四元数正定阵与线性方程组Ax＝b的反问题

Quaternion Positive Definite Matrices and Inverse Problem of System of Quaternion Linear Equations Ax=b

引入了四元数正定矩阵的概念，给出了ｎ阶四元数矩阵为正定的充要条件，得到了四元数线性方程组Ａｘ＝ｂ的反问题有正定阵解、正定自共轭阵解的充要条件及解的一般形式．

The concept of quaternion positive definite matrix is introduced,a necessary and sufficient condition is given for n-th order quaternion matrix to be positive definite.In addition,a necessary and sufficient condion is found for the inverse problem of the system if quaternion linear equations Ax=b to have solutions of positive definite matrices and solutions of self conjugate positive definte matrices. The general forms of the solutions are given.