Perturbation Bounds for Williamson's Symplectic Normal Form

  title={Perturbation Bounds for Williamson's Symplectic Normal Form},
  author={Martin Idel and S. Gaona and M. Wolf},
  journal={arXiv: Spectral Theory},
Given a real-valued positive semidefinite matrix, Williamson proved that it can be diagonalised using symplectic matrices. The corresponding diagonal values are known as the symplectic spectrum. This paper is concerned with the stability of Williamson's decomposition under perturbations. We provide norm bounds for the stability of the symplectic eigenvalues and prove that if $S$ diagonalises a given matrix $M$ to Williamson form, then $S$ is stable if the symplectic spectrum is nondegenerate… Expand
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