A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation. (12th January 2014)

• Record Type: Journal Article
• Authors: Song, Caiqin; Feng, Jun-e; Wang, Xiaodong; Zhao, Jianli
• Other Names: Wong Ngai-Ching Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-01-12
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/285086
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : A new approach is presented for obtaining the solutions to Yakubovich-j -conjugate quaternion matrix equation X − A X ^ B = C Y 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 − A X ¯ B = C Y 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 − A X ^ B = C Y . Numerical example shows the effectiveness of the proposed results.