<?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="ja" xml:id="fullrfk">

    <refnamediv>

        <refname>fullrfk</refname>

        <refpurpose>A^kのフルランク分解</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[Bk,Ck]=fullrfk(A,k)</synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>A</term>

                <listitem>

                    <para>実数または複素数の行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>k</term>

                <listitem>

                    <para>整数</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>Bk,Ck</term>

                <listitem>

                    <para>実数または複素数の行列</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            この関数は,<literal>A^k</literal>のフルランク分解,

            すなわち, <literal>Bk*Ck=A^k</literal> を計算します.

            ただし, <literal>Bk</literal> は列フルランク,

            <literal>Ck</literal>は行フルランクです.

            range(<literal>Bk</literal>)=range(<literal>A^k</literal>)

            および ker(<literal>Ck</literal>)=ker(<literal>A^k</literal>)となります.

        </para>

        <para>

            <literal>k=1</literal>の場合, <literal>fullrfk</literal> は

            <literal>fullrf</literal>と等価になります.

        </para>

    </refsection>

    <refsection>

        <title>例</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>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="fullrf">fullrf</link>

            </member>

            <member>

                <link linkend="range">range</link>

            </member>

        </simplelist>

    </refsection>

</refentry>

