正定Hermite矩阵的性质  

Properties of positive definite Hermite matrix

作　　者：刘兴祥[1] 黄美愿[1] 

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《西南民族大学学报（自然科学版）》2010年第1期16-20,共5页Journal of Southwest Minzu University(Natural Science Edition)

摘　　要：Hermite矩阵在酉空间、酉变换及复二次型中都有很重要的地位.一方面是对称矩阵的自然推广;另一方面它在复矩阵中的地位相当于实数在复数中的地位.文中主要给出正定Hermite矩阵子式阵正定性的判定、正定Hermite矩阵行列式、迹的多个不等式以及有关Hadamard乘积的行列式的不等式,同时也给出正定Hermite二次型的标准型.Hermite matrix holds an important position in unitary space, unitary transformation and complex quadratic form. On the one hand, it is the natural generalization of the real symmetry matrix; on the other hand, its role of complex matrix is equivalent to the real numbers in the plural. This paper presents the judgment of positive definite sub-type array of positive definite Hermite matrix, several determinant and trace inequalities of positive definite Hermite matrix, as well as a determinant inequality for Hadamard products of positive definite Hermite. Finally standard form of positive definite Hermite matrix is discussed in this paper.

关 键 词：正定HERMITE矩阵 行列式 迹 子式阵 不等式 正定Hermite二次型 

分 类 号：O241.6[理学—计算数学]