关于“奇异M-阵和广义对角占优阵的实用判定准则”一文的注记

A Note on "Some Practial Criteria for Singular M-Matrices and Generalized Diagonally Dominant Matrices

指出文 [1]中的一处错误 ,并给出反例 ,分析其证明中产生错误的原因 .由于定理本身的错误结果 ,导致其后判定程序的错误 ,因此对满足文 [1]定理 3条件的判定还需进一步研究 .本文给出了矩阵主子式与其 Schur补的行列式之间的一个性质 ,通过其可以直观地观察到矩阵本身的某些性质 ,又对这一性质给出几个应用 ,即为文 [1]中的几个定理提供了另一种简捷的证明方法 .

This paper is to point out a mistake in and analyze its causes.Then it provides a counterexample.As the result of Theorem 3 is not correct,so the following criteria procedure is not correct.Thus the Theorem needs further improvements.It can be seen that there is still much work to do when it comes to singular generalized diagonally dominant matrices.This paper also presents a property between the principal minor of a matrix and the determinant of its Schur complement.From it ,we can easily observe some properties of matrices.We also provide it with a few applications,i.e.the different proofs in theorems of and .