<?xml version="1.0" encoding="UTF-8"?>
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 * Copyright (C) 2008 - INRIA
 *
 * Copyright (C) 2012 - 2016 - Scilab Enterprises
 *
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 * pursuant to article 5.3.4 of the CeCILL v.2.1.
 * This file was originally licensed under the terms of the CeCILL v2.1,
 * and continues to be available under such terms.
 * For more information, see the COPYING file which you should have received
 * along with this program.
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<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="fullrfk">
    <refnamediv>
        <refname>fullrfk</refname>
        <refpurpose>full rank factorization of A^k</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>[Bk,Ck]=fullrfk(A,k)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>A</term>
                <listitem>
                    <para>real or complex matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>k</term>
                <listitem>
                    <para>integer</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Bk,Ck</term>
                <listitem>
                    <para>real or complex matrices</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            This function computes the full rank factorization of <literal>A^k</literal> i.e.
            <literal>Bk*Ck=A^k</literal> where <literal>Bk</literal> is full column rank and <literal>Ck</literal> full row rank.
            One has range(<literal>Bk</literal>)=range(<literal>A^k</literal>) and ker(<literal>Ck</literal>)=ker(<literal>A^k</literal>).
        </para>
        <para>
            For <literal>k=1</literal>, <literal>fullrfk</literal> is equivalent to <literal>fullrf</literal>.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
A=rand(5,2)*rand(2,5);[Bk,Ck]=fullrfk(A,3);
norm(Bk*Ck-A^3,1)
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="fullrf">fullrf</link>
            </member>
            <member>
                <link linkend="range">range</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
