In this paper we consider bounded families F of complex n × n matrices. We give sufficient conditions under which the sequence {r_k(F)^(1/k)}, where r_k(F) is the supremum of the spectral radii of all possible products of k matrices chosen in F, is convergent to its supremum r(F), the so-called (generalized) spectral radius of F. We also illustrate a possible practical application. The research that led to the present paper was partially supported by a grant of the group GNCS of INdAM.
On the asymptotic regularity of a family of matrices
ZENNARO, MARINO
2012-01-01
Abstract
In this paper we consider bounded families F of complex n × n matrices. We give sufficient conditions under which the sequence {r_k(F)^(1/k)}, where r_k(F) is the supremum of the spectral radii of all possible products of k matrices chosen in F, is convergent to its supremum r(F), the so-called (generalized) spectral radius of F. We also illustrate a possible practical application. The research that led to the present paper was partially supported by a grant of the group GNCS of INdAM.File in questo prodotto:
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Linear Algebra Appl. 436(2012), 2093-2104.pdf
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