On the sign characteristics of Hermitian matrix polynomials

DOI10.1016/j.laa.2016.09.002zbMath1352.15027OpenAlexW2177869558MaRDI QIDQ331179

Vanni Noferini, Volker Mehrmann, Françoise Tisseur, Hong-guo Xu

Publication date: 26 October 2016

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

Full work available at URL: https://doi.org/10.1016/j.laa.2016.09.002

zbMATH Keywords

perturbation theoryMöbius transformationsHamiltonian systemsHermitian matrix polynomialinfinite eigenvaluessign characteristicsign characteristic at infinitysign featuresignature constraint

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Matrices over function rings in one or more variables (15A54) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)

Related Items (12)

Linearizations of Hermitian Matrix Polynomials Preserving the Sign Characteristic ⋮ Unnamed Item ⋮ Constructing Strong Linearizations of Matrix Polynomials Expressed in Chebyshev Bases ⋮ On the Rellich eigendecomposition of para-Hermitian matrices and the sign characteristics of \(\ast \)-palindromic matrix polynomials ⋮ Parameter-Dependent Rank-One Perturbations of Singular Hermitian Or Symmetric Pencils ⋮ Generic Eigenstructures of Hermitian Pencils ⋮ The Deformed Graph Laplacian and Its Applications to Network Centrality Analysis ⋮ Low-rank perturbation of regular matrix pencils with symmetry structures ⋮ On the sign characteristic of Hermitian linearizations in \(\mathbb{DL}(P)\) ⋮ Beyond non-backtracking: non-cycling network centrality measures ⋮ Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory ⋮ Inertia laws and localization of real eigenvalues for generalized indefinite eigenvalue problems

Uses Software

• mftoolbox

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