<?xml version="1.0" encoding="UTF-8"?>
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 * Scilab ( http://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="en" xml:id="proj">
    <refnamediv>
        <refname>proj</refname>
        <refpurpose>projection</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>P = proj(X1,X2)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>X1,X2</term>
                <listitem>
                    <para>two real matrices with equal number of columns</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>P</term>
                <listitem>
                    <para>
                        real projection matrix (<literal>P^2=P</literal>)
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>P</literal> is the projection on <literal>X2</literal> parallel to <literal>X1</literal>.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
X1=rand(5,2);X2=rand(5,3);
P=proj(X1,X2);
norm(P^2-P,1)
trace(P)    // This is dim(X2)
[Q,M]=fullrf(P);
svd([Q,X2])   // span(Q) = span(X2)
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="projspec">projspec</link>
            </member>
            <member>
                <link linkend="orth">orth</link>
            </member>
            <member>
                <link linkend="orthProj">orthProj</link>
            </member>
            <member>
                <link linkend="fullrf">fullrf</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
