Stieltjes函数生成的广义Loewner矩阵的秩不变性

On Rank Invariance of Generalized Loewner Matrices Generated by Stieltjes Function

研究由Stieltjes函数生成的两类广义Loewner矩阵的秩不变性,证明了由同一Stieltjes函数生成的第一类同型的广义Loewner矩阵的秩是相等的,而生成的第二类同型的广义Loewner矩阵的秩相等或者相差1.

In this paper we study the statements on rank invariance of generalized Loewner matrices of two types generated by the values of a given Stieltjes function.We show that the ranks of such matrices of the first type of the same size are equal,while the ranks of such matrices of the second type with the same size are either equal or differ with difference one.