Definition:General Linear Group

Definition
Let $K$ be a field.

The set of all invertible order-$n$ square matrices over $K$ is a group under (conventional) matrix multiplication.

This group is called the general linear group and is denoted $\operatorname{GL} \left({n, K}\right)$, or $\operatorname{GL} \left({n}\right)$ if the field is implicit.

The field itself is usually $\R$, $\Q$ or $\C$, but can be any field.

Also see

 * General Linear Group is Group