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<?xml version="1.0" encoding="ISO-8859-1"?>
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<refentry version="5.0-subset Scilab" xml:id="backslash" xml:lang="en"
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xmlns="http://docbook.org/ns/docbook"
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xmlns:xlink="http://www.w3.org/1999/xlink"
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xmlns:svg="http://www.w3.org/2000/svg"
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xmlns:ns4="http://www.w3.org/1999/xhtml"
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xmlns:mml="http://www.w3.org/1998/Math/MathML"
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xmlns:db="http://docbook.org/ns/docbook">
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<pubdate>$LastChangedDate$</pubdate>
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<refname>backslash (\)</refname>
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<refpurpose>divis�o matricial direita-esquerda</refpurpose>
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<title>Seq��ncia de Chamamento</title>
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<synopsis>x=A\b</synopsis>
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<title>Descri��o</title>
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<para>(\) denota a divis�o matricial direita-esquerda.
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<literal>x=A\b</literal> � a solu��o para <literal>A*x=b</literal>.</para>
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<para>Se <literal>A</literal> � quadrada e n�o-singular,
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<literal>x=A\b</literal> (unicamente definida) � equivalente a
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<literal>x=inv(A)*b</literal> (mas as computa��es s�o menos custosas).
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<para>Se <literal>A</literal> n�o � quadrada, <literal>x</literal> � uma
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solu��o de m�nimo quadrado, i.e., <literal>norm(A*x-b)</literal> � m�nima
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(norma euclidiana). Se <literal>A</literal> � de posto coluna cheio, a
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solu��o de m�nimo quadrado, <literal>x=A\b</literal> , � unicamente
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definida (h� um �nico <literal>x</literal> que minimiza
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<literal>norm(A*x-b)</literal>). Se <literal>A</literal>n�o � de posto
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coluna cheio, ent�o a solu��o de m�nimo quadrado n�o � �nica e
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<literal>x=A\b</literal> , em geral, n�o � a solu��o com norma m�nima (a
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solu��o com norma m�nima � <literal>x=pinv(A)*b</literal>).</para>
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<para><literal>A.\B</literal> � a matriz com entrada
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<literal>(i,j)</literal> igual a <literal>A(i,j)\B(i,j)</literal>. Se
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<literal>A</literal> (ou <literal>B</literal>� um escalar,
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<literal>A.\B</literal> � equivalente a <literal>A*ones(B).\B</literal>
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(ou <literal>A.\(B*ones(A))</literal></para>
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<para><literal>A\.B</literal> � um operador sem significado predefinido.
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Pode ser usado para definir um novo operador (ver overloading) com a mesma
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preced�ncia que * ou /. </para>
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<title>Exemplos</title>
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<programlisting role="example">
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A=rand(3,2);b=[1;1;1]; x=A\b; y=pinv(A)*b; x-y
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A=rand(2,3);b=[1;1]; x=A\b; y=pinv(A)*b; x-y, A*x-b, A*y-b
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A=rand(3,1)*rand(1,2); b=[1;1;1]; x=A\b; y=pinv(A)*b; A*x-b, A*y-b
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A=rand(2,1)*rand(1,3); b=[1;1]; x=A\b; y=pinv(A)*b; A*x-b, A*y-b
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<title>Ver Tamb�m </title>
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<simplelist type="inline">
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<member><link linkend="slash">slash</link></member>
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<member><link linkend="inv">inv</link></member>
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<member><link linkend="pinv">pinv</link></member>
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<member><link linkend="percent">percent</link></member>
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<member><link linkend="ieee">ieee</link></member>