Is there something known about the set of all homomorphisms from the free group on $n$ generators $F_n$ to the real general linear group $GL_k(\mathbb{R})$ mod.conjugation, i.e.

$$
Hom(F_n, GL_k(\mathbb{R}))/GL_k(\mathbb{R}),
$$

or differently formulated of the set
{$\{ (A_1, \ldots, A_n)| A_i \in GL_k(\mathbb{R}) \}$ }$ /GL_k(\mathbb{R}).$