Solving reduced biquaternion matrices equation $ \sum\limits_{i = 1}^{k}A_iXB_i = C $ with special structure based on semi-tensor product of matrices

Abstract

In this paper, we propose a real vector representation of reduced quaternion matrix and study its properties. By using this real vector representation, Moore-Penrose inverse, and semi-tensor product of matrices, we study some kinds of solutions of reduced biquaternion matrix equation (1.1). Several numerical examples show that the proposed algorithm is feasible at last.

Keywords

• semi-tensor product of matrices
• reduced biquaternion
• matrix equation
• real vector representation