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Eigenvalues of graded matrices and the condition numbers of a multiple eigenvalue (1990)

Stewart, G. W. ; Zhang, G.

Springer

Numerische Mathematik 58 (1990), S. 703-712

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ISSN: 0945-3245

Keywords: AMS(MOS): 65F15 ; CR: G1.3

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary 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 of a multiple eigenvalue tend to characterize its behavior when its matrix is slightly perturbed.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01385650

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