I'm looking for method to define a subgroup of General Linear group, similar to Special Linear Group. The special linear group $\text{SL}_n(\mathbf{R})$ is the group of $n \times n$ matrix with determinant 1. And I want to define another group that is also the group of $n \times n$, but with non-negative determinant. I am wondering if there is an existing definition ?
thanks you!