Perturbation theorems for the matrix eigenvalue problem
Elsner, L. (1985-1986)
Portugaliae mathematica
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Displaying similar documents to “A bound for the spectral variation of two matrices.”
Perturbation theorems for the matrix eigenvalue problem
New bounds for the minimum eigenvalue ofM-matrices
Feng Wang, Deshu Sun (2016)
Open Mathematics
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Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.
A note on the integral criterion for spectral dichotomy of regular pencils.
Sadkane, Miloud (2004)
Applied Mathematics E-Notes [electronic only]
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On the 2-norm distance from a normal matrix to the set of matrices with a multiple zero eigenvalue.
Ikramov, Kh.D., Nazari, A.M. (2005)
Zapiski Nauchnykh Seminarov POMI
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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.
Spectral variation bounds for diagonalisable matrices.
R. Bhatia, L. Elsner, G.M. Krause (1997)
Aequationes mathematicae
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On some spectral characteristics of multiparameter polynomial matrices.
Khazanov, V.B. (2004)
Zapiski Nauchnykh Seminarov POMI
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Some bounds for the spectral radius of the Hadamard product of matrices.
Cheng, Guang-Hui, Cheng, Xiao-Yu, Huang, Ting-Zhu, Tam, Tin-Yau (2005)
Applied Mathematics E-Notes [electronic only]
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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.
Bounds of modulus of eigenvalues based on Stein equation
Guang-Da Hu, Qiao Zhu (2010)
Kybernetika
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This paper is concerned with bounds of eigenvalues of a complex matrix. Both lower and upper bounds of modulus of eigenvalues are given by the Stein equation. Furthermore, two sequences are presented which converge to the minimal and the maximal modulus of eigenvalues, respectively. We have to point out that the two sequences are not recommendable for practical use for finding the minimal and the maximal modulus of eigenvalues.
Unified Spectral Bounds on the Chromatic Number
Clive Elphick, Pawel Wocjan (2015)
Discussiones Mathematicae Graph Theory
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One of the best known results in spectral graph theory is the following lower bound on the chromatic number due to Alan Hoffman, where μ1 and μn are respectively the maximum and minimum eigenvalues of the adjacency matrix: χ ≥ 1+μ1/−μn. We recently generalised this bound to include all eigenvalues of the adjacency matrix. In this paper, we further generalize these results to include all eigenvalues of the adjacency, Laplacian and signless Laplacian matrices. The various known bounds...