<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>fullrfk</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="fullrfk"> full rank factorization of <VERB>A^k</VERB></SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[Bk,Ck]=fullrfk(A,k)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>A</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: real or complex matrix</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>k</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: integer</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>Bk,Ck</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: real or complex matrices</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    This function computes the full rank factorization of <VERB>A^k</VERB> i.e.
    <VERB>Bk*Ck=A^k</VERB> where <VERB>Bk</VERB> is full column rank and <VERB>Ck</VERB> full row rank.
    One has range(<VERB>Bk</VERB>)=range(<VERB>A^k</VERB>) and ker(<VERB>Ck</VERB>)=ker(<VERB>A^k</VERB>).</P>
    <P>
    For <VERB>k=1</VERB>, <VERB>fullrfk</VERB> is equivalent to <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>
