Symplectic Elimination
Group Theory
2025-07-29 v1 Systems and Control
Systems and Control
Symplectic Geometry
Spectral Theory
Abstract
We develop the symplectic elimnation algorithm. This algorithm using simple row operations reduce a symplectic matrix to a diagonal matrix. This algorithm gives rise to a decomposition of an arbitrary matrix into a product of a symplectic matrix and a reduced matrix. This decomposition is similar to the SR decomposition studied for a long time, which is analogous to the QR decomposition.
Cite
@article{arxiv.2507.20563,
title = {Symplectic Elimination},
author = {Ayan Mahalanobis},
journal= {arXiv preprint arXiv:2507.20563},
year = {2025}
}