Related papers: The inverse eigenvalue problem for symmetric anti-…
We give sufficient conditions of the nonnegative inverse eigenvalue problem (NIEP) for normal centrosymmetric matrices. These sufficient conditions are analogous to the sufficient conditions of the NIEP for normal matrices given by Xu [16]…
For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This new specialized inverse eigenvalue problem is considered for…
We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner…
We study analogues of classical inequalities for the eigenvalues of sums of pseudo-Hermitian matrices.
We consider semi-infinite Jacobi matrices with discrete spectrum. We prove that the Jacobi operator can be uniquely recovered from one spectrum and subsets of another spectrum and norming constants corresponding to the first spectrum. We…
We consider real non-symmetric matrices and their factorisation as a product of real symmetric matrices. The number of complex eigenvalues of the original matrix reveals restrictions on such factorisations as we shall prove.
We consider the inverse eigenvalue problem for entanglement witnesses, which asks for a characterization of their possible spectra (or equivalently, of the possible spectra resulting from positive linear maps of matrices). We completely…
In this paper, we answer the various forms of nonnegative inverse eigenvalue problems with prescribed diagonal entries for order three: real or complex general matrices, symmetric stochastic matrices, and real or complex doubly stochastic…
Given two real symmetric matrices, their eigenvalue configuration is the relative arrangement of their eigenvalues on the real line. In this paper, we consider the following problem: given two parametric real symmetric matrices and an…
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
We consider the problem of finding nonzero eigenvalues and the corresponding eigenvectors of a matrix $AA^{\top}$, where $A$ is a special incidence matrix; This matrix can equivalently be defined based on a match relation between some…
Symplectic geometry plays an increasingly important role in mathematics, physics and applications, and naturally gives rise to interesting matrix families and properties. One of these is the notion of symplectic eigenvalues, whose existence…
The worst situation in computing the minimal nonnegative solution of a nonsymmetric algebraic Riccati equation associated with an M-matrix occurs when the corresponding linearizing matrix has two very small eigenvalues, one with positive…
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the join of a connected graph with a path. We then focus on…
We present a comprehensive treatment of relative oscillation theory for finite Jacobi matrices. We show that the difference of the number of eigenvalues of two Jacobi matrices in an interval equals the number of weighted sign-changes of the…
A new class of exact solutions to the axisymmetric and stationary vacuum Einstein equations containing n arbitrary complex parameters and one arbitrary real solution of the axisymmetric three-dimensional Laplace equation is presented. The…
Bidiagonal matrices are widespread in numerical linear algebra, not least because of their use in the standard algorithm for computing the singular value decomposition and their appearance as LU factors of tridiagonal matrices. We show that…
This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…
Building on previous work that provided analytical solutions to generalised matrix eigenvalue problems arising from numerical discretisations, this paper develops exact eigenvalues and eigenvectors for a broader class of $n$-dimensional…