复正定矩阵的标准性及判定  

THE STANDARD FORM AND THE DISCRIMINATION OF COMPLEX POSITIVE DEFINITE MATRIX

作　　者：张慎语[1] 王毅[1] 

机构地区：[1]四川联合大学数学系,四川轻化工学院基础部

出　　处：《四川轻化工学院学报》1996年第4期48-51,共4页Journal of Sichuan Institute of Light Industry and Chemical Technology

摘　　要：研究复正定矩阵的性质，提出了矩阵的第二特征多项式和第二特征值的新概念，得到复正定矩阵的＊相合标准形的存在性和唯一性定理；给出由第二特征值计算复正定矩阵＊相合标准形的方法；给出由第二特征多项式判定复正定矩阵的＊相合的方法；给出由低阶矩阵的正定性判定高阶矩阵正定的方法。The new concepts of second characteristic polynomial and second characteristic value are proposed in the paper. These are applied to study the unique existence theorem of the standard form of complex positive dofinte matrix. The standard form of complex positive definite matrix is determined by second characteristie values of com plex positive definite matrix. Whether two complex positive definite matrices are conjunctive is completely detrmined by their second charateristic polynomials. Finally, one of the methods of discriminating complex positive definite matrix is discussed by com plex positive definite matrix which has lower order.

关 键 词：复正定矩阵 第二特征多项式 第二特征值 矩阵 

分 类 号：O151.21[理学—数学]