三对角逆M-矩阵性质的探讨

Research on Tridiagonal Inverse M-Matrix

本文研究一类特殊的逆M-矩阵:三对角逆M-矩阵。用图论的方法完全刻划了三对角逆M-矩阵的结构特征和性质,给出了三对角非负矩阵是逆M-矩阵的充要条件。最后,证明了具有唯一路M-矩阵的逆在Hadamard乘积下的封闭性。

This paper studies a class of inverse M-Matrices:tridiagonal inverse M-matrix. Graph theory is used to discuss the structure and properties of tridiagonal inverse M-matrix. A sufficient and necessary condition for a nonnegative tridiagonal matrix to be an inverse M-matrix is given. Finally,it is proved that the set of the inverses of M-matrices with unipathic is closed under Hadamard product.