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[scilab.git] / scilab / modules / linear_algebra / help / en_US / factorization / householder.xml
1 <?xml version="1.0" encoding="UTF-8"?>
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17 <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="householder">
18     <refnamediv>
19         <refname>householder</refname>
20         <refpurpose>Householder orthogonal reflexion matrix</refpurpose>
21     </refnamediv>
22     <refsynopsisdiv>
23         <title>Calling Sequence</title>
24         <synopsis>u=householder(v [,w])</synopsis>
25     </refsynopsisdiv>
26     <refsection>
27         <title>Arguments</title>
28         <variablelist>
29             <varlistentry>
30                 <term>v</term>
31                 <listitem>
32                     <para>real or complex column vector</para>
33                 </listitem>
34             </varlistentry>
35             <varlistentry>
36                 <term>w</term>
37                 <listitem>
38                     <para>
39                         real or complex column vector with same size as <literal>v</literal>. Default value is <literal>eye(v)</literal>
40                     </para>
41                 </listitem>
42             </varlistentry>
43             <varlistentry>
44                 <term>u</term>
45                 <listitem>
46                     <para>real or complex column vector</para>
47                 </listitem>
48             </varlistentry>
49         </variablelist>
50     </refsection>
51     <refsection>
52         <title>Description</title>
53         <para>
54             given 2 column vectors <literal>v</literal>, <literal> w</literal> of same size, <literal>householder(v,w)</literal> returns a unitary 
55             column vector <literal>u</literal>, such that <literal> (eye()-2*u*u')*v</literal> is proportional to <literal>w</literal>.
56             <literal>(eye()-2*u*u')</literal> is the orthogonal Householder reflexion matrix .
57         </para>
58         <para>
59             <literal>w</literal> default value is <literal> eye(v)</literal>. In this case vector <literal> (eye()-2*u*u')*v</literal> is the 
60             vector  <literal> eye(v)*norm(v)</literal>.
61         </para>
62     </refsection>
63     <refsection role="see also">
64         <title>See Also</title>
65         <simplelist type="inline">
66             <member>
67                 <link linkend="qr">qr</link>
68             </member>
69             <member>
70                 <link linkend="givens">givens</link>
71             </member>
72         </simplelist>
73     </refsection>
74 </refentry>