general linear group

Noun

 * 1)  For given field F and order n, the group of invertible n×n matrices, with the group operation of matrix multiplication.
 * 2) * 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.

Usage notes
The general linear group can be denoted GL(n, F) or GLn(F) — or, if the field is understood, GL(n) or GLn.

In the cases that F is the field of the real or of the complex numbers, GL(n, F) is a Lie group.