Real representation for solving reduced biquaternion matrix equations XF−AX=BY$$ XF- AX= BY $$ and XF−AX˜=BY$$ XF-A\tilde{X}= BY $$

Abstract

In this paper, a new real representation of reduced biquaternion matrix is proposed, and the solutions of the reduced biquaternion matrix equations XF − AX = BY and XF − A X = BY are solved by means of this method. The corresponding numerical algorithm is provided, and the effectiveness of this method is verified by numerical examples.