Determinant of the distance matrix of a tree with matrix weights

被引：23

作者：

Bapat, RB ^{[1
]}

机构：

[1] Indian Stat Inst, New Delhi 110016, India

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 416卷 / 01期

关键词：

tree; distance matrix; Laplacian matrix; matrix weights; determinant;

D O I：

10.1016/j.laa.2005.02.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let T be a tree with n vertices and let D be the distance matrix of T. According to a classical result due to Graham and Pollack, the determinant of D is a function of n, but does not depend on T. We allow the edges of T to carry weights, which are square matrices of a fixed order. The distance matrix D of T is then defined in a natural way. We obtain a formula for the determinant of D, which involves only the determinants of the sum and the product of the weight matrices. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：2 / 7

页数：6