Year: 2026
Type: preprint
Abstract: In this paper the generic behavior of the Jordan structure of symplectic matrices under low-rank structure-preserving transformations is considered. So far, only the case of rank-one perturbations was covered in the literature, and this result is now extended to the case of arbitrary rank $k$. As a key step toward the main result, it is shown that all symplectic matrices that differ from the identity by rank $k$ can be represented as a product of $k$ symplectic reflectors unless they are similar to a diagonalizable matrix having only the eigenvalues $\pm 1$.
Source: arXiv (Cornell University)
Author: Mehl, Christian
Institution: Technische Universität Berlin
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222654686