矩阵方程XA＝B的亚（半）正定自共轭四元数矩阵解  

Positive Meta-(Semi-) Definite Self Conjugate Solutions to Matrix Equation XA=B over the Quaternion Field

作　　者：王卿文[1] 杨昌兰[1] 

机构地区：[1]昌潍师专数学系,山东工业大学数理系

出　　处：《烟台师范学院学报（自然科学版）》1996年第1期10-14,共5页Yantai Teachers University journal(Natural Science Edition)

摘　　要：给出了四元数体Ｑ上ｎ×ｎ分块矩阵为亚（半）正定自共轭矩阵的一个充要条件，进而给出了Ｑ上矩阵方程ＸＡｎｍ＝Ｂｎｍ有亚（半）正定自共轭四元数矩阵解的充要条件及解集合的显式表示，从而推广改进了数城上线性方程组的反问题及矩阵反问题的相应结果．It is given that a partitioned n × n matrix over the quaternion field Q is a necessary and sufficient condition of meta-(semi-) positive definite matrix. A Criterion for meta- (semi-) positive definite self conjugate solution of the matrix equation XA=B over Q and the distinct expressions of solutions are presented. Therefore, the results about the inverse problems of linear equation sets and matrices over scalar fields are improved and generalized.

关 键 词：四元数体 矩阵方程 正定自共轭矩阵 

分 类 号：O151.21[理学—数学]