  Let $X\subset A^{Z^d}$ be a $2$-dimensional subshift of finite type. We prove
that any $2$-dimensional multidimensional subshift of finite type can be
characterized by a square matrix of infinite dimension. We extend our result to
a general $d$-dimensional case. We prove that the multidimensional shift space
is non-empty if and only if the matrix obtained is of positive dimension. In
the process, we give an alternative view of the necessary and sufficient
conditions obtained for the non-emptiness of the multidimensional shift space.
We also give sufficient conditions for the shift space $X$ to exhibit periodic
points.
