general linear group

Noun

general linear group (plural general linear groups)

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