Related papers: A New Perspective on Eigenvalues and Eigenvectors …

This paper studies boundedness and closedness of linear relations, which include both single-valued and multi-valued linear operators. A new (single-valued) linear operator induced by a linear relation is introduced, and its relationships…

We propose a theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigenvalues. These notions are particularly…

Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…

There has been much recent interest, initiated by work of the physicists Hatano and Nelson, in the eigenvalues of certain random non-Hermitian periodic tridiagonal matrices and their bidiagonal limits. These eigenvalues cluster along a…

Explicit representations of the eigenvalues of the peridynamic operator have been recently derived in [5]. These representations are given in terms of generalized hypergeometric functions. Asymptotic analysis of the hypergeometric functions…

Eigenvalue spectrum has been a long term unsolved problem for plasma physicists. In this paper, some numerical calculations are conducted about the minimum eigenvalues of the linearized Rosenbluth collision operator and the differential…

This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…

The paper explores the concept of the rank of a bicomplex matrix, delving into four distinct types of ranks and investigating conditions under which these ranks are equivalent. It also defines and analyzes the concept of idempotent row…

Eigenvectors of tensors, as studied recently in numerical multilinear algebra, correspond to fixed points of self-maps of a projective space. We determine the number of eigenvectors and eigenvalues of a generic tensor, and we show that the…

This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a…

I propose a proof of the existence of the existence of eigenvectors and eigenvalues in the spirit of Argand's proof of the fundamental theorem of algebra. The proof only relies on Weierstrass's theorem, the definition of the inverse of a…

We give a condition ensuring that the operators in a nilpotent Lie algebra of linear operators on a finite dimensional vector space have a common eigenvector.

We study schemes of tensor eigenvectors from an algebraic and geometric viewpoint. We characterize determinantal defining equations of such eigenschemes via linear equations in their coefficients, both in the general and in the symmetric…

We present exact expressions for the eigenvalues and eigenvectors of the d-dimensional Laplace operator in a cut Fock basis.

In modeling quantum systems or wave phenomena, one is often interested in identifying eigenstates that approximately carry a specified property; scattering states approximately align with incoming and outgoing traveling waves, for instance,…

Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…

We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…

In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in…

For a large class of linear neutral type systems the problem of eigenvalues and eigenvectors assignment is investigated, i.e. finding the system which has the given spectrum and almost all, in some sense, eigenvectors.