Some considerations in relation to the matrix equation AXB=C

TL;DR

This paper introduces a new condition for the consistency of the matrix equation AXB=C, providing a general solution framework that includes reproductive and non-reproductive solutions, with applications to related matrix systems.

Contribution

It presents a novel consistency condition and a comprehensive general solution form for AXB=C, incorporating reproductive solutions and their applications.

Findings

New consistency condition for AXB=C

General solution includes reproductive and non-reproductive solutions

Applications to related matrix systems

Abstract

In this paper we represent a new form of condition for the consistency of the matrix equation AXB=C. If the matrix equation AXB=C is consistent, we determine a form of general solution which contains both reproductive and non-reproductive solutions. Also, we consider applications of the concept of reproductivity for obtaining general solutions of some matrix systems which are in relation to the matrix equation AXB=C.