Summary
This paper concerns with measures of the sensitivity of a nondefective multiple eigenvalue of a matrix. Different condition numbers are introduced starting from directional derivatives of the multiple eigenvalue. Properties of the condition numbers defined by Stewart and Zhang [4] are studied; especially, the Wilkinson's theorem on matrices with a very ill-conditioned eigenproblem is extended.
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References
Demmel, J. (1987): On condition numbers and the distance to the nearest ill-posed problem. Numer. Math.51, 251–289
Stewart, G.W. (1977): On the perturbation of pseudo-inverses, projections and linear least squares problem. SIAM Rev.19, 634–662
Stewart, G.W., Sun, J.-G. (1990): Matrix Perturbation Theory. Academic Press, Boston
Stewart, G.W., Zhang, G. (1991): Eigenvalues of graded matrices and the condition numbers of a multiple eigenvalue. Numer. Math.58, 703–712
Sun, J.-G. On the sensitivity of semisimple multiple eigenvalues. J. Comput. Math. (to appear)
Sun, J.-G. (1990): Multiple eigenvalue sensitivity analysis. Linear Algebra Appl.137/138, 183–211
Wilkinson, J.H. (1965): The Algebraic Eigenvalue Problem. Clarendon, Oxford
Wilkinson, J.H. (1972): Note on matrices with a very ill-conditioned eigenproblem. Numer. Math.19, 176–178
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This research was supported by the Institute for Advanced Computer Studies of the University of Maryland and the Swedish Natural Science Research Council
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Sun, Jg. On condition numbers of a nondefective multiple eigenvalue. Numer. Math. 61, 265–275 (1992). https://doi.org/10.1007/BF01385508
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DOI: https://doi.org/10.1007/BF01385508