An Exact Solution to a Quaternion Matrix Equation with an Application

In this paper, we establish the solvability conditions and the formula of the general solution to a Sylvester-like quaternion matrix equation. As an application, we give some necessary and sufficient conditions for a system of quaternion matrix equations to be consistent, and present an expression of the general solution of the system when it is solvable. We present an algorithm and an example to illustrate the main results of this paper. The findings of this paper generalize the known results in the literature.

Automated summary

In this paper, the solvability conditions and the general solution formula for a Sylvester-like quaternion matrix equation are established. A sufficient and necessary conditions for a system of quaternion matrix equations to be consistent are also given, along with an expression of the general solution when the system is solvable. An algorithm and an example are presented to illustrate the main results of this paper. The findings of this paper generalize the known results in the literature.