The Minimal Norm Hermitian Solutions of the Reduced Biquaternion Matrix Equation MO + OT N = Z

In the present work, a new real representation of reduced biquaternion matrix and the special properties of Vec(ΦEOF ) are used to solve the minimal norm Hermitian solution, pure imaginary Hermitian solution and pure real Hermitian solution of reduced biquaternion matrix equation, and the necessary and sufficient conditions are provided. Moreover, the corresponding numerical algorithms are given, and the real representation method and complex representation method are compared in a numerical example. And it is shown that the method of this paper produces less error and shorter CPU time than the complex representation method, which is demonstrated the effectiveness and reasonableness of these algorithms.