BLOCK MATRICES AND MULTISPHERICAL STRUCTURE OF DISTANCE MATRICES

The block structure of a matrix and its relation to the block structur e of the corresponding eigenvectors is investigated. A set of points i s said to have multispherical structure if they lie on a collection of concentric spheres. When the centroid of each of the clusters lies at the common center, the associated distance matrix has a block structu re with simple relations between the blocks. Further, such block struc ture may be recognized from the structure of the eigenvectors of the d istance matrix. A computational procedure is proposed to find the leas t number of concentric spheres containing the points represented by a distance matrix.