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Perturbation Bound for the Eigenvalues of a Singular Diagonalizable Matrix

Published online by Cambridge University Press:  28 May 2015

Yimin Wei*
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, 200433, China Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China
Yifei Qu*
Affiliation:
Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China
*
Corresponding author. Email: ymwei@fudan.edu.cn, yimin.wei@gmail.com
Corresponding author. Email: 08302010026@fudan.edu.cn
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Abstract

In this short note, we present a sharp upper bound for the perturbation of eigenvalues of a singular diagonalizable matrix given by Stanley C. Eisenstat [3].

Type
Research Article
Copyright
Copyright © Global-Science Press 2014

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References

[1]Ben-Israel, A. and Greville, T.N.E., Generalized Inverses: Theoryand Applications, Wiley, New York, 1974; 2nd Edition, Springer, New York, 2003.Google Scholar
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[8]Wei, Y., Li, X., Bu, F., and Zhang, F., Relative perturbation bounds for the eigenvalues of diagonal-izable and singular matrices-application of perturbation theory for simple invariant subspaces, Linear Algebra Appl. 419, 765771 (2006).CrossRefGoogle Scholar
[9]Wei, Y., Generalized inverses of matrices, Chapter 27 in Handbook of Linear Algebra, 2nd Edition, Hogben, L. (Ed.), Chapman and Hall/CRC, 2014.Google Scholar

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