Matrix/K/General linear group/Definition

For a field ${\displaystyle {}K}$ and ${\displaystyle {}n\in \mathbb {N} _{+}}$, the set of all invertible ${\displaystyle {}n\times n}$-matrices with entries in ${\displaystyle {}K}$ is called the general linear group over ${\displaystyle {}K}$. It is denoted by ${\displaystyle {}\operatorname {GL} _{n}\!{\left(K\right)}}$.