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Symmetries and Variation of Spectra

Published online by Cambridge University Press:  20 November 2018

R. Bhatia  and
L. Elsner
R. Bhatia
Affiliation:
Indian Statistical Institute, Delhi Center, 7 S.J.S. Sansanwal Marg, New Delhi 110016, India
L. Elsner
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, 4800 Bielefeld 1, Germany
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Abstract

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An interesting class of matrices is shown to have the property that the spectrum of each of its elements is invariant under multiplication by p-th. roots of unity. For this class and for a class of Hamiltonian matrices improved spectral variation bounds are obtained.

Keywords

15 A 4215 A 5765 F 15eigenvaluesspectral variationCarrollian spectraHamiltonian matrices
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 6 , 01 December 1992 , pp. 1155 - 1166
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Bhatia, R., Perturbation Bounds for Matrix Eigenvalues, Pitman Research Notes in Mathematics 162, Longman, Essex, 1987.Google Scholar
2. Bhatia, R., On the rate of change of spectra of operators II, Linear Algebra and Appl. 36(1981), 25–32.Google Scholar
3. Bhatia, R., Davis, C. and Koosis, P., An extremal problem in Fourier analysis with applications to operator theory, J. Functional Anal. 82(1989), 138–150.Google Scholar
4. Bhatia, R., Davis, C. and Mcintosh, A., Perturbation of spectral subspaces and solution of linear operator equations, Linear Algebra and Appl. 52-53.1983), 45–67.Google Scholar
5. Bhatia, R., Eisner, L. and Krause, G., Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix, Linear Algebra and Appl. 142(1990), 195–210.Google Scholar
6. Bhatia, R. and Friedland, S., Variation of Grassman powers and spectra, Linear Algebra and Appl. 40(1981), 1–18.Google Scholar
7. Choi, M.D., Almost commuting matrices need not be nearly commuting, Proc. Amer. Math. Soc. 102(1988), 529–533.Google Scholar
8. Eisner, L., An optimal bound for the spectral variation of two matrices, Linear Algebra and Appl. 71(1985), 77–80.Google Scholar
9. Horn, R. and Johnson, C.R., Matrix Analysis, Cambridge University Press, 1985.Google Scholar
10. Kato, T., Perturbation Theory for Linear Operators, Springer, Berlin, 1976.Google Scholar
11. Krause, G., Obère Schrankenfur die EigenwertvariationkomplexerMatrizen, Dissertation, Bielefeld, 1990.Google Scholar
12. Phillips, D., Improving spectral variation bounds with Chebyshevpolynomials, Linear Algebra and Appl. 133(1990), 165–174.Google Scholar
13. Stewart, G.W. and Ji-guang Sun, Matrix Perturbation Theory, Academic Press, 1990.Google Scholar
14. Wilkinson, J.H., The Algebraic Eigenvalue Problem, Oxford University Press, 1965.Google Scholar