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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>fr</LANGUAGE>
  <TITLE>fullrfk  </TITLE>
  <TYPE>Scilab Function  </TYPE>
  <DATE>April 1993  </DATE>
  <SHORT_DESCRIPTION name="fullrfk"> factorisation de rang plein de A^k  </SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
  <CALLING_SEQUENCE_ITEM>[Q,M]=fullrfk(A,k)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
 <PARAM_INDENT>
  <PARAM_ITEM>
  <PARAM_NAME>A  </PARAM_NAME>
  <PARAM_DESCRIPTION>
  <SP>
    : matrice réelle ou complexe
</SP>
  </PARAM_DESCRIPTION> 
  </PARAM_ITEM>
  <PARAM_ITEM>
  <PARAM_NAME>k  </PARAM_NAME>
  <PARAM_DESCRIPTION>
  <SP>
    : entier
</SP>
  </PARAM_DESCRIPTION> 
  </PARAM_ITEM>
  <PARAM_ITEM>
  <PARAM_NAME>Q,M  </PARAM_NAME>
  <PARAM_DESCRIPTION>
  <SP>
    : matrices réelles ou complexes
</SP>
  </PARAM_DESCRIPTION> 
  </PARAM_ITEM>
 </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
  <P>
    Cette fonction calcule la factorisation de rang plein de <VERB>A^k</VERB> : <VERB>fullrfk</VERB> renvoie <VERB>Q</VERB> et <VERB>M</VERB> telles que <VERB>A^k = Q*M</VERB>
    avec Im(<VERB>Q</VERB>)=Im(<VERB>A^k</VERB>) et ker(<VERB>M</VERB>)=ker(<VERB>A^k</VERB>),
    <VERB>Q</VERB> de rang maximal, et les lignes de <VERB>M</VERB> sont linéairement indépendantes, 
  </P>
  <P>
    Pour <VERB>k=1</VERB>, <VERB>fullrfk</VERB> est équivalent à <VERB>fullrf</VERB>.
  </P>
  </DESCRIPTION>
  <EXAMPLE><![CDATA[
A=rand(5,2)*rand(2,5);[Bk,Ck]=fullrfk(A,3);
norm(Bk*Ck-A^3,1)
 ]]></EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM> <LINK>fullrf</LINK> </SEE_ALSO_ITEM>     <SEE_ALSO_ITEM> <LINK>range</LINK> </SEE_ALSO_ITEM>
  </SEE_ALSO>
  <AUTHOR>F.D (1990);   </AUTHOR>
</MAN>
