Quaternion polynomial matrices: computing normal forms
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Date
2017
Authors
Liu, Yijian
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Abstract
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.
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Mathematics