Perturbations of Jordan matrices

JOURNAL OF APPROXIMATION THEORY

卷:156

Article

Davies, E. B.¹  Hager, Mildred^2,3 

[1] Kings Coll London, Dept Math, London WC2R 2LS, England

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[3] Lund Univ, Matemat Ctr, S-22100 Lund, Sweden

关键词: Jordan matrices;    Eigenvalues;    Perturbations;    Lidskii;    Random matrices;    Spectrum;    Pseudospectrum;   

DOI  :  10.1016/j.jat.2008.04.021

来源: Elsevier

【 摘 要 】

We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In the case of random perturbations we obtain explicit estimates which show that as the size of the matrix increases, most of the eigenvalues of the perturbed matrix converge to a certain circle with centre at the origin. In the case of finite rank perturbations we completely determine the spectral asymptotics as the size of the matrix increases. (C) 2008 Elsevier Inc. All fights reserved.

【 授权许可】

Free