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

(1)得到了多球欧氏距离矩阵的一些新的刻画结果。(2)证明了如果一个中心半正定矩阵的特征值优于另一个中心半正定矩阵的特征值，则相应的两个欧氏距离矩阵的特征值也是相同的。(3)研究了胞元矩阵的一些性质，它们是特殊的欧氏距离矩阵。(4)得到了多元混合分布主点集所在的线性子空间上的一些新结果。

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.