<?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="pencan">

    <refnamediv>

        <refname>pencan</refname>

        <refpurpose>行列ペンシルの正準形</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[Q,M,i1]=pencan(Fs)

            [Q,M,i1]=pencan(E,A)

        </synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>Fs</term>

                <listitem>

                    <para>

                        標準ペンシル <literal>s*E-A</literal>

                    </para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>E,A</term>

                <listitem>

                    <para>実数正方行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>Q,M</term>

                <listitem>

                    <para>正則実数行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>i1</term>

                <listitem>

                    <para>整数</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            標準ペンシル <literal>Fs=s*E-A</literal>を指定すると,

            <literal>pencan</literal> は,

            <literal>M*(s*E-A)*Q</literal>が"正準"形となるような

            行列<literal>Q</literal> および<literal>M</literal>を返します.

        </para>

        <para>

            <literal>M*E*Q</literal> はブロック行列です.

        </para>

        <programlisting role=""><![CDATA[
[I,0;
 0,N]
 ]]></programlisting>

        <para>

            ただし,<literal>N</literal>は冪零行列<literal>N</literal>,

            <literal>i1</literal> = 行列<literal>I</literal>の大きさです.

        </para>

        <para>

            <literal>M*A*Q</literal> は以下のようなブロック行列です:

        </para>

        <programlisting role=""><![CDATA[
[Ar,0;
 0,I]
 ]]></programlisting>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
F=randpencil([],[1,2],[1,2,3],[]);
F=rand(6,6)*F*rand(6,6);
[Q,M,i1]=pencan(F);
W=clean(M*F*Q)
roots(det(W(1:i1,1:i1)))
det(W($-2:$,$-2:$))
 ]]></programlisting>

    </refsection>

    <refsection role="see also">

        <title>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="glever">glever</link>

            </member>

            <member>

                <link linkend="penlaur">penlaur</link>

            </member>

            <member>

                <link linkend="rowshuff">rowshuff</link>

            </member>

        </simplelist>

    </refsection>

</refentry>

