  In this paper, we characterize the accessibility of discrete-time linear
control systems on Lie groups. Using an exceptional notion of derivative, we
construct a subalgebra $\mathfrak{h}$ based on the infinitesimal automorphism
of the system such that if its dimension is maximal, the system is accessible.
Our criteria provide simple conditions in a general context for the
discrete-time case. Additionally, we prove a sufficient condition for local
controllability at the identity using the infinitesimal automorphism, akin to
the ad-rank condition in the continuous case.
