general linear group

plural general linear groups

1. group theoryFor 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.

   2 more examples

   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.

   2003, Maks Aizikovich Akivis, translated by Vladislav V. Goldberg, Tensor Calculus with Applications, World Scientific, page 119

   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.

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