GENERALIZED ULTRAMETRIC MATRICES - A CLASS OF INVERSE M-MATRICES

被引：32

作者：

NABBEN, R ^{[1
]}

VARGA, RS ^{[1
]}

机构：

[1] KENT STATE UNIV,INST COMPUTAT MATH,KENT,OH 44242

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1995年 / 220卷

基金：

美国国家科学基金会;

关键词：

D O I：

10.1016/0024-3795(94)00086-S

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

Recently, Martinet, Michon, and San Martin introduced the new class of (symmetric) strictly ultrametric matrices. They proved that the inverse of a strictly ultrametric matrix is a strictly row and strictly column diagonally dominant Stieltjes matrix. Here, we generalize their result by introducing a class of nonsymmetric matrices, called generalized ultrametric matrices. We give a necessary and sufficient condition for the regularity of these matrices and prove that the inverse of a nonsingular generalized ultrametric matrix is a row and column diagonally dominant M-matrix. We establish that a nonnegative matrix is a generalized ultrametric matrix if and only if the matrix is a certain sum of at most rank-two matrices. Moreover, we give a characterization of generalized ultrametric matrices, based on weighted trees. The entries of generalized ultrametric matrices then arise as certain ''distances'' between the leaves and the root of the tree.

引用

页码：365 / 390

页数：26

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