Some considerations of matrix equations using the concept of reproductivity

TL;DR

This paper investigates various matrix equations, including Cline's and generalized Penrose's systems, focusing on their reproductive and non-reproductive solutions to enhance understanding of their solution structures.

Contribution

It introduces a comprehensive analysis of reproductive and non-reproductive solutions for several matrix equations, expanding the theoretical framework of matrix equation solutions.

Findings

Determined reproductive solutions for Cline's matrix equation.

Established non-reproductive solutions for generalized Penrose's system.

Analyzed solutions for k-commutative {1}-inverses.

Abstract

In this paper we analyse Cline's matrix equation, generalized Penrose's matrix system and a matrix system for k-commutative {1}-inverses. We determine reproductive and non-reproductive general solutions of analysed matrix equation and analysed matrix systems.