Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-08T21:33:43.222Z Has data issue: false hasContentIssue false
  • English
  • Français

Perturbation Bound for the Eigenvalues of a Singular Diagonalizable Matrix

Published online by Cambridge University Press:  28 May 2015

Yimin Wei  and
Yifei Qu
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: [email protected], [email protected]
Corresponding author. Email: [email protected]
Get access

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].

Keywords

15A0965F20Bauer-Fike theoremdiagonalizable matrixgroup inverseJordan canonical form
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 1 , February 2014 , pp. 88 - 94
Copyright
Copyright © Global-Science Press 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
[2]Bauer, F. and Fike, C., Norms and exclusion theorems, Numer. Math. 2, 137–141 (1960).Google Scholar
[3]Eisenstat, S.C., A perturbation bound for the eigenvalues of a singular diagonalizable matrix, Linear Algebra Appl. 416, 742–744 (2006).Google Scholar
[4]Eisenstat, S.C. and Ipsen, I.C.F., Three absolute perturbation bounds for matrix eigenvalues imply relative bounds, SIAM J. Matrix Anal. Appl. 20, 149–158 (1999).CrossRefGoogle Scholar
[5]Jin, X. and Wei, Y., Numerical Linear Algebra and Its Applications, Science Press, Beijing, 2004; 4th printing, Science Press and Alpha Science International Ltd., Oxford, UK, 2012.Google Scholar
[6]Shi, X. and Wei, Y., A sharp version of Bauer-Fike's theorem, J. Comput. Appl. Math. 236, 3218–3227 (2012).CrossRefGoogle Scholar
[7]Wei, Y., Li, X., Bu, F., and Zhang, F., Relative perturbation bounds for the eigenvalues of singular matrices, 2005. Available from: http://www.math.umn.edu/~buxxx001/publications/R_perturbation.pdf.Google Scholar
[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, 765–771 (2006).Google 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