论复亚正定矩阵

WEAKLY POSITIVE DEFINITE MATRICES IN COMPLEX FIELD

复亚正定矩阵是正定Ｈｅｒｍｉｔｅ矩阵概念的推广。本文详细地讨论了复亚正定矩阵的一系列基本性质，给出了复亚正定阵的标准形，并得到了两复亚正定矩阵的Ｋｒｏｎｅｃｋｅｒ积和Ｈａｄａｍａｎｄ积为复亚正定矩阵的条件，同时指出了［１］中叙述的正定复矩阵的概念及本文定义的复亚正定概念是等价的等重要的结果。

Weakly positive definite matrix is a kind of extensions of positive definite Hermite matrix. In this paper. a series of basic properties of weakly positive definite matrix is discussed, the standard forms of weakly positive definite matrices is given, and the condition on which kronecker product and Hadamand product of two weakly positive definite matrices become a weakly positive definite matrix is obtained meanwhile, the equivalence between positive definite complex matrix in [1] and complex wealkly positive definite matrix in this paper is deduced.