Weierstrass Structure and Eigenvalue Placement of Regular Matrix Pencils under Low Rank Perturbations

DOI10.1137/18M1200245zbMath1416.15012OpenAlexW2936331478MaRDI QIDQ4631269

Alicia Roca, Itziar Baragaña

Publication date: 24 April 2019

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1200245

zbMATH Keywords

matrix pencillow rank perturbationspectral perturbation theoryWeierstrass structure

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Perturbation theory of linear operators (47A55) Matrix pencils (15A22)

Related Items (8)

The number of distinct eigenvalues of a regular pencil and of a square matrix after rank perturbation ⋮ Fixed rank perturbations of regular matrix pencils ⋮ On the Change of the Weyr Characteristics of Matrix Pencils After Rank-One Perturbations ⋮ Bounded rank perturbations of regular pencils over arbitrary fields ⋮ On Characteristic Invariants of Matrix Pencils and Linear Relations ⋮ Rank-one perturbations of matrix pencils ⋮ Lower and upper bounds for the number of distinct eigenvalues of a perturbed regular matrix pencil ⋮ Rank One Perturbations of Matrix Pencils

Cites Work

• Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations
• Typical changes in spectral properties under perturbation by an operator of rank one.
• Partially specified matrices and operators: classification, completion, applications
• The rank distance problem for pairs of matrices and a completion of quasi-regular matrix pencils
• Generic rank-one perturbations of structured regular matrix pencils
• On the change in the spectral properties of a matrix under perturbations of sufficiently low rank
• Generic Change of the Partial Multiplicities of Regular Matrix Pencils under Low-Rank Perturbations
• Sign Characteristics of Regular Hermitian Matrix Pencils under Generic Rank-1 and Rank-2 Perturbations
• The Jordan forms of AB and BA
• Low Rank Perturbation of Weierstrass Structure
• The rank of the difference of matrices with prescribed similarity classes
• The rank of the difference of matrices with prescribed invariant factors
• Invariant Factors Under Rank One Perturbations
• Low Rank Perturbation of Jordan Structure
• Pole Assignment and Additive Perturbations of Fixed Rank
• Eigenvalue Placement for Regular Matrix Pencils with Rank One Perturbations
• Low Rank Perturbation of Kronecker Structures without Full Rank
• Matrices

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