文献类型：期刊文献

英文题名：RANKS OF THE COMMON SOLUTION TO SOME QUATERNION MATRIX EQUATIONS WITH APPLICATIONS

作者：Wang, Q. W.[3,4];Yu, S. W.[1,2]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Fudan Univ, Inst financial studies, Shanghai 200433, Peoples R China;[3]Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China;[4]Nanyang Technol Univ, Div Math Sci, Singapore 637371, Singapore

年份：2012

卷号：38

期号：1

起止页码：131

外文期刊名：BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000312720300010)】；

基金：This research was supported by the grants from the Ph.D. Programs Foundation of Ministry of Education of China (20093108110001), Natural Science Foundation of Shanghai (11ZR1412500), Natural Science Foundation of China (11171205), Singapore MoE Tier 1 Research Grant RG60/07, Shanghai Leading Academic Discipline Project (J50101), and China Postdoctoral Science Foundation (2012M511014).

语种：英文

外文关键词：Quaternion matrix equation; maximal and minimal rank; generalized inverse; real solution; complex solution

摘要：We derive the formulas of the maximal and minimal ranks of four real matrices X-1, X-2, X-3 and X-4 in common solution X = X-1 + X(2)i + X(3)j + X(4)k to quaternion matrix equations A(1)X = C-1, XB2 = C-2, A(3)XB(3) = C-3. As applications, we establish necessary and sufficient conditions for the existence of the common real and complex solutions to the matrix equations. We give the expressions of such solutions to this system when the solvability conditions are met. Moreover, we present necessary and sufficient conditions for the existence of real and complex solutions to the system of quaternion matrix equations A(1)X - C-1, XB2 - C-2, A(3)XB(3) - C-3, A(4)XB(4) - C-4. The findings of this paper extend some known results in the literature.