the analysis of cross-correlations is extensively applied for understanding of interconnections in stock markets. variety of methods are used in order to search stock cross-correlations including the random matrix theory (rmt), the principal component analysis (pca) and the hierachical ‎structures.‎ in ‎this work‎, we analyze cross-crrelations between price fluctuations of 20 ‎company ‎stocks‎‎...

In this article we consider the sequences of sample and population covariance operators for a sequence of arrays of Hilbertian random elements. Then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...

We will discuss a few basic facts about the distribution of eigenvalues of the adjacency matrix, and some applications. Then we discuss the question of computing the eigenvalues of a symmetric matrix. 1 Eigenvalue distribution Let us consider a d-regular graph G on n vertices. Its adjacency matrix AG is an n× n symmetric matrix, with all of its eigenvalues lying in [−d, d]. How are the eigenval...

Let f be a normalized Hecke–Maass cusp form of weight zero for the group $$SL_2({\mathbb {Z}})$$ . This article presents several quantitative results about distribution Hecke eigenvalues f. Applications to $$\Omega _{\pm }$$ -results and its symmetric square sym $$^2(f)$$ are also given.

The distribution of the eigenvalues of a quantum Hamiltonian is a central subject that is studied in quantum chaos. There are some generally accepted conjectures about the nearest-neighbor spacing distributions of the eigenvalues. Unless otherwise stated we use the following assumptions: The quantum mechanical system is desymmetrized with respect to all its unitary symmetries, and whenever we e...

An efficient technique is presented for optimum design of structures with both natural frequency and complex frequency response constraints. The main ideals to reduce the number of dynamic analysis by introducing high quality approximation. Eigenvalues are approximated using the Rayleigh quotient. Eigenvectors are also approximated for the evaluation of eigenvalues and frequency responses. A tw...