  Dual quaternion matrices have important applications in multi-agent formation
control. In this paper, we first address the concept of spectral norm of dual
quaternion matrices. Then, we introduce a von Neumann type trace inequality and
a Hoffman-Wielandt type inequality for general dual quaternion matrices, where
the latter characterizes a simultaneous perturbation bound on all singular
values of a dual quaternion matrix. In particular, we also present two variants
of the above two inequalities expressed by eigenvalues of dual quaternion
Hermitian matrices. Our results are helpful for the further study of dual
quaternion matrix theory, algorithmic design, and applications.
