| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 9498611 | Linear Algebra and its Applications | 2005 | 8 Pages |
Abstract
LetA=H1EâEH2andAâ¼=H1OOH2 be Hermitian matrices with eigenvalues λ1 ⩾ â¯Â ⩾ λk and λâ¼1⩾â¯â©¾Î»â¼k, respectively. Denote by â¥E⥠the spectral norm of the matrix E, and η the spectral gap between the spectra of H1 and H2. It is shown that|λi-λâ¼i|⩽2âEâ2η+η2+4âEâ2, which improves all the existing results. Similar bounds are obtained for singular values of matrices under block perturbations.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chi-Kwong Li, Ren-Cang Li,