Quaternion polynomial matrices: computing normal forms
The applications of quaternion polynomial matrices appear in many fields like applied mathematics, engineering and statistics. In this thesis, we discuss some well-known normal forms of quaternion polynomial matrices. In the first chapter, we outline some of the basic mathematical definitions and results relevant to quaternions. In the second chapter, we introduce some properties of polynomial matrices. In the third chapter, we discuss some properties of quaternion polynomial matrices. Firstly, the definitions and algorithms of greatest common right divisors (GCRDs) and least common left multiples (LCLMs) of the quaternion polynomials are given. Secondly, we discuss the algorithms for computing several normal forms including the Hermite form, the Smith form and the Popov form. The Maple codes for constructing examples are presented in the fourth chapter.