关于正定四元数方阵的注记  

A NOTE ON THE POSITIVE DEFINITE QUATERNION MATRIX

作　　者：郑秉文[1] 

机构地区：[1]吉林电气化高等专科学校,吉林1320213

出　　处：《松辽学刊（自然科学版）》1999年第3期44-46,共3页Songliao Journal (Natural Science Edition)

摘　　要：这篇文章给出了四元数方阵为正定的充要条件，另外还给出了线性方程组 Ａｘ ＝ β的反问题具有正定四元数方阵解的充要条件，以及线性方程组Ａｘ ＝In this paper a necessary and sufficient condition is given for the quaternion matrix to be positive definite.In addition a necessary and sufficient condition is fund for the inuerse problem of the system of Li near equations Ax=β to have a solution of positive definite quaternion matrix as well as the general form of solutions of positive definite quater nion matrices is given for the inverse problem of the system of Li near equations Ax=β . In this paper a necessary and sufficient condition is given for the quaternion matrix to be positive definite.In addition a necessary and sufficient condition is fund for the inuerse problem of the system of Li near equations Ax=β to have a solution of positive definite quaternion matrix as well as the general form of solutions of positive definite quater nion matrices is given for the inverse problem of the system of Li near equations Ax=β .

关 键 词：正定四元数方阵 共轭转置矩阵 四元数方阵 

分 类 号：O151.21[理学—数学]