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.
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页码：2 / 7
页数：6
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