A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation
A new approach is presented for obtaining the solutions to Yakubovich-j-conjugate quaternion matrix equation X−AX^B=CY based on the real representation of a quaternion matrix. Compared to the existing results, there are no requirements on the coefficient matrix A. The closed form solution is establi...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/285086 |
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| author | Caiqin Song Jun-e Feng Xiaodong Wang Jianli Zhao |
| author_facet | Caiqin Song Jun-e Feng Xiaodong Wang Jianli Zhao |
| author_sort | Caiqin Song |
| collection | DOAJ |
| description | A new approach is presented for obtaining the solutions to Yakubovich-j-conjugate quaternion
matrix equation X−AX^B=CY based on the real representation of a quaternion matrix. Compared
to the existing results, there are no requirements on the coefficient matrix A. The closed
form solution is established and the equivalent form of solution is given for this Yakubovich-j-conjugate
quaternion matrix equation. Moreover, the existence of solution to complex conjugate
matrix equation X−AX¯B=CY is also characterized and the solution is derived in an explicit
form by means of real representation of a complex matrix. Actually, Yakubovich-conjugate matrix
equation over complex field is a special case of Yakubovich-j-conjugate quaternion matrix equation
X−AX^B=CY. Numerical example shows the effectiveness of the proposed results. |
| format | Article |
| id | doaj-art-c1a35bbeddef4ec5858ba24edd8fa926 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c1a35bbeddef4ec5858ba24edd8fa9262025-02-03T01:04:49ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/285086285086A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix EquationCaiqin Song0Jun-e Feng1Xiaodong Wang2Jianli Zhao3School of Mathematics, Shandong University, Jinan 250100, ChinaSchool of Mathematics, Shandong University, Jinan 250100, ChinaSchool of Astronautics, Harbin Institute of Technology, Harbin 150001, ChinaCollege of Mathematics Science, Liaocheng University, Liaocheng 252059, ChinaA new approach is presented for obtaining the solutions to Yakubovich-j-conjugate quaternion matrix equation X−AX^B=CY based on the real representation of a quaternion matrix. Compared to the existing results, there are no requirements on the coefficient matrix A. The closed form solution is established and the equivalent form of solution is given for this Yakubovich-j-conjugate quaternion matrix equation. Moreover, the existence of solution to complex conjugate matrix equation X−AX¯B=CY is also characterized and the solution is derived in an explicit form by means of real representation of a complex matrix. Actually, Yakubovich-conjugate matrix equation over complex field is a special case of Yakubovich-j-conjugate quaternion matrix equation X−AX^B=CY. Numerical example shows the effectiveness of the proposed results.http://dx.doi.org/10.1155/2014/285086 |
| spellingShingle | Caiqin Song Jun-e Feng Xiaodong Wang Jianli Zhao A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation Abstract and Applied Analysis |
| title | A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation |
| title_full | A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation |
| title_fullStr | A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation |
| title_full_unstemmed | A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation |
| title_short | A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation |
| title_sort | real representation method for solving yakubovich j conjugate quaternion matrix equation |
| url | http://dx.doi.org/10.1155/2014/285086 |
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