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
收藏
页码：2 / 7
页数：6
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