"Sylvester's criterion" meaning in All languages combined

{
  "etymology_text": "Named after James Joseph Sylvester.",
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      "expansion": "Sylvester's criterion",
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  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
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        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
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        {
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          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
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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",
      "links": [
        [
          "mathematics",
          "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": [
    {
      "args": {},
      "expansion": "Sylvester's criterion",
      "name": "en-proper noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English proper nouns",
        "English terms with non-redundant non-automated sortkeys",
        "English uncountable nouns",
        "en:Mathematics"
      ],
      "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"
      ],
      "wikipedia": [
        "James Joseph Sylvester",
        "Sylvester's criterion"
      ]
    }
  ],
  "word": "Sylvester's criterion"
}