一类矩阵方程的Hermite广义Hamilton解及其最佳逼近  

Hermite generalized Hamiltonian solutions for matrix equation and its optimal approximation

作　　者：李迎春[1] 刘志宏[1] 

机构地区：[1]红河学院数学学院,云南蒙自661100

出　　处：《高师理科学刊》2010年第3期6-9,共4页Journal of Science of Teachers＇College and University

基　　金：云南省教育厅科研基金项目(09C0206);红河学院博;硕启动项目(XSS08012)

摘　　要：利用矩阵的广义奇异值分解定理,得到了矩阵方程AHXA=B存在Hermite广义Hamilton解的充分必要条件,并在有解时得到了通解的表达式,同时得到了相应解集中与已知矩阵最佳逼近的Hermite广义Hamilton解和最小范数解.Applying the generalized singular value decomposition of matrices,the necessary and sufficient conditions for the existence and the expression for the Hermite generalized Hamiltonian solutions of the matrix equation AHXA=Bwas derived.In addition,in Hermite generalized Hamiltonian solutions set of the equation,the expressions of the optimal approximation solutions and of the minimum norm solutions to the given matrix was obtained.

关 键 词：矩阵方程 Hermite广义Hamilton矩阵 最佳逼近解 最小范数解 

分 类 号：O151.21[理学—数学]