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

Desi Lira Antika (Universitas Andalas)
Yanita Yanita (Department of Mathematics, Universitas Andalas)
Monika Rianti Helmi

Jurnal Matematika UNAND
Vol. 15 No. 3 (2026)

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.