THE MOORE–PENROSE INVERSE OF SYMMETRIC MATRICES WITH EQUITABLE PARTITIONS AND DIVISOR MATRICES
DOI:
https://doi.org/10.25077/jmua.15.3.427-435.2026Keywords:
Moore-Penrose inverse, symmetric matrix, divisor matrix, balanced partitionAbstract
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.
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