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.
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15 citations
TL;DR: In this article, normalized adjacency eigenvalues and normalized adjACency energy of connected threshold graphs were investigated and the normalized eigenvalue of a threshold graph can be obtained directly from its binary representation and evaluated from its normalized equitable partition matrix.
14 citations
TL;DR: In this paper, the eigenvalues of the transition matrix of the dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces were obtained by making use of the spectral decimation technique.
Abstract: The eigenvalue spectrum of the transition matrix of a network contains much information about its structural properties and is related to the behavior of various dynamical processes performed on it. In this paper, we study the eigenvalues of the transition matrix of the dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces. We obtain all the eigenvalues, as well as their corresponding degeneracies, by making use of the spectral decimation technique. We then apply the obtained eigenvalues to determine the exact number of spanning trees in the studied fractals and derive an explicit formula of the eigentime identity for random walks taking place on them.
14 citations
CERN1
TL;DR: In this paper, a simple but efficient computational procedure for calculating bound state solutions of wave equations, valid even for absorptive interactions and corresponding complex eigenvalues, is given. But the integration is deliberately made in the direction of instabilities, but this does not spoil the accuracy.
14 citations
02 Nov 2009
TL;DR: The idea is to convert the Hamiltonian matrix to an equivalent sparse form, termed the “extended Hamiltonian pencil”, and solve for its eigenvalues efficiently using a special eigensolver, which demonstrates an 80X speed-up compared with standard direct eIGensolvers.
Abstract: Passivity is an important property for a macro-model generated from measured or simulated data. Existence of purely imaginary eigenvalues of a Hamiltonian matrix provides useful information in assessing and correcting the passivity of a system. Since direct computation of eigenvalues is very expensive for large-scale systems, several authors have proposed to solve iteratively for a subset of the eigenvalues based on heuristic sampling along the imaginary axis. However, completeness is not guaranteed in such methods and thus potential risk of missing important eigenvalues is difficult to avoid. In this paper we are aiming at finding all eigenvalues efficiently to avoid both the high cost and the potential risk of missing important eigenvalues. The idea of the proposed method is to convert the Hamiltonian matrix to an equivalent sparse form, termed the "extended Hamiltonian pencil", and solve for its eigenvalues efficiently using a special eigensolver. Experiments on several realistic systems demonstrate an 80X speed-up compared with standard direct eigensolvers.
14 citations