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<?xml version="1.0" encoding="ISO-8859-1"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
-->
<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" version="5.0-subset Scilab" xml:id="spanplus" xml:lang="en">
<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>
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