Displaying similar documents to “Some properties of the spectral radius of a set of matrices”

The Direct and Inverse Spectral Problems for some Banded Matrices

Zagorodnyuk, S. M. (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 15A29. In this paper we introduced a notion of the generalized spectral function for a matrix J = (gk,l)k,l = 0 Ґ, gk,l О C, such that gk,l = 0, if |k-l | > N; gk,k+N = 1, and gk,k-N № 0. Here N is a fixed positive integer. The direct and inverse spectral problems for such matrices are stated and solved. An integral representation for the generalized spectral function is obtained.

On a devil’s staircase associated to the joint spectral radii of a family of pairs of matrices

Ian D. Morris, Nikita Sidorov (2013)

Journal of the European Mathematical Society

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The joint spectral radius of a finite set of real d × d matrices is defined to be the maximum possible exponential rate of growth of products of matrices drawn from that set. In previous work with K. G. Hare and J. Theys we showed that for a certain one-parameter family of pairs of matrices, this maximum possible rate of growth is attained along Sturmian sequences with a certain characteristic ratio which depends continuously upon the parameter. In this note we answer some open questions...

A sharp upper bound for the spectral radius of a nonnegative matrix and applications

Lihua You, Yujie Shu, Xiao-Dong Zhang (2016)

Czechoslovak Mathematical Journal

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We obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance Laplacian spectral radius, the distance signless Laplacian spectral radius of an undirected graph or a digraph. These results are new or generalize some known results.