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
Similarity:
Ikramov, Kh.D., Nazari, A.M. (2005)
Zapiski Nauchnykh Seminarov POMI
Similarity:
Elsner, L. (1985-1986)
Portugaliae mathematica
Similarity:
Clive Elphick, Pawel Wocjan (2015)
Discussiones Mathematicae Graph Theory
Similarity:
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...
Guang-Da Hu, Qiao Zhu (2010)
Kybernetika
Similarity:
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.
Cheng, Guang-Hui, Cheng, Xiao-Yu, Huang, Ting-Zhu, Tam, Tin-Yau (2005)
Applied Mathematics E-Notes [electronic only]
Similarity:
Gil, Michael I. (2002)
Applied Mathematics E-Notes [electronic only]
Similarity:
M. Smyth, T. West (1998)
Studia Mathematica
Similarity:
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.
Francesco Tudisco (2015)
Special Matrices
Similarity:
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...
Gregory, David A., Kirkland, Stephen J. (1999)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Similarity:
Vanesa Cortés, Juan Peña, Tomas Sauer (2012)
Open Mathematics
Similarity:
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.