Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416293 | Linear Algebra and its Applications | 2015 | 9 Pages |
Abstract
Let T be a tree on n vertices and let the nâ1 edges e1,e2,â¦,enâ1 have weights that are sÃs matrices W1,W2,â¦,Wnâ1, respectively. For two vertices i, j, let the unique ordered path between i and j be pi,j=er1er2â¦erk. Define the distance between i and j as the sÃs matrix Ei,j=âp=1kWep. Consider the nsÃns matrix D whose (i,j)-th block is the matrix Ei,j. We give a formula for detâ¡(D) and for its inverse, when it exists. These generalize known results for the product distance matrix when the weights are real numbers.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
R.B. Bapat, Sivaramakrishnan Sivasubramanian,