A Real Representation Method for Solving Yakubovich-Conjugate Quaternion Matrix EquationReport as inadecuate




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

Research Article

School of Mathematics, Shandong University, Jinan 250100, China

College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China

School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

College 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.

Abstract

A new approach is presented for obtaining the solutions to Yakubovich-conjugate quaternionmatrix equation based on the real representation of a quaternion matrix. Comparedto the existing results, there are no requirements on the coefficient matrix . The closedform solution is established and the equivalent form of solution is given for this Yakubovich-conjugatequaternion matrix equation. Moreover, the existence of solution to complex conjugatematrix equation is also characterized and the solution is derived in an explicitform by means of real representation of a complex matrix. Actually, Yakubovich-conjugate matrixequation over complex field is a special case of Yakubovich-conjugate quaternion matrix equation. Numerical example shows the effectiveness of the proposed results.





Author: Caiqin Song, Jun-e Feng, Xiaodong Wang, and Jianli Zhao

Source: https://www.hindawi.com/



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