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.

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.

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.

General linear group

Meaning

Noun