Displaying similar documents to “Falseness of the finiteness property of the spectral subradius”

The minimum, diagonal element of a positive matrix

M. Smyth, T. West (1998)

Studia Mathematica

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Properties of the minimum diagonal element of a positive matrix are exploited to obtain new bounds on the eigenvalues thus exhibiting a spectral bias along the positive real axis familiar in Perron-Frobenius theory.

A spectral characterization of the behavior of discrete time AR–representations over a finite time interval

E. N. Antoniou, Antonis I. G. Vardulakis, Nikolas P. Karampetakis (1998)

Kybernetika

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In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the AR-equation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary conditions, are also gived.

Some properties of the spectral radius of a set of matrices

Adam Czornik, Piotr Jurgas (2006)

International Journal of Applied Mathematics and Computer Science

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In this paper we show new formulas for the spectral radius and the spectral subradius of a set of matrices. The advantage of our results is that we express the spectral radius of any set of matrices by the spectral radius of a set of symmetric positive definite matrices. In particular, in one of our formulas the spectral radius is expressed by singular eigenvalues of matrices, whereas in the existing results it is expressed by eigenvalues.

A new bound for the spectral radius of Brualdi-Li matrices

Xiaogen Chen (2015)

Special Matrices

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Let B2m denote the Brualdi-Li matrix of order 2m, and let ρ2m = ρ(B2m ) denote the spectral radius of the Brualdi-Li Matrix. Then [...] . where m > 2, e = 2.71828 · · · , [...] and [...] .

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...