Related papers: Explicit eigenvalues of certain scaled trigonometr…
We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…
This work presents conjectures about eigenvalues of matrices associated with $k$-path graphs, the algebraic connectivity, defined as the second smallest eigenvalue of the Laplacian matrix, and the $\alpha$-index, as the largest eigenvalue…
In this paper we express the eigenvalues of a sort of real heptadiagonal symmetric matrices as the zeros of explicit rational functions establishing upper and lower bounds for each of them. From these prescribed eigenvalues we compute also…
Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a…
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine…
In this paper we show that if R is a discrete valuation ring, then R is a filtered ring. We prove some properties and relation when R is a discrete valuation ring.
The purpose of this paper is to introduce new parametric families of complex Hadamard matrices in two different ways. First, we prove that every real Hadamard matrix of order N>=4 admits an affine orbit. This settles a recent open problem…
Random matrices arise in many mathematical contexts, and it is natural to ask about the properties that such matrices satisfy. If we choose a matrix with integer entries at random, for example, what is the probability that it will have a…
General properties of eigenvalues of $A+\tau uv^*$ as functions of $\tau\in\Comp$ or $\tau\in\Real$ or $\tau=\e^{\ii\theta}$ on the unit circle are considered. In particular, the problem of existence of global analytic formulas for…
In this paper we study the eigenvalues of the laplacian matrices of the cyclic graphs with one edge of weight $\alpha$ and the others of weight $1$. We denote by $n$ the order of the graph and suppose that $n$ tends to infinity. We notice…
This is a first paper by the authors dedicated to the distribution of eigenvalues for random perturbations of large bidiagonal Toeplitz matrices.
We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…
The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
A Toeplitz matrix is one in which the matrix elements are constant along diagonals. The Fisher-Hartwig matrices are much-studied singular matrices in the Toeplitz family. The matrices are defined for all orders, $N$. They are parametrized…
We derive new perturbation bounds for eigenvalues of Hermitian matrices with block structures. The structures we consider range from a standard 2-by-2 block form to block tridiagonal and tridigaonal forms. The main idea is the observation…
This paper presents an innovative set of tools developed to support a methodology to find the left eigenvalues of $m$ order quaternion square matrix. It is solving four real polynomial equations of order not greater than $4m-3$ in four…
We characterize real and complex functions which, when applied entrywise to square matrices, yield a positive definite matrix if and only if the original matrix is positive definite. We refer to these transformations as sign preservers.…
Convergence properties of binary stationary subdivision schemes for curves have been analyzed using the techniques of z-transforms and eigenanalysis. Eigenanalysis provides a way to determine derivative continuity at specific points based…
In a recent paper published in the Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87, 5309-5419 (2007), arXiv:0705.1045], the author advances a conjectured solution for various properties of the three-dimensional Ising model. Here we…