Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations
We constitute some necessary and sufficient conditions for the system A1X1=C1, X1B1=C2, A2X2=C3, X2B2=C4, A3X1B3+A4X2B4=Cc, to have a solution over the quaternion skew field in this paper. A novel expression of general solution to this system is also established when it has a solution. The least nor...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2019/9072690 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832546152804777984 |
|---|---|
| author | Abdur Rehman Ivan Kyrchei Muhammad Akram Ilyas Ali Abdul Shakoor |
| author_facet | Abdur Rehman Ivan Kyrchei Muhammad Akram Ilyas Ali Abdul Shakoor |
| author_sort | Abdur Rehman |
| collection | DOAJ |
| description | We constitute some necessary and sufficient conditions for the system A1X1=C1, X1B1=C2, A2X2=C3, X2B2=C4, A3X1B3+A4X2B4=Cc, to have a solution over the quaternion skew field in this paper. A novel expression of general solution to this system is also established when it has a solution. The least norm of the solution to this system is also researched in this article. Some former consequences can be regarded as particular cases of this article. Finally, we give determinantal representations (analogs of Cramer’s rule) of the least norm solution to the system using row-column noncommutative determinants. An algorithm and numerical examples are given to elaborate our results. |
| format | Article |
| id | doaj-art-b0bc3303da5f4c97b7a6704683489619 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b0bc3303da5f4c97b7a67046834896192025-02-03T07:23:51ZengWileyAbstract and Applied Analysis1085-33751687-04092019-01-01201910.1155/2019/90726909072690Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal RepresentationsAbdur Rehman0Ivan Kyrchei1Muhammad Akram2Ilyas Ali3Abdul Shakoor4University of Engineering & Technology, Lahore, PakistanPidstrygach Institute for Applied Problems of Mechanics and Mathematics, NASU, Lviv, UkraineUniversity of Engineering & Technology, Lahore, PakistanUniversity of Engineering & Technology, Lahore, PakistanKhawaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, PakistanWe constitute some necessary and sufficient conditions for the system A1X1=C1, X1B1=C2, A2X2=C3, X2B2=C4, A3X1B3+A4X2B4=Cc, to have a solution over the quaternion skew field in this paper. A novel expression of general solution to this system is also established when it has a solution. The least norm of the solution to this system is also researched in this article. Some former consequences can be regarded as particular cases of this article. Finally, we give determinantal representations (analogs of Cramer’s rule) of the least norm solution to the system using row-column noncommutative determinants. An algorithm and numerical examples are given to elaborate our results.http://dx.doi.org/10.1155/2019/9072690 |
| spellingShingle | Abdur Rehman Ivan Kyrchei Muhammad Akram Ilyas Ali Abdul Shakoor Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations Abstract and Applied Analysis |
| title | Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations |
| title_full | Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations |
| title_fullStr | Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations |
| title_full_unstemmed | Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations |
| title_short | Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations |
| title_sort | least norm of the general solution to some system of quaternion matrix equations and its determinantal representations |
| url | http://dx.doi.org/10.1155/2019/9072690 |
| work_keys_str_mv | AT abdurrehman leastnormofthegeneralsolutiontosomesystemofquaternionmatrixequationsanditsdeterminantalrepresentations AT ivankyrchei leastnormofthegeneralsolutiontosomesystemofquaternionmatrixequationsanditsdeterminantalrepresentations AT muhammadakram leastnormofthegeneralsolutiontosomesystemofquaternionmatrixequationsanditsdeterminantalrepresentations AT ilyasali leastnormofthegeneralsolutiontosomesystemofquaternionmatrixequationsanditsdeterminantalrepresentations AT abdulshakoor leastnormofthegeneralsolutiontosomesystemofquaternionmatrixequationsanditsdeterminantalrepresentations |