General linear group

$GL(n)$, $GL(n,\mathbb{R})$, $GL(n,\mathbb{C})$
The general linear group consists of invertible matrices of rank $n$. It corresponds with the linear isomorphism of ${\mathbb{R}}^n$ into itself. Its Lie algebra is denoted by $\mathfrak{gl}(n)$, and is made of all matrices of order $n$ with the Lie bracket