A System of Four Generalized Sylvester Matrix Equations over the Quaternion Algebra

Abstract

In this paper, we make use of the simultaneous decomposition of eight quaternion matrices to study the solvability conditions and general solutions to a system of two-sided coupled Sylvester-type quaternion matrix equations AiXiCi+BiXi+1Di=Ωi,i=1,2,3,4. We design an algorithm to compute the general solution to the system and give a numerical example. Additionally, we consider the application of the system in the encryption and decryption of color images.

Keywords

• quaternion matrix equation
• matrix decomposition
• solvability
• general solution