  Given an abelian variety $A$ defined over a finite field $k$, we say that $A$
is "cyclic" if its group $A(k)$ of rational points is cyclic. In this paper we
give a bijection between cyclic abelian varieties of an ordinary isogeny class
$\mathcal{A}$ with Weil polynomial $f_{\mathcal{A}}$ and some classes of
matrices with integer coefficients and having $f_{\mathcal{A}}$ as
characteristic polynomial.
