<?xml version="1.0" encoding="UTF-8"?>

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 * Scilab ( https://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) 2008 - INRIA
 *
 * Copyright (C) 2012 - 2016 - Scilab Enterprises
 *
 * This file is hereby licensed under the terms of the GNU GPL v2.0,
 * 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="ja" xml:id="spanplus">

    <refnamediv>

        <refname>spanplus</refname>

        <refpurpose>部分空間の合計</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[X,dim,dima]=spanplus(A,B[,tol])</synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>A, B</term>

                <listitem>

                    <para>同数の行を有する実数または複素数の行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>X</term>

                <listitem>

                    <para>直交またはユニタリ正方行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>dim, dima</term>

                <listitem>

                    <para>整数, 部分空間の次元</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>tol</term>

                <listitem>

                    <para>非負の実数</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            以下の様な基底Xを計算します:

        </para>

        <para>

            <literal>X</literal>の最初の<literal>dima</literal>列が

            range(<literal>A</literal>)に展開し,

            これ以降の(<literal>dim-dima</literal>)列が,

            <literal>A+B</literal> の<literal>A</literal>に関する基底を構成.

        </para>

        <para>

            <literal>X</literal>の最初の<literal>dim</literal>列は,

            <literal>A+B</literal>の基底を構成します.

        </para>

        <para>

            <literal>[A,B]</literal>に関する以下の正準形式が定義されます:

        </para>

        <programlisting role=""><![CDATA[
         [*,*]    (dima 行)
X'*[A,B]=[0,*]    (dim-dima 行)
         [0,0]
 ]]></programlisting>

        <para>

            <literal>tol</literal> はオプションの引数です(関数のコードを参照).

        </para>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
A=rand(6,2)*rand(2,5);      // rank(A)=2
B=[A(:,1),rand(6,2)]*rand(3,3);   //独立なベクトル2つを追加
[X,dim,dimA]=spanplus(A,B);
dimA
dim
 ]]></programlisting>

    </refsection>

    <refsection role="see also">

        <title>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="spaninter">spaninter</link>

            </member>

            <member>

                <link linkend="im_inv">im_inv</link>

            </member>

            <member>

                <link linkend="spantwo">spantwo</link>

            </member>

        </simplelist>

    </refsection>

</refentry>

