A System Of Matrix Equations Over The Commutative Quaternion Ring

Sylvester-type matrix equations are widely used in signal processing,dynamical sys-tems,control theory,image restoration.In this dissertation,we study the necessary and sufficient condition for the solvability of a system of two-sided coupled Sylvester type ma-trix equations over commutative quaternion ring.We give an expression of the general solution to the system when it is consistent,and give the least square solution when it is inconsistent.The main contents of this dissertation are organized as follows.In Chapter 2,based on the definition of commutative quaternion and the complex representation of commutative quaternion matrix,we study some properties of complex representation,and present an application of complex representation.Secondly,we study the structure of(RY U)on commutative quaternion ring,and give the related results.In Chapter 3,we present a solvable condition and an expression of the general solu-tion to the following two-sided coupled Sylvester-type matrix equations over commutative quaternion ring(?)where X,Y,Z are unknown matrices and the other matrices are given with appropriate size.In addition,we derive an expression of the least square solution to the system when it is inconsistent.In Chapter 4,we give a numerical algorithm and design an example to verify it.