Topic
Spectrum of a matrix
About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.
Papers published on a yearly basis
Papers
More filters
TL;DR: The Chebyshev?tau spectral method may produce spurious eigenvalues with large positive real parts, even when all true eigen values of the problem are known to have negative real parts as discussed by the authors.
35 citations
TL;DR: In this article, the spectrum of a polyharmonic operator in unbounded domains is investigated and a two-sided bound for the distribution function of the eigenvalues is obtained in the general case.
Abstract: This paper is devoted to the investigation of the spectrum of a polyharmonic operator in unbounded domains. The class of domains for which the spectrum of the corresponding first boundary value problem is discrete is examined. The classical asymptotic formula for eigenvalues is extended to the case of domains of finite volume. A two-sided bound for the distribution function of the eigenvalues is obtained in the general case. If the domain behaves sufficiently regularly at infinity, then the upper and lower bounds coincide in order. The results are new also for the Laplace operator. Bibliography: 13 items.
35 citations
TL;DR: In this article, lower bounds for the toughness of a graph in terms of its eigenvalues were derived, and the best possible lower bounds were derived for each eigenvalue.
34 citations
TL;DR: For all n > 3, every matrix in K has at least three distinct eigenvalues; such a matrix has exactly three distinct Eigenvalues if and only if it is a Hadamard tournament matrix as discussed by the authors.
34 citations
Journal Article•
TL;DR: In this paper, a model operator associated with the energy operator of a system of three non conserved number of particles is considered, and the essential spectrum of the operator is described by the spectrum of a family of the generalized Friedrichs model.
Abstract: A model operator associated with the energy operator of a system of three non conserved number of particles is considered. The essential spectrum of the operator is described by the spectrum of a family of the generalized Friedrichs model. It is shown that there are infinitely many eigenvalues lying below the bottom of the essential spectrum, if a generalized Friedrichs model has a zero energy resonance.
34 citations