General linear group:GL(2,R)

Definition
The general linear group $$GL(2,\R)$$ is defined as the group of invertible $$2 \times 2$$ matrices with entries from the field of real numbers, and with the group operation being matrix multiplication.

It is a particular case of member of family::general linear group of degree two, member of family::general linear group over reals, and, more generally, of a member of family::general linear group.

Structures
The group can be thought of in any of the following ways:


 * It is a real Lie group.
 * It is a linear algebraic group over the field of real numbers (note that this is not an algebraically closed field).
 * It is a topological group.

Topological/Lie group properties
The topology here is the subspace topology from the Euclidean topology on the set of all matrices, which is identified with the Euclidean space $$\R^4$$.