# 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. 1.

The first non-zero element in any row must be 1.

2. 2.

The first element of value 1 in any row must be the only non-zero value in its column.

An example of a matrix in reduced row echelon form could be:

 $\left(\begin{array}[]{cccccccccc}0&1&2&6&0&1&0&0&4&0\\ 0&0&0&0&1&1&0&0&1&1\\ 0&0&0&0&0&0&1&0&4&1\\ 0&0&0&0&0&0&0&1&2&1\\ 0&0&0&0&0&0&0&0&0&0\\ \end{array}\right)$
Title reduced row echelon form ReducedRowEchelonForm 2013-03-22 12:14:14 2013-03-22 12:14:14 mathcam (2727) mathcam (2727) 9 mathcam (2727) Definition msc 15A06 RowEchelonForm GaussianElimination DeterminingRankOfMatrix Hermite normal form