Products of positive definite symplectic matrices

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Dissertation

Publication Date

2020

Abstract

We show that every symplectic matrix is a product of five positive definite symplectic matrices and five is the best in the sense that there are symplectic matrices which are not product of less. In Chapter 1, we provide a historical background and motivation behind the study. We highlight the important works in the subject that lead to the formulation of the problem. In Chapter 2, we present the necessary mathematical prerequisites and construct a symplectic ∗

congruence canonical form for Sp(2n, C). In Chapter 3, we give the proof of the main the- orem. In Chapter 4, we discuss future research. The main results in this dissertation can be found in [18].

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Disciplines

Mathematics

Keywords

Symplectic groups; Positive-definite functions

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