Reduced row echelon form - Revision history

Vipul: /* The reduced row echelon form of a matrix */

2014-05-01T18:20:01Z

The reduced row echelon form of a matrix

← Older revision		Revision as of 18:20, 1 May 2014
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	===The reduced row echelon form of a matrix===		===The reduced row echelon form of a matrix===

	For a <math>m \times n</math> matrix </math>A</math>, the reduced row echelon form of <math>A</math> is the unique matrix <math>B</math> in reduced row echelon form such that we can write <math>B = SA</math> where <math>S</math> is a <math>m \times m</math> [[invertible matrix]].		For a <math>m \times n</math> matrix <math>A</math>, the reduced row echelon form of <math>A</math> is the unique matrix <math>B</math> in reduced row echelon form such that we can write <math>B = SA</math> where <math>S</math> is a <math>m \times m</math> [[invertible matrix]].

Vipul at 18:19, 1 May 2014

2014-05-01T18:19:13Z

← Older revision		Revision as of 18:19, 1 May 2014
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	{{matrix property}}		{{matrix property}}

	===Definition==		==Definition==

	===A matrix being in reduced row echelon form===		===A matrix being in reduced row echelon form===

Vipul: Created page with "{{matrix property}} ===Definition== ===A matrix being in reduced row echelon form=== A matrix is said to be a '''reduced row echelon matrix''', or said to be in '''reduced..."

2014-05-01T18:18:57Z

Created page with "{{matrix property}} ===Definition== ===A matrix being in reduced row echelon form=== A matrix is said to be a '''reduced row echelon matrix''', or said to be in '''reduced..."

New page

{{matrix property}}

===Definition==

===A matrix being in reduced row echelon form===

A matrix is said to be a '''reduced row echelon matrix''', or said to be in '''reduced row echelon form''' ('''rref'''), if it satisfies the following conditions:

* All nonzero rows are above all zero rows. Here, a ''nonzero row'' is a row that has at least one nonzero entry, and a zero row is a row where ''all'' entries are zero.
* The first nonzero entry in any nonzero row occurs in a strictly later column than the first nonzero entry in the row immediately above it (and hence also, in all the rows above it).
* The first nonzero entry in any nonzero row is 1 (this condition is omitted in some definitions) ''and all other entries in the column of that entry are zero''.

With the exception of the (emphasized) second half of the last condition, the conditions above define [[row echelon form]].

===The reduced row echelon form of a matrix===

For a <math>m \times n</math> matrix </math>A</math>, the reduced row echelon form of <math>A</math> is the unique matrix <math>B</math> in reduced row echelon form such that we can write <math>B = SA</math> where <math>S</math> is a <math>m \times m</math> [[invertible matrix]].