二次广义Hermite矩阵方程的解  

Solutions of Quadratic Generalized Hermite Matrix Equation

作　　者：袁晖坪[1] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《吉林大学学报（理学版）》2012年第2期281-283,共3页Journal of Jilin University:Science Edition

基　　金：重庆市自然科学基金(批准号:CSTS2005BB0243);重庆市教委科技项目基金(批准号:KJ0707023)

摘　　要：利用广义Hermite矩阵探讨一类二次矩阵方程的求解问题,得到了矩阵方程XAX=A存在广义Hermite矩阵解的充分必要条件及其相应解的表达式,并给出了矩阵方程XAY=B当A,B可逆时的通解表达式.The solutions of quadratic matrix equation were discuss ed via the generalized Hermite matrix.The findings show that there are necessar y and sufficient conditions of matrix equation XAX=A having their generalized Hermite matrix solution,and the simple expressions of the generalized Hermite matrix solution can also be obtained.Besides,the ge neral solutions of the matrix equations XAY=B were given.

关 键 词：广义HERMITE矩阵 二次矩阵方程 矩阵解 通解 

分 类 号：O151.21[理学—数学]