A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation. (12th January 2014) - Song, Caiqin; Feng, Jun-e; Wang, Xiaodong; Zhao, Jianli
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.