Advanced search
Publication Cover
Communications in Algebra Volume 40, 2012 - Issue 7
Submit an article Journal homepage
156
Views
14
CrossRef citations to date
0
Altmetric
Original Articles

A New Simultaneous Decomposition of a Matrix Quaternity Over an Arbitrary Division Ring with Applications

Qing-Wen Wang Department of Mathematics, Shanghai University, Shanghai, P.R. ChinaCorrespondence[email protected]
,
Xia Zhang Department of Mathematics, Shanghai University, Shanghai, P.R. China
&
J. W. van Der Woude Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands
Pages 2309-2342 | Received 05 Aug 2010, Published online: 09 Jul 2012
 
Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days

Abstract

In this article, we give a new simultaneous decomposition concerning the general matrix quaternity over an arbitrary division ring ℱ. A practical algorithm for the decomposition of the matrix quaternity is also presented. As applications, we establish some necessary and sufficient conditions for the existence of the general solutions to the systems of matrix equations

and
over ℱ. In addition, we give the expressions of the general solutions to the systems when the solvability conditions are satisfied. Numerical examples are also given to illustrate the results of this article. Moreover, we mention that the findings of this article extend the some known results in the literature.

2000 Mathematics Subject Classification:

ACKNOWLEDGMENTS

This research was supported by the grants from the Ph.D. Programs Foundation of Ministry of Education of China (20093108110001), the Scientific Research Innovation Foundation of Shanghai Municipal Education Commission (09YZ13), Natural Science Foundation of China (60672160, 11171205), Singapore MoE Tier 1 Research Grant RG60/07, and Shanghai Leading Academic Discipline Project (J50101).

The authors would like to thank a referee very much for his or her valuable suggestions and comments, which resulted in a great improvement of the original manuscript.

Notes

Communicated by J.-T. Yu.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related Research Data

On a variational formulation of the QSVD and the RSVD
Source: Elsevier BV
Vandermonde and Wronskian matrices over division rings
Source: Published by Elsevier Inc.
A System of Four Matrix Equations over von Neumann Regular Rings and Its Applications
Source: Springer Science and Business Media LLC
A system of real quaternion matrix equations with applications
Source: Elsevier BV
Generalizing the Singular Value Decomposition
Source: Society for Industrial & Applied Mathematics (SIAM)
Holomorphic curvature of complex Finsler submanifolds
Source: Springer Science and Business Media LLC
Matrix equivalence and isomorphism of modules
Source: Elsevier BV
Theory and method for updating least-squares finite element model of symmetric generalized centro-symmetric matrices
Source: Elsevier BV
Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra
Source: Elsevier Science Inc.
Least squares Hermitian solution of the matrix equation (AXB,CXD)=(E,F) with the least norm over the skew field of quaternions
Source: Elsevier BV
Extreme Ranks of Real Matrices in Solution of the Quaternion Matrix Equation AXB = C with Applications
Source: World Scientific Pub Co Pte Lt
Symmetric and skew-antisymmetric solutions to systems of real quaternion matrix equations
Source: Elsevier BV
Centrohermitian and Skew-Centrohermitian Solutions to the Minimum Residual and Matrix Nearness Problems of the Quaternion Matrix Equation $${(AXB,DXE) = (C,F)}$$
Source: SPRINGER BASEL AG
QUIVERS AND MATRIX EQUATIONS
Source: Elsevier BV
Algebra
Source: Springer New York
The similarity reduction of matrices over a skew field
Source: Springer Science and Business Media LLC
Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
Source: Elsevier BV
Extreme Ranks of a Partial Banded Block Quaternion Matrix Expression Subject to Some Matrix Equations with Applications
Source: World Scientific Pub Co Pte Lt
Roth's theorems and decomposition of modules
Source: Elsevier BV
Semisimilarity for matrices over a division ring
Source: Published by Elsevier Inc.
Ranks and the least-norm of the general solution to a system of quaternion matrix equations
Source: Elsevier Inc.
Towards a Generalized Singular Value Decomposition
Source: Society for Industrial & Applied Mathematics (SIAM)
Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications
Source: World Scientific Pub Co Pte Lt
An iterative algorithm for the least squares bisymmetric solutions of the matrix equations A1XB1=C1,A2XB2=C2
Source: Elsevier BV
Common solutions to a pair of linear matrix equations A 1 XB 1 = C 1 and A 2 XB 2 = C 2
Source: Cambridge University Press (CUP)
An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation
Source: Elsevier BV
A finite iterative method for solving a pair of linear matrix equations (AXB,CXD)=(E,F)
Source: Elsevier BV
A representation of the general common solution to the matrix equations A1XB1 = C1 and A2XB2 = C2 with applications
Source: Elsevier BV
Some Theorems On Matrices With Real Quaternion Elements
Source: Canadian Mathematical Society
An iterative algorithm for solving a pair of matrix equations AYB=E,CYD=F over generalized centro-symmetric matrices
Source: Elsevier BV
On matrix equivalence and matrix equations
Source: Published by Elsevier Inc.
On the Centro-symmetric Solution of a System of Matrix Equations over a Regular Ring with Identity
Source: World Scientific Pub Co Pte Lt
A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
Source: Elsevier BV
On consistency, natural restrictions and estimability under classical and extended growth curve models
Source: Elsevier BV
A System of Periodic Discrete-time Coupled Sylvester Quaternion Matrix Equations
Source: World Scientific Pub Co Pte Lt
The Real Solutions to a System of Quaternion Matrix Equations with Applications
Source: Informa UK Limited
Maps on idempotent matrices over division rings
Source: Elsevier Inc.
The solvability of two linear matrix equations
Source: Informa UK Limited
The general solution to a system of real quaternion matrix equations
Source: Elsevier BV
The general solutions to some systems of matrix equations
Source: Informa UK Limited

Linking provided by 

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.