This paper proposes an eigenvector-based method for analysis and design of hierarchical networks for multi-agent systems. We first define the concept of eigen-connection by characterizing low rank information flow between layers based on the eigenvector of lower level interconnection structures. It is shown that the resulting intergroup interconnections affect only a few eigenvalues of intercon...

Ulam’s method is a rigorous numerical scheme for approximating invariant densities of dynamical systems. The phase space is partitioned into connected sets and an inter-set transition matrix is computed from the dynamics; an approximate invariant density is read off as the leading left eigenvector of this matrix. When a hole in phase space is introduced, one instead searches for conditional inv...

Let Ak, k ∈ N be a sequence of n×n complex valued matrices which converge to a matrix A. If A and each Ak is positive then the product AkAk−1...A2A1 ||AkAk−1...A2A1|| converges to a rank one matrix positive matrix uw, where u is a positive column eigenvector of A. If each Ak is nonsingular and A has exactly one simple eigenvalue λ of the maximal modulus with the corresponding eigenvector u, the...

In 8] and 9] W. Mackens and the present author presented two generalizations of a method of Cybenko and Van Loan 4] for computing the smallest eigenvalue of a symmetric, positive deenite Toeplitz matrix. Taking advantage of the symmetry or skew symmetry of the corresponding eigenvector both methods are improved considerably.

Since the financial crisis of 2008, network analysis systems has attracted a lot attention. In this paper, we analyze global banking via method Random Matrix Theory. By applying that on cross border lending network, it is shown while connectivity between different parts risen and profile transactions diversified, role hubs remains important in weighted perspective. The largest eigenvalue transa...

We continue with F being an arbitrary field and V a finite dimensional vector space over F ; dimV = n. Conditions on F may be added later on. We assume T ∈ L(V ). Definition 1 We say that an element λ ∈ F is an eigenvalue of T iff there exists x ∈ V , x ̸= 0 such that Tx = λx. We call x ∈ V , x ̸= 0 such that Tx = λx an eigenvector of T , corresponding to the eigenvector λ. If λ is an eigenvector...

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...

We use the algebraic nested Bethe ansatz to solve the eigenvalue and eigenvector problem of the supersymmetric SUq(n|m) model with open boundary conditions. Under an additional condition that model is related to a multicomponent supersymmetric t-J model. We also prove that the transfer matrix with open boundary condition is SUq(n|m) invariant. PACS: 7510J, 0520,0530

A modal decomposition strategy based on state-variable ensembles is formulated. A nonsymmetric, generalized eigenvalue problem is constructed. The data-based eigenvalue problem is related to the generalized eigenvalue problem associated with free-vibration solutions of the state-variable formulation of linear multi-degree-of-freedom systems. For linear free-response data, the inverse-transpose ...