Document Type

Thesis

Degree Name

Master of Science (MSc)

Department

Mathematics

Program Name/Specialization

<--Please Select Program Name/Specialization-->

Faculty/School

Faculty of Science

First Advisor

Dr. Kaiming Zhao

Advisor Role

Thesis Supervisor

Abstract

This thesis aims to study two-sided quaternionic equations and develop efficient methods for solving them.

By introducing the notion of the discriminant space, we completely characterized the solutions of general two-sided linear quaternionic equations and established analogous results for systems of equations and equations involving conjugation.

We then addressed the nonlinear case x2 = axb by deriving explicit formula solutions. The main method is to introduce an efficient way of eliminating the number of real parameters from a, b. By using the Lefschetz fixed point theorem, we can show that any binomial polynomial quaternionic equation has a non-zero solution, and this result cannot be further generalized.

Convocation Year

2026

Convocation Season

Fall

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Available for download on Friday, October 30, 2026

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