Related papers: On rigorous estimates of eigenspaces and eigenvalu…
We present a prescription for forming matrices with specified eigenvalues and known eigenvectors. With this method, we can form Hermitian, anti-Hermitian, symmetric and general matrices with arbitrary eigenvalues. In addition we propose an…
We characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal $n$ by $n$ matrices subject to arbitrary boundary conditions, i.e. with arbitrary elements on the first and last rows of the matrix. %By boundary…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
A real square matrix is Perron-like if it has a real eigenvalue $s$, called the principal eigenvalue of the matrix, and $\mbox{Re}\,\mu<s$ for any other eigenvalue $\mu$. Nonnegative matrices and symmetric ones are typical examples of this…
We prove that the point process of the eigenvalues of real or complex non-Hermitian matrices $X$ with independent, identically distributed entries is hyperuniform: the variance of the number of eigenvalues in a subdomain $\Omega$ of the…
Given a ternary homogeneous polynomial, the fixed points of the map from $\mathbb{P}^2$ to itself defined by its gradient are called its eigenpoints. We focus on cubic polynomials, and analyze configurations of eigenpoints that admit one or…
This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables…
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…
The main objective of this article is to develop a matrix pencil approach for the study of the controllability and reachability of a class of linear singular discrete time systems. The description equation of a practical system may be…
Evaluation of the eigenvectors of symmetric tridiagonal matrices is one of the most basic tasks in numerical linear algebra. It is a widely known fact that, in the case of well separated eigenvalues, the eigenvectors can be evaluated with…
Eigenvalues of stochastic matrices have been studied from two complementary perspectives. The individual eigenvalues are characterised through the well-established Karpelevich regions. The spectrum as a whole has also been analysed,…
In this paper, a rigorous computational method to enclose eigendecompositions of complex interval matrices is proposed. Each eigenpair $x=(\lambda,v)$ is found by solving a nonlinear equation of the form $f(x)=0$ via a contraction argument.…
We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…
Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to…
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each…
We introduce a unified method for study of 2-dimensional invariant subspaces of matrices and their corresponding super-eigenvalues. As a novel application to non-commutative algebra, we present a connection between the eigenvalues of…
We prove that few largest (and most important) eigenvalues of random symmetric matrices of various kinds are very strongly concentrated. This strong concentration enables us to compute the means of these eigenvalues with high precision. Our…
We develop a model-based method for evaluating heterogeneity among several p x p covariance matrices in the large p, small n setting. This is done by assuming a spiked covariance model for each group and sharing information about the space…
We examine some numerical iterative methods for computing the eigenvalues and eigenvectors of real matrices. The five methods examined here range from the simple power iteration method to the more complicated QR iteration method. The…
We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type…