Three minimal norm Hermitian solutions of the reduced biquaternion matrix equation EM+M˜F=G$$ EM+\tilde{M}F=G $$

In this paper, we investigate the minimal norm Hermitian solution, pure imaginary Hermitian solution and pure real Hermitian solution of the reduced biquaternion matrix equation. We introduce the new real representation of the reduced biquaternion matrix and the special properties of . We present the sufficient and necessary conditions of three solutions and the corresponding numerical algorithms for solving the three solutions. Finally, we show that our method is better than the complex representation method in terms of error and CPU time in numerical examples.