<?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:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="spanplus" xml:lang="pt">
    <refnamediv>
        <refname>spanplus</refname>
        <refpurpose>soma de subespaços</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Seqüência de Chamamento</title>
        <synopsis>[X,dim,dima]=spanplus(A,B[,tol])</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Parâmetros</title>
        <variablelist>
            <varlistentry>
                <term>A, B</term>
                <listitem>
                    <para>duas matrizes de reais ou complexos com igual número de
                        linhas
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>X</term>
                <listitem>
                    <para>matriz quadrada ortogonal ou unitária </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>dim, dima</term>
                <listitem>
                    <para>inteiros, dimensões de subespaços </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol</term>
                <listitem>
                    <para>número real não-negativo</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Descrição</title>
        <para>Computa a base X tal que:</para>
        <para>
            as primeiras <literal>dima</literal> colunas de <literal>X</literal>
            geram Im(<literal>A</literal>) e as (<literal>dim-dima</literal>) colunas
            seguintes formam uma base de <literal>A+B</literal> em relação a
            <literal>A</literal>.
        </para>
        <para>
            As <literal>dim</literal> primeiras colunas de <literal>X</literal>
            formam uma base para <literal>A+B</literal>.
        </para>
        <para>Tem-se a seguinte forma canônica para
            <literal>[A,B]</literal>:
        </para>
        <programlisting role=""><![CDATA[
         [*,*]    (dima rows)
X'*[A,B]=[0,*]    (dim-dima rows)
         [0,0]
 ]]></programlisting>
        <para>
            <literal>tol</literal> é um argumento opcional (ver código da
            função).
        </para>
    </refsection>
    <refsection>
        <title>Exemplos</title>
        <programlisting role="example"><![CDATA[
A=rand(6,2)*rand(2,5);      // rank(A)=2 (posto(A)=2)
B=[A(:,1),rand(6,2)]*rand(3,3);   //dois vetores adicionais independentes
[X,dim,dimA]=spanplus(A,B);
dimA
dim
 ]]></programlisting>
    </refsection>
    <refsection>
        <title> Ver Também</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>
