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.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
北大核心
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
