Global Properties of Eigenvalues of Parametric Rank One Perturbations for Unstructured and Structured Matrices

被引：6

作者：

Ran, Andre C. M. ^{[1
,2
]}

Wojtylak, Michal ^{[3
]}

机构：

[1] Vrije Univ Amsterdam, Fac Exacte Wetenschappen, Afdeling Wiskunde, De Boelelaan 1111, NL-1081 HV Amsterdam, Netherlands

[2] North West Univ, Res Focus Pure & Appl Analyt, Potchefstroom, South Africa

[3] Uniwersytet Jagiellonski, Inst Matemat, Wydzia Matemat & Informat, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2021年 / 15卷 / 03期

关键词：

Eigenvalue perturbation theory; SPECTRAL PROPERTIES; OPERATOR; ZEROS;

D O I：

10.1007/s11785-021-01094-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

General properties of eigenvalues of A + tau uv* as functions of tau is an element of C or tau is an element of R or T = tau = e(i theta) on the unit circle are considered. In particular, the problem of existence of global analytic formulas for eigenvalues is addressed. Furthermore, the limits of eigenvalues with tau -> infinity are discussed in detail. The following classes of matrices are considered: complex (without additional structure), real (without additional structure), complex H-selfadjoint and real J-Hamiltonian.

引用

页数：27

共 39 条

[1] Global Properties of Eigenvalues of Parametric Rank One Perturbations for Unstructured and Structured Matrices
André C. M. Ran
Michał Wojtylak
Complex Analysis and Operator Theory, 2021, 15
[2] Global Properties of Eigenvalues of Parametric Rank One Perturbations for Unstructured and Structured Matrices II
André C. M. Ran
Michał Wojtylak
Complex Analysis and Operator Theory, 2022, 16
[3] Global Properties of Eigenvalues of Parametric Rank One Perturbations for Unstructured and Structured Matrices II
Ran, Andre C. M.
Wojtylak, Michal
COMPLEX ANALYSIS AND OPERATOR THEORY, 2022, 16 (06)
[4] Eigenvalues of rank one perturbations of unstructured matrices
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[5] Eigenvalues of parametric rank-one perturbations of matrix pencils
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[6] Inequalities for the eigenvectors associated to extremal eigenvalues in rank one perturbations of symmetric matrices
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[7] Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations
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LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 435 (03) : 687 - 716
[8] Rank One Perturbations of Diagonal Operators Without Eigenvalues
Klaja, Hubert
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2015, 83 (03) : 429 - 445
[9] Rank One Perturbations of Diagonal Operators Without Eigenvalues
Hubert Klaja
Integral Equations and Operator Theory, 2015, 83 : 429 - 445
[10] The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
Benaych-Georges, Florent
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ADVANCES IN MATHEMATICS, 2011, 227 (01) : 494 - 521

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