Eigenvalue perturbation theory of symplectic, orthogonal, and unitary matrices under generic structured rank one perturbations

DOI10.1007/s10543-013-0451-3zbMath1291.15061OpenAlexW1977241983MaRDI QIDQ2450889

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

Publication date: 23 May 2014

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-013-0451-3

zbMATH Keywords

eigenvalueindefinite inner productJordan formperturbation analysisorthogonal matrixunitary matrixsymplectic matrixrank one perturbationCayley transformationgeneric perturbation

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Perturbation theory of linear operators (47A55) Quadratic and bilinear forms, inner products (15A63) Canonical forms, reductions, classification (15A21) Orthogonal matrices (15B10)

Related Items (20)

Direct and inverse spectral problems for rank-one perturbations of self-adjoint operators ⋮ Generic Change of the Partial Multiplicities of Regular Matrix Pencils under Low-Rank Perturbations ⋮ Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle ⋮ Generic symmetric matrix pencils with bounded rank ⋮ Generic complete eigenstructures for sets of matrix polynomials with bounded rank and degree ⋮ First order structure-preserving perturbation theory for eigenvalues of symplectic matrices. II ⋮ First Order Structure-Preserving Perturbation Theory for Eigenvalues of Symplectic Matrices ⋮ Bounded Rank Perturbations of Quasi-Regular Pencils Over Arbitrary Fields ⋮ Low-rank perturbation of regular matrix pencils with symmetry structures ⋮ On eigenvalue perturbation bounds for Hermitian block tridiagonal matrices ⋮ Spectra of rank-one perturbations of self-adjoint operators ⋮ Preserving spectral properties of structured matrices under structured perturbations ⋮ A singular M-matrix perturbed by a nonnegative rank one matrix has positive principal minors; is it D-stable? ⋮ Eigenvalue perturbation theory of structured real matrices and their sign characteristics under generic structured rank-one perturbations ⋮ Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices ⋮ ON A PERTURBATION THEORY OF HAMILTONIAN SYSTEMS WITH PERIODIC COEFFICIENTS ⋮ First Order Asymptotic Expansions for Eigenvalues of Multiplicatively Perturbed Matrices ⋮ Rank One Perturbations of Matrix Pencils ⋮ Spectra of $\mathcal{PT}$-symmetric operators under rank-one perturbations ⋮ Random perturbations of matrix polynomials

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