"general linear group" meaning in English

{
  "forms": [
    {
      "form": "general linear groups",
      "tags": [
        "plural"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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          "kind": "topical",
          "langcode": "en",
          "name": "Group theory",
          "orig": "en:Group theory",
          "parents": [
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      ],
      "derived": [
        {
          "word": "projective general linear group"
        }
      ],
      "examples": [
        {
          "text": "1993, Peter J. Olver, Applications of Lie Groups to Differential Equations, Springer, 2000, Softcover Reprint, page 17,\nOften Lie groups arise as subgroups of certain larger Lie groups; for example, the orthogonal groups are subgroups of the general linear groups of all invertible matrices."
        },
        {
          "ref": "2003, Maks Aizikovich Akivis, translated by Vladislav V. Goldberg, Tensor Calculus with Applications, World Scientific, page 119",
          "text": "We will again call this group the general linear group and denote it by GL₃.\nIn just the same way, the set of all nonsingular linear transformations of the plane L₂ is a group denoted by GL₂ and called the general linear group of order two.",
          "type": "quotation"
        },
        {
          "ref": "2009, Roe Goodman, Nolan R. Wallach, Symmetry, Representations, and Invariants, Springer, page 1",
          "text": "We show how to put a Lie group structure on a closed subgroup of the general linear group and determine the Lie algebras of the classical groups.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "For given field F and order n, the group of invertible n×n matrices, with the group operation of matrix multiplication."
      ],
      "id": "en-general_linear_group-en-noun-8DXrYgj-",
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        [
          "invertible",
          "invertible matrix"
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      "raw_glosses": [
        "(group theory) For given field F and order n, the group of invertible n×n matrices, with the group operation of matrix multiplication."
      ],
      "related": [
        {
          "word": "linear group"
        },
        {
          "word": "Lie group"
        },
        {
          "word": "matrix group"
        },
        {
          "word": "special linear group"
        }
      ],
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        "group-theory",
        "mathematics",
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      ],
      "wikipedia": [
        "general linear group"
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    }
  ],
  "word": "general linear group"
}

{
  "derived": [
    {
      "word": "projective general linear group"
    }
  ],
  "forms": [
    {
      "form": "general linear groups",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "linear group"
    },
    {
      "word": "Lie group"
    },
    {
      "word": "matrix group"
    },
    {
      "word": "special linear group"
    }
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      "examples": [
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          "text": "1993, Peter J. Olver, Applications of Lie Groups to Differential Equations, Springer, 2000, Softcover Reprint, page 17,\nOften Lie groups arise as subgroups of certain larger Lie groups; for example, the orthogonal groups are subgroups of the general linear groups of all invertible matrices."
        },
        {
          "ref": "2003, Maks Aizikovich Akivis, translated by Vladislav V. Goldberg, Tensor Calculus with Applications, World Scientific, page 119",
          "text": "We will again call this group the general linear group and denote it by GL₃.\nIn just the same way, the set of all nonsingular linear transformations of the plane L₂ is a group denoted by GL₂ and called the general linear group of order two.",
          "type": "quotation"
        },
        {
          "ref": "2009, Roe Goodman, Nolan R. Wallach, Symmetry, Representations, and Invariants, Springer, page 1",
          "text": "We show how to put a Lie group structure on a closed subgroup of the general linear group and determine the Lie algebras of the classical groups.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "For given field F and order n, the group of invertible n×n matrices, with the group operation of matrix multiplication."
      ],
      "links": [
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          "invertible",
          "invertible matrix"
        ],
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        ],
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        "(group theory) For given field F and order n, the group of invertible n×n matrices, with the group operation of matrix multiplication."
      ],
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      ],
      "wikipedia": [
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  "word": "general linear group"
}