reduced row echelon formReducedRowEchelonForm2002-01-26 10:29:382009-04-04 05:40:00DefinitionHermite normal form% this is the default PlanetMath preamble. as your knowledge
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% define commands hereFor a matrix to be in \emph{reduced row echelon form} (or \emph{Hermite normal form}) it has to first satisfy the requirements to be in row echelon form and additionally satisfy the following requirements:
\begin{enumerate}
\item The first non-zero element in any row must be 1.
\item The first element of value 1 in any row must be the only non-zero value in its column.
\end{enumerate}
An example of a matrix in reduced row echelon form could be:
\begin{displaymath}
\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)
\end{displaymath}