Yair Weiss School of CS & Engr. The Hebrew Univ. [email protected] Despite many empirical successes of spectral clustering methodsalgorithms that cluster points using eigenvectors of matrices derived from the datathere are several unresolved issues. First , there are a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these algorithms have no pr...

Determination of the eigenvalues and eigenvectors of a matrix is important in many areas of science, for example in web ranking [8, 15], computer graphics and visualization [24], quantum mechanics [5], statistics [12, 20], medicine, communications, construction vibration analysis [3, 23]. One of the most important numerical methods designed to calculate the eigenvalues and eigenvectors of matri...

Backward errors and condition numbers are defined and evaluated for eigenvalues and eigenvectors of generalized eigenvalue problems. Both normwise and componentwise measures are used. Unstructured problems are considered first, and then the basic definitions are extended so that linear structure in the coefficient matrices (for example, Hermitian, Toeplitz, Hamiltonian, or band structure) is pr...

The aim of this paper is to give a precise proof the completeness Lamb modes and associated modes. This relatively simple short but relies on two powerful mathematical theorems. first one theorem elliptic systems with parameter due Agranovich Vishik. second Locker which gives criterion show set generalized eigenvectors Hilbert-Schmidt discrete operator.

The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-frequency operators have been defined on graphs using Laplacian eigenvalues and eigenvectors. We extend these results and prove that the translation operator to the i’th node is invertible if and only if all eigenvectors ar...

The paper presents an approximated and compact derivation of the mutual displacement of Floquet eigenvectors in a class of LC tank oscillators with time varying bias. In particular it refers to parallel tank oscillators of which the energy restoring can be modeled through a train of current pulses. Since Floquet eigenvectors are acknowledged to give a correct decomposition of noise perturbation...

abstract The theory of eigenvalues and eigenvectors of rectangular matrix pencils is complicated by the fact that arbitrarily small perturbations of the pencil can cause them disappear. However, there are applications in which the properties of the pencil ensure the existence of eigen-values and eigenvectors. In this paper it is shown how to develop a perturbation theory for such pencils. ABSTR...

Helen Au-Yang Eigenvectors of the superintegrable chiral Potts model We show that the eigenspaces of eigenvalues (1−ωt)+ω(1− t) of the τ2(t) matrix of size N×N are degenerate. In the Q = 0 case, it has 2 independent eigenvectors, where r = L(N − 1)/N and L is chosen to be a multiple of N . They can be written in terms of the generators of r simple sl2 algebras, E±m and Hm (m = 1, · · · , r). Ne...

We present an approximated and compact derivation of the mutual displacement of Floquet eigenvectors in a class of LC tank oscillators with time-varying bias. The paper refers to parallel tank oscillators in which the energy restoring can be modeled by current pulses controlled by the oscillation voltage. The goal is to show, for the proposed class, the possibility to guide the design of oscill...

The HITS and the PageRank algorithms are eigenvector methods for identifying “authoritative” or “influential” articles, given hyperlink or citation information. That such algorithms should give consistent answers is surely a desideratum, and in this paper, we address the question of when they can be expected to give stable rankings under small perturbations to the hyperlink patterns. Using tool...