  In \cite{SiVe2} and \cite{BlMa1}, the authors proved the existence of a
so-called higher rank amplifier and in \cite{HoRiRo2}, the authors described an
explicit version of a $GL(3)$ amplifier. This article provides, for $n\geq 4$,
a totally explicit $GL(n)$ amplifier and gives all the results required to use
it effectively.
