In this paper we consider bounded families ${\cal F}$ of complex $n\times n$ matrices. We give sufficient conditions under which the sequence $\{\bar{\rho}_k({\cal F})^{1/k}\}_{k\ge 1}$, where $\bar{\rho}_k({\cal F})$ is the supremum of the spectral radii of all possible products of $k$ matrices chosen in ${\cal F}$, is convergent to its supremum $\rho({\cal F})$, the so-called {\em (generalized) spectral radius} of ${\cal F}$. We also illustrate a possible practical application.
On the asymptotic regularity of a family of matrices.
GUGLIELMI, NICOLA;
2012-01-01
Abstract
In this paper we consider bounded families ${\cal F}$ of complex $n\times n$ matrices. We give sufficient conditions under which the sequence $\{\bar{\rho}_k({\cal F})^{1/k}\}_{k\ge 1}$, where $\bar{\rho}_k({\cal F})$ is the supremum of the spectral radii of all possible products of $k$ matrices chosen in ${\cal F}$, is convergent to its supremum $\rho({\cal F})$, the so-called {\em (generalized) spectral radius} of ${\cal F}$. We also illustrate a possible practical application.File in questo prodotto:
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