  In the field of robotics research, a crucial applied problem is the hand-eye
calibration issue. The corresponding matrix equation $AX=YB$ in hand-eye
calibration can be equivalently transformed into the dual quaternion equation
$q_Aq_X=q_Yq_B$. However, the dual quaternion equation $q_Aq_X=q_Yq_B$ is
merely a specific case of the more general dual quaternion matrix equation
$AX-YB=C$, which also holds significant applications in system and control
theory. Therefore, we in this paper establish the solvability conditions of the
dual quaternion matrix equation $AX-YB=C$ and provide a general expression for
its solutions when it is solvable. As an application, we investigate the
analytical solutions of the dual quaternion matrix equation $AX=YB$. Finally,
we validate the main results of this paper through a numerical example.
