Open Access
2014 A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation
Caiqin Song, Jun-e Feng, Xiaodong Wang, Jianli Zhao
Abstr. Appl. Anal. 2014: 1-9 (2014). DOI: 10.1155/2014/285086


A new approach is presented for obtaining the solutions to Yakubovich-j-conjugate quaternion matrix equation XAX^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 XAX¯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 XAX^B=CY. Numerical example shows the effectiveness of the proposed results.


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Caiqin Song. Jun-e Feng. Xiaodong Wang. Jianli Zhao. "A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation." Abstr. Appl. Anal. 2014 1 - 9, 2014.


Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07022091
MathSciNet: MR3166590
Digital Object Identifier: 10.1155/2014/285086

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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