一类矩阵方程的解  

The solutions of a class of matrix equations

作　　者：袁晖坪[1,2] 罗光耀[2] 

机构地区：[1]重庆工商大学电子商务及供应链系统重庆市重点实验室,重庆400067 [2]重庆工商大学数学与统计学院,重庆400067

出　　处：《华中师范大学学报（自然科学版）》2013年第1期8-11,共4页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11271388);电子商务及供应链系统重庆市重点实验室专项基金项目(2012ECSC0216)

摘　　要：利用Hermite矩阵探讨了一类矩阵方程的求解问题,获得了一些新结果,导出了矩阵方程XAX=A与X*AX=A存在Hermite矩阵解的充分必要条件及其通解表达式,削弱了杨昌兰和王龙波文中定理的条件,推广了Jameson和杨昌兰等的结果.In this paper,the solutions of the matrix equation are discussed by employing the Hermite matrix,and some new results are gained.The necessary and sufficient conditions of having their Hermite matrix solution for the matrix equation XAX=A and X＊AX=A and the general solutions have been also obtained.In addition,the conditions in the theorem of Yang Changlan and Wang Longbo＇s paper are weakened,and the results obtained by Jameson and Yang Changlan etc.are generalized.

关 键 词：HERMITE矩阵 矩阵方程 矩阵解 通解 

分 类 号：O151.21[理学—数学]