On perturbations of matrix pencils with real spectra, a revisit

Author:
Ren-Cang Li

Journal:
Math. Comp. **72** (2003), 715-728

MSC (2000):
Primary 15A22, 15A42, 65F15

DOI:
https://doi.org/10.1090/S0025-5718-02-01449-7

Published electronically:
May 16, 2002

MathSciNet review:
1954964

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper continues earlier studies by Bhatia and Li on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectra. A unifying framework for creating crucial perturbation equations is developed. With the help of a recent result on generalized commutators involving unitary matrices, new and much sharper bounds are obtained.

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Additional Information

**Ren-Cang Li**

Affiliation:
Department of Mathematics, University of Kentucky, Lexington, KY 40506

Email:
rcli@ms.uky.edu

DOI:
https://doi.org/10.1090/S0025-5718-02-01449-7

Keywords:
Diagonalizable matrix pencil,
definite pencil,
real spectrum,
unitarily invariant norm,
perturbation bound

Received by editor(s):
January 10, 2001

Received by editor(s) in revised form:
August 24, 2001

Published electronically:
May 16, 2002

Additional Notes:
This work was supported in part by the National Science Foundation under Grant No. ACI-9721388 and by the National Science Foundation CAREER award under Grant No. CCR-9875201.

Article copyright:
© Copyright 2002
American Mathematical Society