Eigenvalue perturbation theory of structured real matrices and their sign characteristics under generic structured rank-one perturbations

DOI10.1080/03081087.2015.1053425zbMath1335.15013OpenAlexW2162718543MaRDI QIDQ2787615

Volker Mehrmann, Christian Mehl, André C. M. Ran, Leiba Rodman

Publication date: 4 March 2016

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

Full work available at URL: https://doi.org/10.1080/03081087.2015.1053425

zbMATH Keywords

indefinite inner productperturbation analysiseigenvalue perturbation theorysymmetric matrix polynomialinvariant Lagrangian subspaces\(T\)-even matrix polynomialbounded solution of differential equationsgeneric rank-one perturbationreal \(H\)-symmetric matricesreal \(J\)-Hamiltonian matricesrobustly bounded solution of differential equations

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Linear ordinary differential equations and systems (34A30) Quadratic and bilinear forms, inner products (15A63) Matrices over function rings in one or more variables (15A54) Canonical forms, reductions, classification (15A21)

Related Items (8)

Direct and inverse spectral problems for rank-one perturbations of self-adjoint operators ⋮ Linearizations of Hermitian Matrix Polynomials Preserving the Sign Characteristic ⋮ Unnamed Item ⋮ Complex symplectic Lie algebras with large abelian subalgebras ⋮ Low-rank perturbation of regular matrix pencils with symmetry structures ⋮ Spectra of rank-one perturbations of self-adjoint operators ⋮ Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices ⋮ Spectra of $\mathcal{PT}$-symmetric operators under rank-one perturbations

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