Annals of Mathematical Sciences and Applications

Volume 4 (2019)

Number 1

The classification of symplectic matrices and pairs

Pages: 35 – 52

DOI: https://dx.doi.org/10.4310/AMSA.2019.v4.n1.a2

Authors

Yueh-Cheng Kuo (Department of Applied Mathematics, National University of Kaohsiung, Taiwan)

Shih-Feng Shieh (Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan)

Yi-Siang You (Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan)

Abstract

In this paper we classify symplectic matrices and regular symplectic pairs. By applying a complementary bases theorem (Lemma 2.2), the classification is indexed by symplectic swap matrices. Both symplectic matrices and regular symplectic pairs are classified into $2^n$ categories. We show that the classification is minimal and each category forms an open set.

Keywords

symplectic matrices, symplectic pairs, complementary bases theorem, minimal classification

Full Text (PDF format)

Received 13 July 2018

Published 26 February 2019