广义正定复矩阵的若干性质  

Several Properties of the Generalized Positive Definite Complex Matrix

作　　者：张福阁[1] 刘雅芳[1] 

机构地区：[1]泉州师范学院理工学院,福建泉州362000

出　　处：《泉州师范学院学报》2007年第6期5-9,共5页Journal of Quanzhou Normal University

摘　　要：正定复矩阵是矩阵论中的一个重要概念,人们已经掌握了它的若干性质与结构.当引入广义正定复矩阵这个概念之后,也应该讨论它相应的性质与结构,这对丰富矩阵论的内容无疑是有意义的.文章在正定复矩阵的基础上,研究了广义正定复矩阵的一些相关事实,并给出了6个广义正定复矩阵的等价定义、3个性质以及4个有关广义正定复矩阵行列式或模的不等式.Positive definite complex matrix is an important concept of the matrix theory,several properties and structures of which have been comprehended. When the concept of the generalized positive definite complex matrix is introduced, we should also discuss corresponding properties and structures which are undoubtedly meaningful to enrich the content of the matrix theory. This paper discusses some relevant facts of the generalized positive definite complex matrix on the basis of the positive definite complex matrix, provides six equivalent definitions of the generalized positive definite complex matrix,three properties and four inequalities for the generalized positive definite complex matrix determinant or its mold.

关 键 词：正定复矩阵 广义正定复矩阵 正定HERMITE矩阵 

分 类 号：O151.21[理学—数学]