Eigenvalues of Graded Matrices and the Condition Numbers of a
Multiple Eigenvalue
Eigenvalues of Graded Matrices and the Condition Numbers of a
Multiple Eigenvalue
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Date
1998-10-15
Authors
Stewart, G. W.
Zhang, G.
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Abstract
This paper concerns two closely related topics: the behavior of the
eigenvalues of graded matrices and the perturbation of a nondefective
multiple eigenvalue. We will show that the eigenvalues of a graded matrix
tend to share the graded structure of the matrix and give precise
conditions insuring that this tendency is realized. These results are
then applied to show that the secants of the canonical angles between the
left and right invariant subspaces of a multiple eigenvalue tend to
characterize its behavior when its matrix is slightly perturbed.
(Also cross-referenced as UMIACS-TR-90-31)
Appeared in Numerische Mathematik 58 (1991) 703--712.