linsolve.xml updated - examples replaced by demos.
[scilab.git] / scilab / modules / linear_algebra / help / en_US / proj.xml
1 <?xml version="1.0" encoding="UTF-8"?>
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16 <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">
17     <refnamediv>
18         <refname>proj</refname>
19         <refpurpose>projection</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>Syntax</title>
23         <synopsis>P = proj(X1,X2)</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>Arguments</title>
27         <variablelist>
28             <varlistentry>
29                 <term>X1,X2</term>
30                 <listitem>
31                     <para>two real matrices with equal number of columns</para>
32                 </listitem>
33             </varlistentry>
34             <varlistentry>
35                 <term>P</term>
36                 <listitem>
37                     <para>
38                         real projection matrix (<literal>P^2=P</literal>)
39                     </para>
40                 </listitem>
41             </varlistentry>
42         </variablelist>
43     </refsection>
44     <refsection>
45         <title>Description</title>
46         <para>
47             <literal>P</literal> is the projection on <literal>X2</literal> parallel to <literal>X1</literal>.
48         </para>
49     </refsection>
50     <refsection>
51         <title>Examples</title>
52         <programlisting role="example"><![CDATA[
53 X1=rand(5,2);X2=rand(5,3);
54 P=proj(X1,X2);
55 norm(P^2-P,1)
56 trace(P)    // This is dim(X2)
57 [Q,M]=fullrf(P);
58 svd([Q,X2])   // span(Q) = span(X2)
59  ]]></programlisting>
60     </refsection>
61     <refsection role="see also">
62         <title>See also</title>
63         <simplelist type="inline">
64             <member>
65                 <link linkend="projspec">projspec</link>
66             </member>
67             <member>
68                 <link linkend="orth">orth</link>
69             </member>
70             <member>
71                 <link linkend="fullrf">fullrf</link>
72             </member>
73         </simplelist>
74     </refsection>
75 </refentry>