"general linear group" meaning in All languages combined

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  "lang_code": "en",
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      "derived": [
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          "word": "projective general linear group"
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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.",
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        },
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          "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.",
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      "glosses": [
        "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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        "(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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  "word": "general linear group"
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        },
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          "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.",
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        "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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