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Let be a tree with vertices. To each edge of we assign a weight which is a positive definite matrix of some fixed order, say, . Let denote the sum of all the weights lying in the path connecting the vertices and of . We now say that is the distance between and . Define , where is the null matrix and for , is the distance between and . Let be an arbitrary connected weighted graph with vertices, where each weight is a positive definite matrix of order . If and...
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