Spectral properties of certain sequences of products of two real matrices

The aim of this paper is to analyze the asymptotic behavior of the eigenvalues and eigenvectors of particular sequences of products involving two square real matrices $A$ and $B$, namely of the form $B^kA$, as $k\rightarrow \infty$. This analysis represents a detailed deepening of a particular case within a general theory on finite families $\mathcal{F} = \{ A_1, \ldots, A_m \}$ of real square matrices already available in the literature. The Bachmann-Landau symbols and related results are largely used and are presented in a systematic way in the final Appendix.