Echeleon Forms
Echeleon forms are special matrices such that they are in the form:
$$ \begin{bmatrix} 0 & P & * & * & * \\0 & 0 & P & * & * \\0 & 0 & 0 & 0 & P \\0 & 0 & 0 & 0 & 0 \end{bmatrix} $$
In this matrice, $P$’s are called pivot points, meaning that they can be any value besides 0. While $*$’s can be any value.