<?xml version="1.0" encoding="UTF-8"?>
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 * 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
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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:ns4="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="im_inv" xml:lang="pt">
    <refnamediv>
        <refname>im_inv</refname>
        <refpurpose>imagem inversa</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title> Seqüência de Chamamento </title>
        <synopsis>[X,dim]=im_inv(A,B [,tol])
            [X,dim,Y]=im_inv(A,B, [,tol])
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Parâmetros</title>
        <variablelist>
            <varlistentry>
                <term>A,B</term>
                <listitem>
                    <para>duas matirzes de reais ou complexos com igual número de
                        colunas
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>X</term>
                <listitem>
                    <para>matriz quadrada ortogonal ou unitária de ordem igual ao número
                        de colunas de <literal>A</literal>
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>dim</term>
                <listitem>
                    <para>inteiro (dimensão do subespaço) </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Y</term>
                <listitem>
                    <para>matriz ortogonal de ordem igual ao número de linhas de
                        <literal>A</literal> e <literal>B</literal>.
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Descrição</title>
        <para>
            <literal>[X,dim]=im_inv(A,B)</literal>
            computa<literal>(A^-1)(B)</literal> ,i.e, vetores cujas imagens através de
            <literal>A</literal> estão em Im(<literal>B</literal>)
        </para>
        <para>
            As <literal>dim</literal> primeiras colunas de <literal>X</literal>
            geram<literal> (A^-1)(B)</literal>
        </para>
        <para>
            <literal>tol</literal> é um limiar usado para testar a inclusão de
            subespaço ; o valor padrão é <literal>tol = 100*%eps</literal>. Se
            <literal>Y</literal> é retornado, então <literal>[Y*A*X,Y*B]</literal> é
            particionado como segue:
            <literal>[A11,A12;0,A22]</literal>,<literal>[B1;0]</literal>
        </para>
        <para>
            onde <literal>B1</literal> tem posto-linha cheio (igual a
            posto<literal>(B)</literal>) e <literal>A22</literal> tem posto-coluna
            cheio e tem <literal>dim</literal> colunas.
        </para>
    </refsection>
    <refsection>
        <title>Exemplos</title>
        <programlisting role="example"><![CDATA[
A=[rand(2,5);[zeros(3,4),rand(3,1)]];B=[[1,1;1,1];zeros(3,2)];
W=rand(5,5);A=W*A;B=W*B;
[X,dim]=im_inv(A,B)
svd([A*X(:,1:dim),B])   //vetores A*X(:,1:dim) pertencem a range(B) (Imagem de B: Im(B))
[X,dim,Y]=im_inv(A,B);[Y*A*X,Y*B]
 ]]></programlisting>
    </refsection>
    <refsection>
        <title> Ver Também</title>
        <simplelist type="inline">
            <member>
                <link linkend="rowcomp">rowcomp</link>
            </member>
            <member>
                <link linkend="spaninter">spaninter</link>
            </member>
            <member>
                <link linkend="spanplus">spanplus</link>
            </member>
            <member>
                <link linkend="linsolve">linsolve</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
