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Product distance matrix of a tree with matrix weights

DSpace at IIT Bombay

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Field Value
 
Title Product distance matrix of a tree with matrix weights
 
Creator BAPAT, RB
SIVASUBRAMANIAN, S
 
Subject Trees
Distance matrix
Determinant
Matrix weights
 
Description Let T be a tree on n vertices and let the n - 1 edges e(1), e(2), ..., e(n-1) have weights that are s x s matrices W-1, W-2, ..., Wn-1, respectively. For two vertices i, j, let the unique ordered path between i and j be p(i,j) = e(r1), e(r2) ... e(rk). Define the distance between i and j as the s x s matrix E-i,E-j = Pi(k)(p=1) W-ep. Consider the ns x ns matrix D whose (i, j)-th block is the matrix E-i,E-j. We give a formula for det(D) and for its inverse, when it exists. These generalize known results for the product distance matrix when the weights are real numbers. (C) 2014 Elsevier Inc. All rights reserved.
 
Publisher ELSEVIER SCIENCE INC
 
Date 2016-01-15T04:32:13Z
2016-01-15T04:32:13Z
2015
 
Type Article
 
Identifier LINEAR ALGEBRA AND ITS APPLICATIONS, 468,145-153
0024-3795
1873-1856
http://dx.doi.org/10.1016/j.laa.2014.03.034
http://dspace.library.iitb.ac.in/jspui/handle/100/17765
 
Language en