\begin{definition}[Definition:General Linear Group]
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 (of degree $n$)''' and is denoted $\GL {n, K}$, or $\GL n$ if the field is implicit.
The field itself is usually $\R$, $\Q$ or $\C$, but can be ''any'' field.
\end{definition}