Finite-dimensional Calogero representation of the $q$-differential operator

A finite-dimensional matrix representation of the Jackson $q$-differential operator $D_q$, defined by $D_qf(x)$ $=$ $(f(qx)-f(x))/(x(q-1))$, is written down following Calogero. Such a representation of $D_q$ should have applications in $q$-analysis leading to the corresponding extensions of the numerous results of Calogero's work.