Oscillation criteria for Hamiltonian matrix difference systems

We obtain some oscillation criteria for the Hamiltonian difference system

$$\left\{ \begin{gathered}\Delta Y(t) = B(t)Y(t + 1) + C(t)Z(t), \h... ...lta Z(t) = - A(t)Y(t + 1) - {B^{\ast}}(t)Z(t), \hfill \\ \end{gathered} \right.$$

where $A,B,C,Y,Z$ are $d \times d$ matrix functions. As a corollary, we establish the validity of an earlier conjecture for a second-order matrix difference system.