广义正定Hermite矩阵与广义特征值的性质  

Some Properties of Generalized Positive Hermite Matrices and Their Generalized Eigenvalues

作　　者：杜鹃[1] 冯思臣[1] 谭仁俊[1] 

机构地区：[1]成都理工大学信息管理学院,四川成都610059

出　　处：《四川师范大学学报（自然科学版）》2010年第3期328-330,共3页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10471112);四川省教育厅自然科学重点基金(08ZA114)资助项目

摘　　要：证明广义正定Hermite矩阵对应矩阵逆的广义特征值为正,给出广义正定Hermite矩阵乘幂为广义正定Hermite矩阵的充分条件;指明Hermite矩阵A关于正定Hermite矩阵B是广义正定Hermite矩阵的充要条件及Hermite矩阵与正定Hermite矩阵同时对角化的方法;推导广义正定Hermite矩阵特征值的性质.It is proved that the generalized eigenvalues of a generalized positive Hermite matrix for its corresponding inverse matrix are positive.A sufficient condition for powers of a generalized positive Hermite matrix to be a generalized positive Hermite matrix is given.The sufficient and necessary condition for a Hermite matrix A to be generalized positive Hermite matrix related to a positive Hermite matrix B is proved and the simuataneous diagonalization algorithm of a Hermite matrix and positive Hermite matrix is presented.The properties of the eigenvalues of the generalized positive Hermite matrices are deduced.

关 键 词：广义正定Hermite矩阵 广义特征值 对角化 

分 类 号：O151.21[理学—数学]