ELA, Volume 16, pp. 435-443, December 2007, abstract.

Block Distance Matrices

R. Balaji and R.B. Bapat

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
D_{ij}=F_{ii}+F_{jj}-2F_{ij}. When each block in F is 1x1 (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.