Solvability conditions and general solutions to some quaternion matrix equations

Abstract

This paper studies some quaternion matrix equations. We use the equivalence canonical form to present some practical necessary and sufficient conditions for the existence of a solution to the system of quaternion matrix equations in terms of ranks We derive the general solution to the above system in terms of block matrices. As an application of the system, we give some practical necessary and sufficient conditions for the existence of a ϕ‐Hermitian solution to the system of quaternion matrix equations where X, Y, and Z are ϕ‐Hermitian unknowns. We also provide the general ϕ‐Hermitian solution to the system when the solvability conditions are satisfied. Moreover, we present some numerical examples to illustrate the results of this paper.