First order structured perturbation theory for multiple zero eigenvalues of skew-adjoint matrices
نویسندگان
چکیده
منابع مشابه
Perturbation of Multiple Eigenvalues of Hermitian Matrices
This paper is concerned with the perturbation of a multiple eigenvalue μ of the Hermitian matrix A = diag(μI, A22) when it undergoes an off-diagonal Email addresses: [email protected] (Ren-Cang Li), [email protected] (Yuji Nakatsukasa), [email protected] (Ninoslav Truhar), [email protected] (Wei-guo Wang) Supported in part by National Science Foundation Grants DMS-0810506 and DMS1115...
متن کاملStructured perturbation for eigenvalues of symplectic matrices: a multiplicative approach
Given an eigenvalue of a symplectic matrix, we analyze its change under small structure-preserving perturbations, i.e., perturbations which maintain the symplectic nature of the matrix. Modelling such perturbations multiplicatively allows us to make use of the first order multiplicative perturbation theory developed in [2] via Newton diagram techniques. This leads to both leading exponents and ...
متن کاملSecond Order Perturbation Theory for Embedded Eigenvalues
We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonia...
متن کاملConstructive Perturbation Theory for Matrices with Degenerate Eigenvalues
Abstract. Let A (ε) be an analytic square matrix and λ0 an eigenvalue of A (0) of multiplicity m ≥ 1. Then under the generic condition, ∂ ∂ε det (λI −A (ε)) |(ε,λ)=(0,λ0) 6= 0, we prove that the Jordan normal form of A (0) corresponding to the eigenvalue λ0 consists of a single m × m Jordan block, the perturbed eigenvalues near λ0 and their eigenvectors can be represented by a single convergent...
متن کاملThe Asymptotic Eigenvalues of First-Order Spectral Differentiation Matrices
We complete and extend the asymptotic analysis of the spectrum of Jacobi Tau approximations that were first considered by Dubiner. The asymptotic formulas for Jacobi polynomials N P ( , ) , , 1 > − α β α β are derived and confirmed by numerical approximations. More accurate results for the slowest decaying mode are obtained. We explain where the large negative eigenvalues come from. Furthermore...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2015
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.05.025