Eigenvalues of graded matrices and the condition numbers of a multiple eigenvalue | Zendy

G. W. Stewart | Zendy; G. Zhang | Zendy

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Eigenvalues of graded matrices and the condition numbers of a multiple eigenvalue

Author(s) -

G. W. Stewart,

G. Zhang

Publication year - 1990

Publication title -

numerische mathematik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.214

H-Index - 90

eISSN - 0945-3245

pISSN - 0029-599X

DOI - 10.1007/bf01385650

Subject(s) - eigenvalues and eigenvectors , mathematics , eigenvalue perturbation , matrix differential equation , spectrum of a matrix , perturbation (astronomy) , matrix (chemical analysis) , mathematical analysis , invariant (physics) , pure mathematics , differential equation , mathematical physics , physics , quantum mechanics , materials science , composite material

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.

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