Spectral properties of certain sequences of products of two real matrices

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Michela Brundu
Marino Zennaro


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.

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