摘要
设 HF 为域 F上的广义四元数除环 ,Ch F≠ 2 .本文利用拟线性变换 T(X) =AX - DXB讨论HF 上矩阵方程 AX - DXB =R的求解问题 ,获得了上方程存在 (唯一 )解的几个充分必要条件 ,并给出了解的显式公式 .
Let H\-F be the generalized quaternion division algebra over a field F with Char F≠2 . In this paper, the matrix equation AX-DXB=R over H f is considered. By using the quasilinear transformation T(X)=AX-DXB, this paper obtains several necessary and sufficient conditions for the existence of a solution or a unique solution to the matrix equation,and gives some explicit formulas of solutions.
出处
《数学杂志》
CSCD
北大核心
2002年第3期281-286,共6页
Journal of Mathematics
关键词
广义四元数矩阵
矩阵方程
表示矩阵
Matrix generalized quaternion matrix
Matrix equation
Representation matrix
