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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Displaying similar documents to “New bounds for the minimum eigenvalue ofM-matrices”
On the 2-norm distance from a normal matrix to the set of matrices with a multiple zero eigenvalue.
Perturbation theorems for the matrix eigenvalue problem
Elsner, L. (1985-1986)
Portugaliae mathematica
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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...
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.
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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A bound for the spectral variation of two matrices.
Gil, Michael I. (2002)
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.
A note on certain ergodicity coeflcients
Francesco Tudisco (2015)
Special Matrices
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We investigate two ergodicity coefficients ɸ ∥∥ and τn−1, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized version have been shown so far.We provide a further result concerning the limit of its powers. Then we propose a generalization of the second coefficient τ n−1 and we show that, under mild conditions, it can be used to recast the eigenvector...
Singular values of tournament matrices.
Gregory, David A., Kirkland, Stephen J. (1999)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Simultaneous triangularization of commuting matrices for the solution of polynomial equations
Vanesa Cortés, Juan Peña, Tomas Sauer (2012)
Open Mathematics
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We present an extension of the QR method to simultaneously compute the joint eigenvalues of a finite family of commuting matrices. The problem is motivated by the task of finding solutions of a polynomial system. Several examples are included.
Some new bounds of the minimum eigenvalue for the Hadamard product of anM-matrix and an inverseM-matrix
Jianxing Zhao, Caili Sang (2016)
Open Mathematics
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Some convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix B and the inverse of a nonsingular M-matrix A are given by using Brauer’s theorem. It is proved that these sequences are monotone increasing, and numerical examples are given to show that these sequences could reach the true value of the minimum eigenvalue in some cases. These results in this paper improve some known results.