As a powerful tool to represent rigid body motion in 3D spaces, dual
quaternions have been successfully applied to robotics, 3D motion modelling and
control, and computer graphics. Due to the important applications in
multi-agent formation control, this paper addresses the concept of spectral
norm of dual quaternion matrices. 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