Determinant of the distance matrix of a tree with matrix weights
Copyright policy )Determinant of the distance matrix of a tree with matrix weights
AbstractLet 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.
Distance matrix, Numerical Analysis, Algebra and Number Theory, Matrix weights, Determinant, Discrete Mathematics and Combinatorics, Geometry and Topology, Laplacian matrix, Tree
Distance matrix, Numerical Analysis, Algebra and Number Theory, Matrix weights, Determinant, Discrete Mathematics and Combinatorics, Geometry and Topology, Laplacian matrix, Tree
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