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A note on eigenvalues of perturbed Hermitian matrices

✍ Scribed by Chi-Kwong Li; Ren-Cang Li

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
183 KB
Volume
395
Category
Article
ISSN
0024-3795

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✦ Synopsis

be Hermitian matrices with eigenvalues Ξ» 1 β€’ β€’ β€’ Ξ» k and Ξ» 1 β€’ β€’ β€’ Ξ» k , respectively. Denote by E the spectral norm of the matrix E, and Ξ· the spectral gap between the spectra of H 1 and H 2 . It is shown that

, which improves all the existing results. Similar bounds are obtained for singular values of matrices under block perturbations.

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