New solvable conditions and a new expression of the general solution to a system of linear matrix equation over an arbitrary division ring
type: Item
instance of: scholarly article
title: New solvable conditions and a new expression of the general solution to a system of linear matrix equation over an arbitrary division ring
zbMATH Open document ID: 1087.15018
published in: Southeast Asian Bulletin of Mathematics
publication date: 2006-02-22T00:00:00Z
review text: The authors consider the system of matrix equations \(A_1X=C_1\), \(XB_2=C_2\), \(A_3XB_3=C_3\) over an arbitrary division ring \(F\). They find new necessary and sufficient conditions for its solvability, and they present its general solution. They do the same also for the two particular cases \(A_3=I\) and \(B_3=I\), for the three systems obtained from the above one by skipping off one of the three equations, and for the system \(XB_j=C_j\), \(j=1,2\).
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 5008868
zbMATH Keywords: division ring
zbMATH Keywords: system of matrix equations
zbMATH Keywords: inner inverse of a matrix
zbMATH Keywords: reflexive inverse of a matrix
zbMATH Keywords: rank
author: Chun-Yan Lin
author: Qing-Wen Wang
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5008868