<?xml version="1.0" encoding="UTF-8"?>
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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="fr" xml:id="fullrfk">
    <refnamediv>
        <refname>fullrfk</refname>
        <refpurpose>factorisation de rang plein de A^k  </refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Séquence d'appel</title>
        <synopsis>[Q,M]=fullrfk(A,k)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Paramètres</title>
        <variablelist>
            <varlistentry>
                <term>A  </term>
                <listitem>
                    <para>matrice réelle ou complexe
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>k  </term>
                <listitem>
                    <para>entier
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Q,M  </term>
                <listitem>
                    <para>matrices réelles ou complexes
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            Cette fonction calcule la factorisation de rang plein de <literal>A^k</literal> : <literal>fullrfk</literal> renvoie <literal>Q</literal> et <literal>M</literal> telles que <literal>A^k = Q*M</literal>
            avec Im(<literal>Q</literal>)=Im(<literal>A^k</literal>) et ker(<literal>M</literal>)=ker(<literal>A^k</literal>),
            <literal>Q</literal> de rang maximal, et les lignes de <literal>M</literal> sont linéairement indépendantes,
        </para>
        <para>
            Pour <literal>k=1</literal>, <literal>fullrfk</literal> est équivalent à <literal>fullrf</literal>.
        </para>
    </refsection>
    <refsection>
        <title>Exemples</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>Voir aussi</title>
        <simplelist type="inline">
            <member>
                <link linkend="fullrf">fullrf</link>
            </member>
            <member>
                <link linkend="range">range</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
