The solution of the dual matrix equation A^tX+X^TA=D
The solvability conditions for the dual matrix equation A^tX+X^TA=D are deduced by applying the singular value decomposition, and the expression of the general solution to this dual matrix equation is presented. Furthermore, the minimum-norm solution of this dual matrix equation is also provided....
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-01-01
|
| Series: | Kuwait Journal of Science |
| Subjects: | |
| Online Access: | https://www.sciencedirect.com/science/article/pii/S2307410823001827 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849744345675071488 |
|---|---|
| author | Min Zeng Yongxin Yuan |
| author_facet | Min Zeng Yongxin Yuan |
| author_sort | Min Zeng |
| collection | DOAJ |
| description | The solvability conditions for the dual matrix equation
A^tX+X^TA=D are deduced by applying the singular value decomposition, and the expression of the general solution to this dual matrix equation is presented. Furthermore, the minimum-norm solution of this dual matrix equation is also provided. Finally, a numerical example is presented to show the correctness of our results. |
| format | Article |
| id | doaj-art-e8bd3167e83d4fa2a7e26565b5579ad5 |
| institution | DOAJ |
| issn | 2307-4116 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Kuwait Journal of Science |
| spelling | doaj-art-e8bd3167e83d4fa2a7e26565b5579ad52025-08-20T03:19:57ZengElsevierKuwait Journal of Science2307-41162024-01-01511100141https://doi.org/10.1016/j.kjs.2023.10.008The solution of the dual matrix equation A^tX+X^TA=DMin Zeng0Yongxin Yuan1School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, ChinaSchool of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, ChinaThe solvability conditions for the dual matrix equation A^tX+X^TA=D are deduced by applying the singular value decomposition, and the expression of the general solution to this dual matrix equation is presented. Furthermore, the minimum-norm solution of this dual matrix equation is also provided. Finally, a numerical example is presented to show the correctness of our results.https://www.sciencedirect.com/science/article/pii/S2307410823001827dual matrix equationsingular value decompositiongeneral solutionminimum-norm solution |
| spellingShingle | Min Zeng Yongxin Yuan The solution of the dual matrix equation A^tX+X^TA=D Kuwait Journal of Science dual matrix equation singular value decomposition general solution minimum-norm solution |
| title | The solution of the dual matrix equation A^tX+X^TA=D |
| title_full | The solution of the dual matrix equation A^tX+X^TA=D |
| title_fullStr | The solution of the dual matrix equation A^tX+X^TA=D |
| title_full_unstemmed | The solution of the dual matrix equation A^tX+X^TA=D |
| title_short | The solution of the dual matrix equation A^tX+X^TA=D |
| title_sort | solution of the dual matrix equation a tx x ta d |
| topic | dual matrix equation singular value decomposition general solution minimum-norm solution |
| url | https://www.sciencedirect.com/science/article/pii/S2307410823001827 |
| work_keys_str_mv | AT minzeng thesolutionofthedualmatrixequationatxxtad AT yongxinyuan thesolutionofthedualmatrixequationatxxtad AT minzeng solutionofthedualmatrixequationatxxtad AT yongxinyuan solutionofthedualmatrixequationatxxtad |