For every cograph there exist bases of the eigenspaces for the eigenvalues 0 and −1 that consist only of vectors with entries from {0, 1,−1}, a property also exhibited by other graph classes. Moreover, the multiplicities of the eigenvalues 0 and −1 of a cograph can be determined by counting certain vertices of the associated cotree.

in this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. some examples are provided to show the accuracy and reliability of the proposed method. it is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to t...

this paper consists of three sections. in the first section an efficient method is used for decomposition of the canonical matrices associated with repetitive structures. to this end, cylindrical coordinate system, as well as a special numbering scheme were employed. in the second section, divide and conquer method have been used for eigensolution of these structures, where the matrices are in ...

An exploratory study of the low-lying eigenvalues of the Wilson-Dirac operator and their corresponding eigen-vectors is presented. Results for the eigenvalues from quenched and unquenched simulations are discussed. The eigenvectors are studied with respect to their localization properties in the quenched approximation for the cases of SU(2) and SU(3).

Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely techniques, in particular in Principal Component Analysis (PCA). In many modern data analysis problems, statisticians are faced with large datasets where the sample si...

We propose a theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigenvalues. These notions are particularly useful in generalizing certain areas where the spectral theory of matrices has traditionally played an important role. For illustration, we will discuss a m...

Eigenvectors and eigenvalues are numbers and vectors associated to square matrices, and together they provide the eigen-decomposition of a matrix which analyzes the structure of this matrix. Even though the eigen-decomposition does not exist for all square matrices, it has a particularly simple expression for a class of matrices often used in multivariate analysis such as correlation, covarianc...

This paper is about the rate of convergence of the Markov chain Xn+1 = AXn+Bn (mod p), where A is an integer matrix with nonzero eigenvalues and {Bn}n is a sequence of independent and identically distributed integer vectors, with support not parallel to a proper subspace of Q invariant under A. If |λi| 6 = 1 for all eigenvalues λi of A, then n = O ( (ln p) ) steps are sufficient and n = O(ln p)...