The equivalence canonical form of five quaternion matrices with applications to imaging and Sylvester-type equations

The equivalence canonical form of five quaternion matrices is investigated. Applications that are discussed include Sylvester-type quaternion matrix equations and color image encryption. A system of one-sided Sylvester-type quaternion matrix equations with six unknowns and five equations is considered by using this equivalence canonical form. Two different types of necessary and sufficient conditions for a solution to this system in terms of ranks and block matrices are presented. An expression of the general solution to the system is provided when it is solvable. Five color images can be encrypted simultaneously by using this equivalence canonical form. Some algorithms and examples are given to illustrate the main result.