Special Linear Group

Definition

The set of matrices with determinant $1$ is denoted by $\mathrm{SL}(n, \mathbb{R})$ and called the special linear group of degree $n$ .

$\mathrm{SL}(n, \mathbb{R}) := {\left\{ A \in M_{n \times n}(\mathbb{R}) : \det{A} = 1 \right\}}$

Since it is a set of matrices with determinant $1$ , only invertible matrices exist. Thus, it forms a group under matrix multiplication and is a subgroup of the general linear group $\mathrm{GL}(n, \mathbb{R})$ .