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.conjugationmodulo conjugation, i.e.
$$ Hom(F_n, GL_k(\mathbb{R}))/GL_k(\mathbb{R}), $$$$ Hom(F_n, GL_k(\mathbb{R}))/GL_k(\mathbb{R}) , $$
or, differently formulated, of the set {$\{ (A_1, \ldots, A_n)| A_i \in GL_k(\mathbb{R}) \}$ }$ /GL_k(\mathbb{R}).$$\{ (A_1, \ldots, A_n)| A_i \in GL_k(\mathbb{R}) \} / GL_k(\mathbb{R})$?
