Related papers: The geometry of spectral interlacing
In this article we prove that a semialgebraic map is a branched covering if and only if its associated spectral map is a branched covering. In addition, such spectral map has a neat behavior with respect to the branching locus, the…
In this paper, we compute the spectral norms of the matrices related with integer squences and we give some example related with Fibonacci, Lucas, Pell and Perrin numbers.
The spectral properties of a multilevel atomic system interacting with multiple electromagnetic fields, a modified inverted-Y system, have been theoretically investigated. In this study, a numerical matrix propagation method has been…
We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…
We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to show the strength and flexibility of such a nonstandard…
In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…
A geometric approach to understanding recursion relations for scattering amplitudes is developed. We achieve this by studying intersection numbers of triangulated accordiohedra presented as hyperplane arrangements. The cancellation of…
Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us…
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…
The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral…
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…
We consider Gaussian fields of real symmetric, complex Hermitian or quaternionic Hermitian matrices over an electrical network, and describe how the isomorphisms between these fields and random walks give rise to topological expansions…
In this paper, we compute the spectral norms of the matrices related with integer squences and we give two examples related with Fibonacci and Lucas numbers.
We generalize classical results in spectral graph theory and linear algebra more broadly, from the case where the underlying matrix is Hermitian to the case where it is non-Hermitian. New admissibility conditions are introduced to replace…
We analyze spectral properties of a quantum graph in the form of a ring chain with a $\delta$ coupling in the vertices exposed to a homogeneous magnetic field perpendicular to the graph plane. We find the band spectrum in the case when the…
This work provides a comprehensive theoretical framework for understanding the symmetry properties of High-Resolution NMR spectra. We analyze the conditions under which a spectrum exhibits mirror symmetry (palindromicity). We demonstrate…
The foundations of matrix geometry are discussed, which provides the basis for recent progress on the effective geometry and gravity in Yang-Mills matrix models. Basic examples lead to a notion of embedded noncommutative spaces (branes)…
Let $A$ be a $n\times n$ complex Hermitian matrix and let $\lambda(A)=(\lambda_1,\ldots,\lambda_n)\in \mathbb{R}^n$ denote the eigenvalues of $A$, counting multiplicities and arranged in non-increasing order. Motivated by problems arising…
The aim of this article is to present a brief overview of spectral perturbation theory for matrices, bounded linear operators and holomorphic operator-valued functions. We focus on bounds for perturbed eigenvalues, eigenvectors and…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…