  This paper is concerned with singular matrix difference equations of mixed
order. The existence and uniqueness of initial value problems for these
equations are derived, and then the classification of them is obtained with a
similar classical Weyl's method by selecting a suitable quasi-difference. An
equivalent characterization of this classification is given in terms of the
number of linearly independent square summable solutions of the equation. The
influence of off-diagonal coefficients on the classification is illustrated by
two examples. In particular, two limit point criteria are established in terms
of coefficients of the equation.
