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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/100/17765

Title: Product distance matrix of a tree with matrix weights
Authors: BAPAT, RB
SIVASUBRAMANIAN, S
Issue Date: 2015
Publisher: ELSEVIER SCIENCE INC
Citation: LINEAR ALGEBRA AND ITS APPLICATIONS, 468,145-153
Abstract: 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.
URI: http://dx.doi.org/10.1016/j.laa.2014.03.034
http://dspace.library.iitb.ac.in/jspui/handle/100/17765
ISSN: 0024-3795
1873-1856
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