文献类型：期刊文献

英文题名：Extreme Ranks of Real Matrices in Solution of the Quaternion Matrix Equation AXB = C with Applications

作者：Wang, Qingwen[1];Yu, Shaowen[2];Xie, Wei[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：2010

卷号：17

期号：2

起止页码：345

外文期刊名：ALGEBRA COLLOQUIUM

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000276455000016)】；

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 the Shanghai Leading Academic Discipline Project (J50101).

语种：英文

外文关键词：quaternion matrix equation; minimal rank; maximal rank; generalized inverse; real solution

摘要：In this paper, for a consistent quaternion matrix equation AXB = C, the formulas are established for maximal and minimal ranks of real matrices X-1, X-2, X-3, X-4 in solution X = X-1 + X(2)i + X(3)j + X(4)k. A necessary and sufficient condition is given for the existence of a real solution of the quaternion matrix equation. The expression is also presented for the general solution to this equation when the solvability conditions are satisfied. Moreover, necessary and sufficient conditions are given for this matrix equation to have a complex solution or a pure imaginary solution. As applications, the maximal and minimal ranks of real matrices E,F,G, H in a generalized inverse (A + Bi + Cj + Dk)(-) = E + Fi + Gj + Hk of a quaternion matrix A + Bi + Cj + Dk are also considered. In addition, a necessary and sufficient condition is derived for the quaternion matrix equations A(1)XB(1) = C-1 and A(2)XB(2) = C-2 to have a common real solution.