Geodesic
Block distance matrices
The electronic journal of linear algebra, Tome 16 (2007), pp. 435-443.

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Summary: In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by Dij = Fii+Fjj -2Fij. When each block in F is 1 * 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interesting properties of Euclidean distance matrices to block distance matrices are extended in this paper. Finally, distance matrices of trees with matrix weights are investigated.
Classification : 51K05, 15A57
Keywords: distance matrices, Laplacian matrices, trees 
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     author = {Balaji, R. and Bapat, R.B.},
     title = {Block distance matrices},
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Balaji, R.; Bapat, R.B. Block distance matrices. The electronic journal of linear algebra, Tome 16 (2007), pp. 435-443. http://geodesic.mathdoc.fr/item/ELA_2007__16__a2/