Definition:Echelon Matrix/Echelon Form/Non-Unity Variant/Definition 1

Definition
Let $\mathbf A = \sqbrk a_{m n}$ be a matrix whose dimensions are $m \times n$.

$\mathbf A$ is in non-unity echelon form :
 * $(1): \quad$ 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.

Also see

 * Equivalence of Definitions of Non-Unity Variant of Echelon Form