Products of symplectic normal matrices

Authors

Ralph John de la Cruz, University of the Philippines Diliman
Darryl Q. Granario

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

Linear Algebra and its Applications

Volume

543

First Page

162

Last Page

172

Publication Date

2018

Abstract

A matrix A ∈ M2n(C) is symplectic if AT 0 In −In 0

A = 0 In −In 0We show that every symplectic matrix is a product of a symplectic unitary and a symplectic skew-Hermitian matrix. We show that every symplectic matrix is a product of four symplectic skew-Hermitian matrices or a product of four symplectic Hermitian matrices. We give the possible Jordan canonical forms of symplectic matrices which can be written as a product of a symplectic Hermitian and a matrix which is either symplectic Hermitian or symplectic skew-Hermitian.

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Recommended Citation

de la Cruz, R., & Granario, D. Q. (2018). Products of symplectic normal matrices. Linear Algebra and its Applications, 543, 162-172. Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/11357

Disciplines

Mathematics

Keywords

Matrices; Symplectic groups; Decomposition (Mathematics)

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