四元数体上矩阵方程的自共轭解

The Self-Conjugate Solutions of Quaternion Matrix Equation

中文关键词:  M-P逆  自共轭阵  子空间

英文关键词:the Moore-Penrose inverse  self-conjugate matrix  subspace

中文摘要:

      利用矩阵的M-P逆和矩阵分块,给出了四元数体上矩阵方程XB=D在子空间上有自共轭解的充要条件以及解的一般形式,并由此给出了矩阵方程AXB=D有自共轭解的充要条件和解的一般形式.

英文摘要:

      By using of Moore-Penrose inverse and Matrix Decomposition, the necessary and sufficient conditions for the existence of the Self-conjugate matrix solutions over subspace for quaternion matrix equation XB = D are obtained together with the general forms of such solutions, and more, the necessary and sufficient conditions are obtained for matrix equation AXB = D to have Self-conjugate matrix splutions, along with the expression for general common solutions.