\begin{definition}[Definition:Echelon Matrix/Echelon Form/Non-Unity Variant/Definition 1]
Let $\mathbf A = \sqbrk a_{m n}$ be a matrix whose order is $m \times n$.
$\mathbf A$ is in '''non-unity echelon form''' {{iff}}:
:$(1): \quad$ Each row (except perhaps row $1$) starts with a sequence of zeroes
:$(2): \quad$ Except when for row $k$ and row $k + 1$ are zero rows, the number of zeroes in this initial sequence in row $k + 1$ is strictly greater than the number of zeroes in this initial sequence in row $k$
:$(3): \quad$ The non-zero rows appear before any zero rows.
\end{definition}