Ordering structure of Euclidean distance matrices with applications to statistical multidimensional scaling

本文的研究成果总结如下：(1)得到了关于多球面欧氏距离矩阵表征的一些新结果。(2)如果一个有中心的正半定矩阵的特征值大于另一个有中心的正半定矩阵的特征值，则相应的两个欧氏距离矩阵的特征值也成立相同的不等式。(3)研究了一类特殊的欧几里得距离矩阵——细胞矩阵的一些性质。(4)在多元混合分布的一组主点的线性子空间上，得到了一些新的结果。

The results of this research are summarized as follows:(1) Some new results on the characterization of multi-spherical Euclidean distance matrices were derived.(2) The authors showed that if the eigenvalues of a centered positive semidefinite matrix majorizes those of another centered positive semidefinite matrix, then the same inequality holds for the eigenvalues of the corresponding two Euclidean distance matrices.(3) The authors investigated some properties of cell matrices, which are special Euclidean distance matrices.(4) The authors derived some new results on the linear subspace in which a set of principal points of a multivariate mixture distribution.