Jordan forms of real and complex matrices under rank one perturbations.

A.C.M. Ran; Chr. Mehl; V. Mehrmann; L. Rodman

doi:10.7153/oam-07-22

Jordan forms of real and complex matrices under rank one perturbations.

A.C.M. Ran, Chr. Mehl, V. Mehrmann, L. Rodman

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

New perturbation results for the behavior of eigenvalues and Jordan forms of real and complex matrices under generic rank one perturbations are discussed. Several results that are available in the complex case are proved as well for the real case and the assumptions on the genericity are weakened. Rank one perturbations that lead to maximal algebraic multiplicities of the "new" eigenvalues are also discussed.

Original language	English
Pages (from-to)	381-398
Journal	Operators and Matrices
Volume	7
DOIs	https://doi.org/10.7153/oam-07-22
Publication status	Published - 2013

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10.7153/oam-07-22

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title = "Jordan forms of real and complex matrices under rank one perturbations.",

abstract = "New perturbation results for the behavior of eigenvalues and Jordan forms of real and complex matrices under generic rank one perturbations are discussed. Several results that are available in the complex case are proved as well for the real case and the assumptions on the genericity are weakened. Rank one perturbations that lead to maximal algebraic multiplicities of the {"}new{"} eigenvalues are also discussed.",

author = "A.C.M. Ran and Chr. Mehl and V. Mehrmann and L. Rodman",

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journal = "Operators and Matrices",

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T1 - Jordan forms of real and complex matrices under rank one perturbations.

AU - Ran, A.C.M.

AU - Mehl, Chr.

AU - Mehrmann, V.

AU - Rodman, L.

PY - 2013

Y1 - 2013

N2 - New perturbation results for the behavior of eigenvalues and Jordan forms of real and complex matrices under generic rank one perturbations are discussed. Several results that are available in the complex case are proved as well for the real case and the assumptions on the genericity are weakened. Rank one perturbations that lead to maximal algebraic multiplicities of the "new" eigenvalues are also discussed.

AB - New perturbation results for the behavior of eigenvalues and Jordan forms of real and complex matrices under generic rank one perturbations are discussed. Several results that are available in the complex case are proved as well for the real case and the assumptions on the genericity are weakened. Rank one perturbations that lead to maximal algebraic multiplicities of the "new" eigenvalues are also discussed.

U2 - 10.7153/oam-07-22

DO - 10.7153/oam-07-22

M3 - Article

SN - 1846-3886

VL - 7

SP - 381

EP - 398

JO - Operators and Matrices

JF - Operators and Matrices

ER -

Jordan forms of real and complex matrices under rank one perturbations.

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