The Classification of Symplectic Matrices and Pairs

• Main Authors: You, Yi-Siang, 游逸翔
• Other Authors: Shieh, Shih-Feng
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/e5krjp

碩士 === 國立臺灣師範大學 === 數學系 === 105 === In applications a symplectic matrix is often required to be partitioned with a nonsingular block. By applying the complementary bases theorem of Dopico and Johnson in [3], we can rearrange a symplectic matrix with a swap matrix to obtain a nonsingular block. We classify symplectic matrices with corresponding swap matrices. Moreover, a rearrangement of symplectic pair by Mehrmann and Poloni in [8] merges a regular symplectic pair into a symplectic matrix. Therefore we can classify regular symplectic pairs with similar approach.