Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation AXB+CXD=E with the Least Norm
Using the Kronecker product of matrices, the Moore-Penrose generalized inverse, and the complex representation of quaternion matrices, we derive the expressions of least squares solution with the least norm, least squares pure imaginary solution with the least norm, and least squares real solution w...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/857081 |
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| _version_ | 1832545922323578880 |
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| author | Shi-Fang Yuan |
| author_facet | Shi-Fang Yuan |
| author_sort | Shi-Fang Yuan |
| collection | DOAJ |
| description | Using the Kronecker product of matrices, the Moore-Penrose generalized inverse, and the complex representation of quaternion matrices, we derive the expressions of least squares solution with the least norm, least squares pure imaginary solution with the least norm, and least squares real solution with the least norm of the quaternion matrix equation AXB+CXD=E, respectively. |
| format | Article |
| id | doaj-art-65b5273e52d746329bd80995d25b2779 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-65b5273e52d746329bd80995d25b27792025-02-03T07:24:20ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/857081857081Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation AXB+CXD=E with the Least NormShi-Fang Yuan0School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, ChinaUsing the Kronecker product of matrices, the Moore-Penrose generalized inverse, and the complex representation of quaternion matrices, we derive the expressions of least squares solution with the least norm, least squares pure imaginary solution with the least norm, and least squares real solution with the least norm of the quaternion matrix equation AXB+CXD=E, respectively.http://dx.doi.org/10.1155/2014/857081 |
| spellingShingle | Shi-Fang Yuan Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation AXB+CXD=E with the Least Norm Journal of Applied Mathematics |
| title | Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation AXB+CXD=E with the Least Norm |
| title_full | Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation AXB+CXD=E with the Least Norm |
| title_fullStr | Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation AXB+CXD=E with the Least Norm |
| title_full_unstemmed | Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation AXB+CXD=E with the Least Norm |
| title_short | Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation AXB+CXD=E with the Least Norm |
| title_sort | least squares pure imaginary solution and real solution of the quaternion matrix equation axb cxd e with the least norm |
| url | http://dx.doi.org/10.1155/2014/857081 |
| work_keys_str_mv | AT shifangyuan leastsquarespureimaginarysolutionandrealsolutionofthequaternionmatrixequationaxbcxdewiththeleastnorm |