On perturbations of matrix pencils with real spectra. II
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- by Rajendra Bhatia and Ren-Cang Li PDF
- Math. Comp. 65 (1996), 637-645 Request permission
Abstract:
A well-known result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let $A$ and $\widetilde A$ be two $n\times n$ Hermitian matrices, and let $\lambda _1$, …, $\lambda _{n}$ and $\widetilde \lambda _1$, …, $\widetilde \lambda _{n}$ be their eigenvalues arranged in ascending order. Then $\left \Vvert \operatorname {diag} (\lambda _1- \widetilde \lambda _1,\ldots ,\lambda _n- \widetilde \lambda _n) \right \Vvert \le \left \Vvert A-\widetilde A \right \Vvert$ for any unitarily invariant norm $\Vvert \cdot \Vvert$. 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.References
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Additional Information
- Rajendra Bhatia
- Affiliation: Indian Statistical Institute, 7, S. J. S. Sansanwal Marg, New Delhi – 110016, India
- Email: rbh@isid.ernet.in
- Ren-Cang Li
- Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, California 94720
- Email: li@math.berkeley.edu
- Received by editor(s): April 13, 1994
- Received by editor(s) in revised form: August 4, 1994
- Additional Notes: The first author thanks NSERC Canada for financial support.
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 637-645
- MSC (1991): Primary 15A22, 15A42, 65F15
- DOI: https://doi.org/10.1090/S0025-5718-96-00699-0
- MathSciNet review: 1333304