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|Title: ||Product distance matrix of a tree with matrix weights|
|Authors: ||BAPAT, RB|
|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.|
|Appears in Collections:||Article|
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