Definition:Echelon Matrix/Reduced Echelon Form

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

The matrix $\mathbf A$ is in reduced echelon form, in addition to being in echelon form, the leading $1$ in any non-zero row is the only non-zero element in the column in which that $1$ occurs.

Such a matrix is called a reduced echelon matrix.

Also known as
The reduced echelon form is also known as row canonical form, or reduced row echelon form.

The abbreviated term ref or rref is often used for reduced (row) echelon form, but it is recommended that it be explained when first invoked in an argument.