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Abstract and Applied Analysis
Volume 2014, Article ID 285086, 9 pages
Research Article

A Real Representation Method for Solving Yakubovich--Conjugate Quaternion Matrix Equation

1School of Mathematics, Shandong University, Jinan 250100, China
2College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China
3School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
4College of Mathematics Science, Liaocheng University, Liaocheng 252059, China

Received 19 October 2013; Revised 12 December 2013; Accepted 14 December 2013; Published 12 January 2014

Academic Editor: Ngai-Ching Wong

Copyright © 2014 Caiqin Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new approach is presented for obtaining the solutions to Yakubovich--conjugate quaternion matrix equation based on the real representation of a quaternion matrix. Compared to the existing results, there are no requirements on the coefficient matrix . The closed form solution is established and the equivalent form of solution is given for this Yakubovich--conjugate quaternion matrix equation. Moreover, the existence of solution to complex conjugate matrix equation 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--conjugate quaternion matrix equation . Numerical example shows the effectiveness of the proposed results.