On perturbations of matrix pencils with real spectra. II

Bhatia, Rajendra ; Li, Ren-Cang (1996) On perturbations of matrix pencils with real spectra. II Mathematics of computation, 65 (214). pp. 637-645. ISSN 0025-5718

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Official URL: http://www.ams.org/journals/mcom/1996-65-214/S0025...

Related URL: http://dx.doi.org/10.1090/S0025-5718-96-00699-0


A well-known result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let A and à be two nxn Hermitian matrices, and let λ1,...,λn and λ1,...,λn be their eigenvalues arranged in ascending order. Then diag |||(λ11,...,λnn) ≤|||A-Ã||| for any unitarily invariant norm ||| .|||. In this paper, we generalize this to the perturbation theory for diagonalizable matrix pencils with real spectra. The much studied case of definite pencils is included in this.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
Keywords:Diagonalizable Matrix Pencil; Definite Pencil; Real Spectrum; Unitarily
ID Code:97464
Deposited On:11 Feb 2013 04:57
Last Modified:19 May 2016 09:37

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