this paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. first, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. this new algorithm ca...

the main aim of this paper is to extend the recently developed methods for calculating the buckling loads of planar symmetric frames to include the effect of semi-rigidity of the joints. this is achieved by decomposing a symmetric model into two submodels and then healing them in such a manner that the ::::union:::: of the eigenvalues of the healed submodels result in the eigenvalues of the ent...

Eigenvectors and eigenvalues of discrete graph Laplacians are often used for manifold learning and nonlinear dimensionality reduction. It was previously proved by Belkin and Niyogi [3] that the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions and eigenvalues of the Laplace-Beltrami operator of the manifold in the limit of infinitely many data points sampled ind...

Let Bn = (1/N)T 1/2 n XnX ∗ nT 1/2 n where Xn is n ×N with i.i.d. complex standardized entries having finite fourth moment, and T 1/2 n is a Hermitian square root of the nonnegative definite Hermitian matrix Tn. It is known that, as n→∞, if n/N converges to a positive number, and the empirical distribution of the eigenvalues of Tn converges to a proper probability distribution, then the empiric...

It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for the eigenvalues of a certain direct sum of Gaussian unitary ensembles subject to an overall constraint that the eigenvalues lie in a hyperplane.

In this paper, we obtain a theorem on the distribution of eigenvalues for Schur complements of H-matrices. Further, we give some properties of diagonal-Schur complements on diagonally dominant matrices and their distribution of eigenvalues. © 2004 Elsevier Inc. All rights reserved. AMS classification: 15A45; 15A48

In this paper, we employ transformation operators and Levinson’s density formula to study the distribution of interior transmission eigenvalues for a spherically stratified media. In particular, we show that under smoothness condition on the index of refraction that there exist an infinite number of complex eigenvalues and there exist situations when there are no real eigenvalues. We also consi...

In this paper we derive some new and practical results on testing and interval estimation problems for the population eigenvalues of a Wishart matrix based on the asymptotic theory for block-wise infinite dispersion of the population eigenvalues. This new type of asymptotic theory has been developed by the present authors in Takemura and Sheena (2005) and Sheena and Takemura (2007a,b) and in th...