient criterion to determine whether a Hermitian matrix is positive-definite: specifically, when all of the leading principal minors have a positive determinant."
      ],
      "id": "en-Sylvester's_criterion-en-name-MRe8FRgE",
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        [
          "mathematics",
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        [
          "Hermitian matrix",
          "Hermitian matrix"
        ],
        [
          "determinant",
          "determinant"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A necessary and sufficient criterion to determine whether a Hermitian matrix is positive-definite: specifically, when all of the leading principal minors have a positive determinant."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "James Joseph Sylvester",
        "Sylvester's criterion"
      ]
    }
  ],
  "word": "Sylvester's criterion"
}

{
  "etymology_text": "Named after James Joseph Sylvester.",
  "head_templates": [
    {
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      "expansion": "Sylvester's criterion",
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  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
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        "English entries with incorrect language header",
        "English eponyms",
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        "en:Mathematics"
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      "glosses": [
        "A necessary and sufficient criterion to determine whether a Hermitian matrix is positive-definite: specifically, when all of the leading principal minors have a positive determinant."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "Hermitian matrix",
          "Hermitian matrix"
        ],
        [
          "determinant",
          "determinant"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A necessary and sufficient criterion to determine whether a Hermitian matrix is positive-definite: specifically, when all of the leading principal minors have a positive determinant."
      ],
      "topics": [
        "mathematics",
        "sciences"
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        "James Joseph Sylvester",
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      ]
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  "word": "Sylvester's criterion"
}