<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>rref</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="rref"> computes  matrix row echelon form by lu transformations</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>R=rref(A)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>A</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>:  m x n matrix with scalar entries</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>R</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>:  m x n matrix,row echelon form of a</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P><VERB>rref</VERB> computes the row echelon form of the given matrix by left lu
    decomposition. If ones need the transformation used just call
    <VERB>X=rref([A,eye(m,m)])</VERB> the row echelon form <VERB>R</VERB> is <VERB>X(:,1:n)</VERB> and
    the left transformation <VERB>L</VERB> is given by <VERB>X(:,n+1:n+m)</VERB> such as <VERB>L*A=R</VERB></P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[
A=[1 2;3 4;5 6];
X=rref([A,eye(3,3)]);
R=X(:,1:2)
L=X(:,3:5);L*A
 ]]>
  </EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>lu</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>qr</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
