泛正定矩阵的进一步研究

A Further Study on Universal Positive Definite Matrices

给出了泛正定矩阵的重要性质与充要条件.进而提出了新的泛正定与泛非负定矩阵子集类的定义.在其基础上给出泛正定子集类的一系列性质,尤其是推广了Minkowski不等式.最后讨论了泛非负定子集类上的一种新的矩阵偏序的性质与充要条件.

For judging the universal positive definite matrices in literature, some necessary and sufficient conditions are given as well as some significant useful properties. Further, two special subsets in universal positive definite matrices and universal nonnegative definite matrices are introduced, and some further properties of the former are discussed, especially the well- known Minkowski inequality of two matrices. Finally, a new partial ordering in the subset of universal nonnegative definite matrices is defined and some properties and conditions for their existence are discussed.