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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:

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

$\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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See Also: row echelon form, row reduction, determining rank of matrix

Also defines:  Hermite normal form
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Cross-references: column, row, row echelon form, matrix

This is version 5 of reduced row echelon form, born on 2002-01-26, modified 2009-04-04.
Object id is 1617, canonical name is ReducedRowEchelonForm.
Accessed 25923 times total.

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