Structure-preserving eigenvalue modification of symplectic matrices and matrix pencils
Numerical Analysis
2023-02-01 v1 Numerical Analysis
Abstract
A famous theorem by R. Brauer shows how to modify a single eigenvalue of a matrix by a rank-one update without changing the remaining eigenvalues. A generalization of this theorem (due to R. Rado) is used to change a pair of eigenvalues of a symplectic matrix S in a structure-preserving way to desired target values. Universal bounds on the relative distance between S and the newly constructed symplectic matrix S' with modified spectrum are given. The eigenvalues Segre characteristics of S' are related to those of S and a statement on the eigenvalue condition numbers of S' is derived. The main results are extended to matrix pencils.
Keywords
Cite
@article{arxiv.2301.13548,
title = {Structure-preserving eigenvalue modification of symplectic matrices and matrix pencils},
author = {Philip Saltenberger},
journal= {arXiv preprint arXiv:2301.13548},
year = {2023}
}