"special linear group" meaning in English

{
  "forms": [
    {
      "form": "special linear groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "special linear group"
      },
      "expansion": "special linear group (plural special linear groups)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "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": "Group theory",
          "orig": "en:Group theory",
          "parents": [
            "Algebra",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "projective special linear group"
        }
      ],
      "examples": [
        {
          "ref": "1972, Johan G. F. Belinfante, Bernard Kolman, A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods, Society for Industrial and Applied Mathematics, page 6:",
          "text": "The complex special linear group SL(n, C) is the subgroup of GL(n, C) consisting of matrices with determinant one.[…]The special linear groups are sometimes also called unimodular groups.",
          "type": "quote"
        },
        {
          "text": "1998, F. Celler, C. R. Leedham-Green, A constructive recognition algorithm for the special linear group, Robert Curtis, Robert Wilson (editors), The Atlas of Finite Groups: Ten Years On, Cambridge University Press, 2003 Digitally Printed Edition, page 11,\nIn the first part of this note we present an algorithm to recognise constructively the special linear group."
        },
        {
          "ref": "2014, Holger Ingmar Meinhardt, The Pre-Kernel as a Tractable Solution for Cooperative Games: An Exercise in Algorithmic Game Theory, Springer, page 100:",
          "text": "Hence, all congruent bases induced from a game context belong to the special linear group SL(m).",
          "type": "quote"
        }
      ],
      "glosses": [
        "For given field F and order n, the group of n×n matrices with determinant 1, with the group operations of matrix multiplication and matrix inversion."
      ],
      "id": "en-special_linear_group-en-noun-i5YZrNbI",
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "field",
          "field"
        ],
        [
          "group",
          "group"
        ],
        [
          "matrices",
          "matrix"
        ],
        [
          "determinant",
          "determinant"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "multiplication",
          "multiplication"
        ],
        [
          "inversion",
          "inversion"
        ]
      ],
      "raw_glosses": [
        "(group theory) For given field F and order n, the group of n×n matrices with determinant 1, with the group operations of matrix multiplication and matrix inversion."
      ],
      "related": [
        {
          "word": "general linear group"
        },
        {
          "word": "Lie group"
        }
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "special linear group"
      ]
    }
  ],
  "word": "special linear group"
}

{
  "derived": [
    {
      "word": "projective special linear group"
    }
  ],
  "forms": [
    {
      "form": "special linear groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "special linear group"
      },
      "expansion": "special linear group (plural special linear groups)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "general linear group"
    },
    {
      "word": "Lie group"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Group theory"
      ],
      "examples": [
        {
          "ref": "1972, Johan G. F. Belinfante, Bernard Kolman, A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods, Society for Industrial and Applied Mathematics, page 6:",
          "text": "The complex special linear group SL(n, C) is the subgroup of GL(n, C) consisting of matrices with determinant one.[…]The special linear groups are sometimes also called unimodular groups.",
          "type": "quote"
        },
        {
          "text": "1998, F. Celler, C. R. Leedham-Green, A constructive recognition algorithm for the special linear group, Robert Curtis, Robert Wilson (editors), The Atlas of Finite Groups: Ten Years On, Cambridge University Press, 2003 Digitally Printed Edition, page 11,\nIn the first part of this note we present an algorithm to recognise constructively the special linear group."
        },
        {
          "ref": "2014, Holger Ingmar Meinhardt, The Pre-Kernel as a Tractable Solution for Cooperative Games: An Exercise in Algorithmic Game Theory, Springer, page 100:",
          "text": "Hence, all congruent bases induced from a game context belong to the special linear group SL(m).",
          "type": "quote"
        }
      ],
      "glosses": [
        "For given field F and order n, the group of n×n matrices with determinant 1, with the group operations of matrix multiplication and matrix inversion."
      ],
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "field",
          "field"
        ],
        [
          "group",
          "group"
        ],
        [
          "matrices",
          "matrix"
        ],
        [
          "determinant",
          "determinant"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "multiplication",
          "multiplication"
        ],
        [
          "inversion",
          "inversion"
        ]
      ],
      "raw_glosses": [
        "(group theory) For given field F and order n, the group of n×n matrices with determinant 1, with the group operations of matrix multiplication and matrix inversion."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "special linear group"
      ]
    }
  ],
  "word": "special linear group"
}