四元数矩阵方程∑A^iXB_i=E

The Quaternion Matrix Equation A iXB i=E

设ＨＦ为域Ｆ上广义四元数可除代数，其中ｃｈａｒＦ≠２．应用伴随矩阵与矩阵表示方法，本文得到ＨＦ上矩阵方程∑ｋｉ＝０ＡｉＸＢｉ＝Ｅ有解或有唯一解的几个充要条件，并且给出了几个解的公式．

Let H F be the generalized quaternion division algebra over a field F with  char F≠2. By using the adjoint matrix and the method of repersentation matrix, this paper obtains several necessary and sufficient conditions for existence of a solution or a unique solution to the matrix equation ki=0A iXB i=E over H F, and gives some explicit formulas of solutions.