四元数半正定矩阵与线性方程组Ax＝b的反问题

Quaternion Positive Semi-definite Matrix and Inverse Problem of System of Linear Equations Ax=b

证得了四元数矩阵为半正定的充要条件，得到四元数线性方程组ＡＸ＝ｂ的反问题有半正定阵解、半正定自共轭阵解的充要条件及解的一般形式．

A sufficient and necessary condition for quaternion matrix to be positive semidefinite is proved.A sufficient and necassary condition and the general form of solutions for the inverse problem of the system of quaternion linear equations Ax=b to have solutions of positive semi-definite matrix and positive semi-definite conjugate matrix are derived.