Definition:Echelon Matrix/Reduced Echelon Form

Definition
Let $\mathbf A = \left[{a}\right]_{m n}$ be a $m \times n$ matrix in echelon form.

The matrix $\mathbf A$ is in reduced row echelon form if, 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
This form is also known as row canonical form.

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