Diagonalizable Matrices as a Result of Rank-One Perturbations of Nilpotent Matrices

Diagonalizable Matrices as a Result of Rank-One Perturbations of Nilpotent Matrices

It is known that every normal matrix with a simple spectrum can be obtained by a rank-one perturbation of some nilpotent matrix . In this assertion, a normal matrix can actually be replaced by an arbitrary diagonalizable matrix. We determine the possible values of the index of nilpotency of the matr...

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Bibliographic Details
Published in:Moscow University computational mathematics and cybernetics Vol. 46; no. 2; pp. 76 - 80
Main Authors: Ikramov, Kh. D., Chugunov, V. N.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 2022
Springer Nature B.V
Subjects:
Mathematics
Mathematics and Statistics
Perturbation
index of nilpotency
diagonalizable matrix
nilpotent matrix
geometric multiplicity of an eigenvalue
Online Access:Get full text
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Summary:It is known that every normal matrix with a simple spectrum can be obtained by a rank-one perturbation of some nilpotent matrix . In this assertion, a normal matrix can actually be replaced by an arbitrary diagonalizable matrix. We determine the possible values of the index of nilpotency of the matrix .
ISSN:0278-6419
1934-8428
DOI:10.3103/S0278641922020042