Recognition of hidden positive row diagonally dominant matrices

Abstract

A hidden positive row diagonally dominant (hprdd) matrix is a square matrix A for
which there exist square matrices C and B so that AC = B and each diagonal entry of B and C is greater than the sum of the absolute values of the off-diagonal entries in its row. A linear program with 5n² − 4n variables and 2n² constraints is defined that takes as input an n × n matrix A and produces C and B satisfying the above conditions if and only if they exist. A 4×4 symmetric positive definite matrix that is not an hprdd matrix is presented.