THE MOORE–PENROSE INVERSE OF SYMMETRIC MATRICES WITH EQUITABLE PARTITIONS AND DIVISOR MATRICES

A balanced partitioned symmetric matrix is a matrix that has partition blocks that have the same average number of rows and columns. The sum of these average rows and columns is then arranged into a matrix, which is called the divisor matrix. The purpose of this paper is to analyze the relationship between the Moore-Penrose inverse divisor matrix of a balanced partitioned symmetric matrix A and the Moore-Penrose inverse divisor matrix of A. Furthermore, it is obtained that the divisor matrix of the Moore-Penrose inverse of matrix A is the same as the Moore-Penrose inverse of the divisor matrix of A.