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

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 A i X i C i + B i X i + 1 D i = Ω i , 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. [ABSTRACT FROM AUTHOR]