Generic Eigenstructures of Hermitian Pencils

DOI10.1137/22m1523297arXiv2209.10495WikidataQ129964836 ScholiaQ129964836MaRDI QIDQ6180361

Froilán M. Dopico, Fernando De Terán, Andrii Dmytryshyn

Publication date: 19 January 2024

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

Full work available at URL: https://arxiv.org/abs/2209.10495

zbMATH Keywords

bundleorbitrankcongruenceclosurematrix pencilsign characteristicstrict equivalenceHermitian matrix pencil

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Canonical forms, reductions, classification (15A21) Matrix pencils (15A22)

Cites Work

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• On the sign characteristics of Hermitian matrix polynomials
• An explicit description of the irreducible components of the set of matrix pencils with bounded normal rank
• The codimension of singular matrix pairs
• The solution of the equation \(XA+AX^T=0\) and its application to the theory of orbits
• The computation of Kronecker's canonical form of a singular pencil
• Pencils of complex and real symmetric and skew matrices
• On perturbations and the equivalence orbit of a matrix pencil
• Computing stable eigendecompositions of matrix pencils
• The algebraic structure of pencils and block Toeplitz matrices
• The dimension of matrices (matrix pencils) with given Jordan (Kronecker) canonical forms
• Skew-symmetric matrix pencils: Codimension counts and the solution of a pair of matrix equations
• Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade
• Miniversal deformations of pairs of symmetric matrices under congruence
• Generic symmetric matrix pencils with bounded rank
• Low-rank perturbation of regular matrix pencils with symmetry structures
• On the Sign Characteristics of Selfadjoint Matrix Polynomials
• Polynomial Eigenvalue Problems: Theory, Computation, and Structure
• A Geometric Description of the Sets of Palindromic and Alternating Matrix Pencils with Bounded Rank
• Points of Continuity of the Kronecker Canonical Form
• A Note on Generic Kronecker Orbits of Matrix Pencils with Fixed Rank
• Accurate Solutions of Ill-Posed Problems in control theory
• The generalized eigenstructure problem in linear system theory
• A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification-Enhanced Staircase Algorithm
• A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations
• The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part I
• Strongly Minimal Self-Conjugate Linearizations for Polynomial and Rational Matrices
• Solving Singular Generalized Eigenvalue Problems by a Rank-Completing Perturbation
• Orbit Closure Hierarchies of Skew-symmetric Matrix Pencils
• Canonical Forms for Hermitian Matrix Pairs under Strict Equivalence and Congruence
• Symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
• ON MATRICES DEPENDING ON PARAMETERS

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