摘要
In this paper,some necessary and sufficient solvability conditions for the system of mixed generalized Sylvester matrix equations A_1X-YB_1=C_1,A_2Y-ZB_2=C_2 are derived,and an expression of the general solution to this system is given when it is solvable.Admissible ranks of the solution,and admissible ranks and inertias of the Hermitian part of the solution are investigated,respectively.As an application of the above system,solvability conditions and the general Hermitian solution to the generalized Sylvester matrix equation are obtained.Moreover,we provide an algorithm and an example to illustrate our results.
In this paper, some necessary and sufficient solvability conditions for the system of mixed generalized Sylvester matrix equations A_1X - YB_1 = Ch A_2Y - ZB_2 = C2 are derived, and an expression of the general solution to this system is given when it is solvable. Admissible ranks of the solution, and admissible ranks and inertias of the Hermitian part of the solution are investigated, respectively. As an application of the above system, solv- ability conditions and the general Hermitian solution to the generalized Sylvester matrix equation are obtained. Moreover, we provide an algorithm and an example to illustrate our results.
出处
《上海大学学报（自然科学版）》
CAS
CSCD
北大核心
2014年第2期138-156,共19页
Journal of Shanghai University:Natural Science Edition
基金
Project supported by the National Natural Science Foundation of China(11171205)
the Key Project of the Scientific Research Innovation Foundation of Shanghai Municipal Education Comm-ission(13ZZ080)
关键词
应用数学
数学分析
数学理论
数学概念
Sylvester equation
rank
inertia
explicit solutions
Moore-Penrose inverse
