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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TL;DR: A study on the transition weight matrix of a weighted network and the recursive relationship of normalized Laplacian matrix’s eigenvalues at two successive generations to get the eigentime identity for weight-dependent walk and weighted counting of spanning trees.
Abstract: The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on some relevant dynamical aspects, in particular those related to weight-dependent ...
9 citations
TL;DR: Asymptotic expansions for negative eigenvalues λ−ke of the Dirichlet problem with the density becoming negatively small in either a subdomain of fixed size, or a small, of diameter O(e 1/m), neighborhood of an interior point are constructed in this article.
Abstract: Asymptotic expansions are constructed for negative eigenvalues λ−ke of the Dirichlet problem with the density becoming negatively small, of order e, in either a subdomain of fixed size, or a small, of diameter O(e1/m), neighborhood of an interior point. Such the eigenvalues lie far away from the coordinate origin and their order with respect to the small parameter is e−1 in the first case and e−m/(m+2) in the second one. The limit problems are formulated and investigated, the eigenvalues of which imply the limits as e → +0 of the quantities −eλ−ke and −em/(m+2)λ−ke, respectively. Asymptotically precise estimates are obtained for the remainders in the expansions of the eigenvalues and eigenfunctions.
9 citations
TL;DR: In this paper, the Sturm-Liouville problem (1.1), and its variants are considered, and conditions for the non-existence of embedded eigenvalues are given.
Abstract: The Sturm-Liouville problem (1.1), (1.2) is considered, which depends rationally on the eigenvalue parameter. Estimates for the eigenvalues and especially for the embedded eigenvalues are proved. Moreover, conditions for the non-existence of embedded eigenvalues are given.
9 citations
01 Aug 2017
TL;DR: In this paper, the eigenvalues of the discrete Schrodinger operator with a complex potential were studied and bounds on the total number of eigen values in the case where V decays exponentially at infinity.
Abstract: We study the eigenvalues of the discrete Schrodinger operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.
9 citations
TL;DR: In this article, the degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt→0 is given first.
Abstract: The degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt→0 is given first. When the continuous-time n-dimensional eigenvalue equation, which has all the eigenvalues located in the left half plane, has beeh reduced from the original 2n-dimensional one, the present paper proposes that several of the eigenvalues nearest to the imaginary axis be obtained by the matrix transformation Ae=eA. All the eigenvalues of Ae are in the unit circle, with the eigenvectors unchanged and the original eigenvalues can be obtained by a logarithm operation. And several of the eigenvalues of Ae nearest to the unit circle can be calculated by the dual subspace iteration method.
9 citations