含有符号矩阵的Hadamard积的性质及其应用

Some Properties of Hadamard Products Involving the Sign Matrix and Their Applications

该文首先导出含有符号矩阵的Ｈａｄａｍａｒｄ积的若干矩阵恒等式，讨论了相应的数值特征（如特征值、秩、迹、行列式），并用所导出的某些结果分析一个包含两个非负定阵的迹的不等式，揭示出其实质，作了较大的推广；然后用这个不等式估计半相依回归系统中广义协方差改进估计（ＧＣＩＥ）的方差阵的迹的界值。

In this paper,the sign matrix and some of its properties (such as eigenvalues,rank,trace,determinant of the product matrix of the sign matrix and some matrix) are introduced.Some of these results are employed to analyse the trace inequality given by Li Hongxi and Leng Gangsong.And a series of inequalites is derived.These results are applied to estimate the boundary of the trace of the difference between the variance matrices of GCIE and CIE in SURS when m=2 and ∑>0 is know.