文献类型：期刊文献

英文题名：THE REAL SOLUTIONS TO A SYSTEM OF QUATERNION MATRIX EQUATIONS WITH APPLICATIONS

作者：Wang, Qing-Wen[1];Yu, Shao-Wen[2];Zhang, Qin[1]

机构：[1]Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China;[2]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2009

卷号：37

期号：6

起止页码：2060

外文期刊名：COMMUNICATIONS IN ALGEBRA

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000266720800017)】；

基金：This research was supported by the Natural Science Foundation of China (60672160), the Scientific Research Innovation Foundation of Shanghai Municipal Education Commission (09YZ13), and Shanghai Leading Academic Discipline Project (J50101).

语种：英文

外文关键词：Generalized inverse; Maximal rank; Minimal rank; Quaternion matrix equation; Real solution

摘要：In this article we establish necessary and sufficient conditions for the existence and the expressions of the general real solutions to the classical system of quaternion matrix equations A(1)XB(1) = C-1, A(2)XB(2) = C-2. Moreover, formulas of the maximal and minimal ranks of four real matrices X-1, X-2, X-3, and X-4 in solution X = X-1 + X(2)i + X(3)j + X(4)k to the system mentioned above are derived. As applications, we give necessary and sufficient conditions for the quaternion matrix equations A(1)XB(1) = C-1, A(2)XB(2) = C-2, A(3)XB(3) = C-3 to have common real solutions. In addition, the maximal and minimal ranks of four real matrices E, F, G, and H in the common generalized inverse of A(1) + B(1)i + C(1)j + D(1)k and A(2) + B(2)i + C(2)j + D(2)k, which can be expressed as E + Fi + Gj + Hk are also presented.