辛矩陣與矩陣對之分類

Abstract

無中文摘要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.