Rank One Perturbations of Matrix Pencils

DOI10.1137/19M1279411zbMath1472.15018MaRDI QIDQ5854654

Marko Stošić, Marija Dodig

Publication date: 17 March 2021

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

zbMATH Keywords

matrix pencilslow rank perturbationsone-row completions

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Perturbation theory of linear operators (47A55) Canonical forms, reductions, classification (15A21) Matrix pencils (15A22)

Related Items

Completion of matrix pencils with a single rank restriction, On the Change of the Weyr Characteristics of Matrix Pencils After Rank-One Perturbations, On Characteristic Invariants of Matrix Pencils and Linear Relations, Bounded rank perturbations of a regular matrix pencil, Bounded Rank Perturbations of Quasi-Regular Pencils Over Arbitrary Fields, Double generalized majorization, Double generalized majorization and diagrammatics

Cites Work

• Perturbation theory of selfadjoint matrices and sign characteristics under generic structured rank one perturbations
• Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations
• Explicit solution of the row completion problem for matrix pencils
• On convexity of polynomial paths and generalized majorizations
• Typical changes in spectral properties under perturbation by an operator of rank one.
• Completion up to a matrix pencil with column minimal indices as the only nontrivial Kronecker invariants
• 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
• Eigenvalue perturbation theory of symplectic, orthogonal, and unitary matrices under generic structured rank one perturbations
• Matrix pencils completion problems
• On the change in the spectral properties of a matrix under perturbations of sufficiently low rank
• On the distance to singularity via low rank perturbations
• Jordan forms of real and complex matrices under rank one perturbations
• Low-rank damping modifications and defective systems
• Combinatorics of Column Minimal Indices and Matrix Pencil Completion Problems
• 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
• Column completion of a pair of matrices
• Low Rank Perturbation of Weierstrass Structure
• The rank of the difference of matrices with prescribed similarity classes
• Invariant Factors Under Rank One Perturbations
• Low Rank Perturbation of Jordan Structure
• The General Matrix Pencil Completion Problem: A Minimal Case
• Weierstrass Structure and Eigenvalue Placement of Regular Matrix Pencils under Low Rank Perturbations
• Pole Assignment and Additive Perturbations of Fixed Rank
• Generic rank-k Perturbations of Structured Matrices
• Eigenvalue Placement for Regular Matrix Pencils with Rank One Perturbations
• Low Rank Perturbation of Kronecker Structures without Full Rank