复矩阵的次正定性及行列式不等式

The Sub-definite Property of the Complex Matrix and Deteminetal Inequality

笔者讨论了复次亚正定矩阵的一些性质及行列式不等式,解决A,A n2的上界、下界问题,进一步研究了分块矩阵的次正定性,将Fischer关于正定矩阵的结果推广到复次亚正定矩阵上,从而得到新的结论;利用A A次正定性,推导出Khatri-Rao乘积的次正定性.

In this paper, we disscuss the property of the complex metapositive sub-definite and the deteminantal inequality,the boundary problems of ｜｜A｜｜,｜｜A｜｜^n/2are given. The sub-definite of matrix generalize Fiseher＇s results on a positive definite matrix to the complex metapositive sub-definite matrix, to get a new conlusion. The Khatric-Rao product sub-definite derives from the A×A sub-definite.