We consider N×N Hermitian or symmetric random matrices with independent entries. The distribution of the (i, j)-th matrix element is given by a probability measure νij whose first two moments coincide with those of the corresponding Gaussian ensemble. We prove that the joint probability distribution of the components of eigenvectors associated with eigenvalues close to the spectral edge agrees ...

In this paper, we study the generation problem of Riesz basis for a general network of strings with joint damping at each vertex. First, we give a basic spectral property of the system operator A. Under certain conditions, we prove that the spectrum of A is distributed in a strip parallel to the imaginary axis. By the discussion of the completeness of generalized eigenvectors of the operator A,...

This paper compares the performance on linear systems of equations of three similar adaptive accelerating strategies for restarted GMRES. The underlying idea is to adaptively use spectral information gathered from the Arnoldi process. The first strategy retains approximations to some eigenvectors from the previous restart and adds them to the Krylov subspace. The second strategy uses also appro...

We consider the covariance matrix for dichotomous Guttman items under a set of uniformity conditions, and obtain closed-form expressions for the eigenvalues and eigenvectors of the matrix. In particular, we describe the eigenvalues and eigenvectors of the matrix in terms of trigonometric functions of the number of items. Our results parallel those of Zwick (1987) for the correlation matrix unde...

An intruder detection method by using time variant Multiple Input Multiple Output (MIMO) channels has been proposed (MIMO sensor). In this letter, the detection performance using eigenvectors, which are obtained by singular value decomposition for MIMO channel matrix, is evaluated in actual indoor propagation environment. Moreover, a new diversity method using multiple eigenvectors is proposed ...

Second order statistics estimates in the form of sample eigenvalues and sample eigenvectors give a sub optimal description of the population density. So far only attempts have been made to reduce the bias in the sample eigenvalues. However, because the sample eigenvectors differ from the population eigenvectors as well, the population eigenvalues are biased estimates of the variances along the ...

We propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized c...

The eigenvalues and eigenvectors of a symmetric matrix are needed in a myriad of applications in computational engineering and computational science. One of the fastest and most accurate eigensolvers is the Algorithm of Multiple Relatively Robust Representations (MRRR). This is the first stable algorithm that computes k eigenvalues and eigenvectors of a tridiagonal symmetric matrix in O(nk) tim...