A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
type: Item
instance of: scholarly article
title: A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
zbMATH Open document ID: 1058.15015
author: Qing-Wen Wang
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: Many problems in systems and control theory require the solution of Sylvester's equation \(AX-YB=C\) or of its generalization \((*)\) \(AXB+CYD=E\). The author studies the couple of matrix equations \((**)\) \(A_1XB_1=C_1,A_2XB_2=C_2\) over an arbitrary regular ring with identity. He obtains necessary and sufficient conditions for the consistency of the system \((**)\) and presents its general solution. The results are used to obtain necessary and sufficient conditions for the consistency of the equation \((*)\) and to derive the form of its general solution.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 2083491
zbMATH Keywords: linear matrix equation
zbMATH Keywords: system of matrix equations
zbMATH Keywords: inner inverse of a matrix
zbMATH Keywords: reflexive inverse of a matrix
zbMATH Keywords: Sylvester matrix equation
zbMATH Keywords: consistency
zbMATH Keywords: regular ring
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: j.laa.2003.12.039
OpenAlex ID: W2095771800
cites work: Q5677596
cites work: A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem
cites work: Q4196544
cites work: Almost non-interacting control by measurement feedback
cites work: A common solution to a pair of linear matrix equations over a principal ideal domain
cites work: A representation of the general common solution to the matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) with applications
cites work: Q4333094
cites work: The Equations AX - YB = C and AX - XB = C in Matrices
cites work: Roth's Equivalence Problem in Unit Regular Rings
cites work: Roth's removal rule revisited
cites work: The generalized inverse of a sum with radical element: Applications
cites work: Matrix equivalence and isomorphism of modules
cites work: Roth's theorems and decomposition of modules
cites work: Roth's theorems for sets of matrices
cites work: On matrix equivalence and matrix equations
cites work: Roth's theorems over commutative rings
cites work: Roth's theorems for matrix equations with symmetry constraints
cites work: Linear matrix equations: The module theoretic approach
cites work: Consistency of a pair of generalized Sylvester equations
cites work: Sylvester matrix equation for matrix pencils
cites work: The extension of Roth's theorem for matrix equations over a ring
cites work: Roth's theorems for constant centroselfconjugate and centroskewselfconjugate solutions to systems of linear polynomial matrix equations over a finite dimensional central algebra
cites work: Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra
cites work: Q5719034
cites work: Q3414024
cites work: The matrix equation AXB+CYD=E
cites work: The Equation $AXB + CYD = E$ over a Principal Ideal Domain
cites work: The matrix equationAXB+CYD=Eover a simple artinian ring
cites work: Q4363962
cites work: The Maximal Regular Ideal of a Ring
DOI: 10.1016/J.LAA.2003.12.039
Recommended article: A system of matrix equations over regular rings
Recommended article: Nikolai Ivanovich Lobachevskii (on the bicentenary of his birth)
Recommended article: Q4351840
Recommended article: Q4780736
Recommended article: Q4948324
Recommended article: The Solvability of a System of Matrix Equations over an Arbitrary Division Ring
Recommended article: Solution of a system of linear equations over a commutative ring
Recommended article: Q3784974
Recommended article: Q4484042
description: scientific article; zbMATH DE number 2083491