The Solution Of Quaternion Matrix Equation

In this paper, we study a quaternion matrix equation under the condition of certain constraints to solve the problem. Its content can be divided into the following three parts.The first part is the preliminary knowledge of the quaternion matrix equation. It includes the background of the quaternion matrix equation, the basic knowledge and the research question and the status quo. The second part is under certain constraints, discussion of the single quaternion matrix equation to solve the problem. This part will study the problem from the perspective of operator. First of all, the mentioned several common constraints will be classified as a class of operator constraints. Then the paper put forward an efficient iterative algorithm, and through a number of lemmas and theorems are given some basic properties of the algorithm. In addition, when the quaternion matrix equation is consistent, then for an arbitrary initial matrix, a solution can be find in a finite number of steps in the absence of roundoff errors. Given a special initial matrix, then through the algorithm we can find out the least F robenius norm solution of it. The third part is under some constraint conditions, the study of the quaternion matrix equations to solve. It is the deeper study on the second portion. we also proposed a similar iterative algorithm. we use this algorithm can seek in some limited conditions of the quaternion matrix equations,the general numerical solution and the least F robenius norm solution of it. As with the second part, this part also gives some properties of the algorithm.