英和和英

名詞

general linear group (複数形 general linear groups)

1. (group theory) For given field F and order n, the group of invertible n×n matrices, with the group operation of matrix multiplication.
   • 1993, Peter J. Olver, Applications of Lie Groups to Differential Equations, Springer, 2000, Softcover Reprint, page 17,

     Often 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.

   • 2003, Vladislav V. Goldberg (translator), Maks Aizikovich Akivis, Tensor Calculus with Applications, World Scientific, page 119,

     We will again call this group the general linear group and denote it by GL₃.

     In 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.

   • 2009, Roe Goodman, Nolan R. Wallach, Symmetry, Representations, and Invariants, Springer, page 1,

     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.