PlanetMath: reduced row echelon form

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reduced row echelon form

(Definition)

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:

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

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

$\displaystyle \left( \begin{array}{cccccccccc} 0 & 1 & 2 & 6 & 0 & 1 & 0 & 0 & ... ...& 0 & 1 & 2 & 1\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\ \end{array}\right)$

"reduced row echelon form" is owned by mathcam. [ full author list (2) | owner history (1) ]

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Also defines:

Hermite normal form

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Cross-references: column, row, row echelon form, matrix

This is version 4 of reduced row echelon form, born on 2002-01-26, modified 2006-06-13.
Object id is 1617, canonical name is ReducedRowEchelonForm.
Accessed 23211 times total.

Classification:

AMS MSC:

15A06 (Linear and multilinear algebra; matrix theory :: Linear equations)

Pending Errata and Addenda

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