Generic Change of the Partial Multiplicities of Regular Matrix Pencils under Low-Rank Perturbations

DOI10.1137/15M1022069zbMath1342.15004MaRDI QIDQ3185669

Fernando De Terán, Froilán M. Dopico

Publication date: 4 August 2016

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

zbMATH Keywords

regular matrix pencilsWeierstrass canonical formmatrix spectral perturbation theorylow-rank perturbationspartial multiplicities

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Canonical forms, reductions, classification (15A21) Matrix pencils (15A22)

Related Items (20)

A Geometric Description of the Sets of Palindromic and Alternating Matrix Pencils with Bounded Rank ⋮ Generic symmetric matrix pencils with bounded rank ⋮ 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 ⋮ 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 ⋮ Eigenvalue Placement for Regular Matrix Pencils with Rank One Perturbations ⋮ Bounded rank perturbations of regular pencils over arbitrary fields ⋮ On Characteristic Invariants of Matrix Pencils and Linear Relations ⋮ Solving Singular Generalized Eigenvalue Problems. Part II: Projection and Augmentation ⋮ Parameter-Dependent Rank-One Perturbations of Singular Hermitian Or Symmetric Pencils ⋮ Bounded rank perturbations of a regular matrix pencil ⋮ Bounded Rank Perturbations of Quasi-Regular Pencils Over Arbitrary Fields ⋮ Rank-one perturbations of matrix pencils ⋮ Low-rank perturbation of regular matrix pencils with symmetry structures ⋮ Weierstrass Structure and Eigenvalue Placement of Regular Matrix Pencils under Low Rank Perturbations ⋮ An explicit description of the irreducible components of the set of matrix pencils with bounded normal rank ⋮ Rank One Perturbations of Matrix Pencils ⋮ Double generalized majorization and diagrammatics

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