Block matrices and multispherical structure of distance matrices Original Research Article

The block structure of a matrix and its relation to the block structure of the corresponding eigenvectors is investigated. A set of points is 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 structure with simple relations between the blocks. Further, such block structure may be recognized from the structure of the eigenvectors of the distance matrix. A computational procedure is proposed to find the least number of concentric spheres containing the points represented by a distance matrix.