Low rank perturbation of regular matrix polynomials

DOI10.1016/j.laa.2008.09.002zbMath1190.15025OpenAlexW2003844998MaRDI QIDQ958049

Froilán M. Dopico, Fernando De Terán

Publication date: 2 December 2008

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.09.002

zbMATH Keywords

elementary divisorsregular matrix polynomialslow rank perturbationsmatrix spectral perturbation theory

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Matrices over function rings in one or more variables (15A54) Canonical forms, reductions, classification (15A21)

Related Items (11)

Generic complete eigenstructures for sets of matrix polynomials with bounded rank and degree ⋮ Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade ⋮ Bounded rank perturbations of a regular matrix pencil ⋮ Low-rank perturbation of regular matrix pencils with symmetry structures ⋮ Eigenvalue perturbation theory of symplectic, orthogonal, and unitary matrices under generic structured rank one perturbations ⋮ Generic Symmetric Matrix Polynomials with Bounded Rank and Fixed Odd Grade ⋮ Rank distance problem for pairs of matrices ⋮ The rank distance problem for pairs of matrices and a completion of quasi-regular matrix pencils ⋮ On the distance to singularity via low rank perturbations ⋮ Fast and Backward Stable Computation of Roots of Polynomials ⋮ Random perturbations of matrix polynomials

Cites Work

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• Interlacing inequalities for invariant factors
• Imbedding conditions for \(\lambda\)-matrices
• Assigning the Kronecker invariants of a matrix pencil by row or column completions
• The change of the Jordan structure under one row perturbations
• Typical changes in spectral properties under perturbation by an operator of rank one.
• On the change in the spectral properties of a matrix under perturbations of sufficiently low rank
• Low Rank Perturbation of Weierstrass Structure
• Invariant Factors Under Rank One Perturbations
• Low Rank Perturbation of Jordan Structure
• A Remark on Perturbations of Compact Operators.
• Pole Assignment and Additive Perturbations of Fixed Rank
• Low Rank Perturbation of Kronecker Structures without Full Rank
• Laurent expansion for the determinant of the matrix of scalar resolvents

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