reduced row echelon form
For a matrix to be in reduced row echelon form (or Hermite normal form) it has to first satisfy the requirements to be in row echelon form^{} and additionally satisfy the following requirements:

1.
The first nonzero element in any row must be 1.

2.
The first element of value 1 in any row must be the only nonzero value in its column.
An example of a matrix in reduced row echelon form could be:
$$\left(\begin{array}{cccccccccc}\hfill 0\hfill & \hfill 1\hfill & \hfill 2\hfill & \hfill 6\hfill & \hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 4\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill & \hfill 4\hfill & \hfill 1\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill & \hfill 2\hfill & \hfill 1\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \end{array}\right)$$ 
Title  reduced row echelon form 

Canonical name  ReducedRowEchelonForm 
Date of creation  20130322 12:14:14 
Last modified on  20130322 12:14:14 
Owner  mathcam (2727) 
Last modified by  mathcam (2727) 
Numerical id  9 
Author  mathcam (2727) 
Entry type  Definition 
Classification  msc 15A06 
Related topic  RowEchelonForm 
Related topic  GaussianElimination 
Related topic  DeterminingRankOfMatrix 
Defines  Hermite normal form 