"Sylvester's criterion" meaning in All languages combined

See Sylvester's criterion on Wiktionary

Proper name [English]

Etymology: Named after James Joseph Sylvester. Head templates: {{en-proper noun}} Sylvester's criterion
  1. (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. Wikipedia link: James Joseph Sylvester, Sylvester's criterion Categories (topical): Mathematics
    Sense id: en-Sylvester's_criterion-en-name-MRe8FRgE Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Topics: mathematics, sciences
{
  "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": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "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"
        ],
        [
          "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 eponyms",
        "English lemmas",
        "English multiword terms",
        "English proper nouns",
        "English uncountable nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "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"
}

Download raw JSONL data for Sylvester's criterion meaning in All languages combined (1.1kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-03-06 from the enwiktionary dump dated 2025-03-02 using wiktextract (b81b832 and 633533e). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.