131bd99a42f06e7f06732bdac82837d6174b5dab
[scilab.git] / scilab / modules / linear_algebra / help / en_US / factorization / householder.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="householder">
17     <refnamediv>
18         <refname>householder</refname>
19         <refpurpose>Householder orthogonal reflexion matrix</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>Calling Sequence</title>
23         <synopsis>u=householder(v [,w])</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>Arguments</title>
27         <variablelist>
28             <varlistentry>
29                 <term>v</term>
30                 <listitem>
31                     <para>real or complex column vector</para>
32                 </listitem>
33             </varlistentry>
34             <varlistentry>
35                 <term>w</term>
36                 <listitem>
37                     <para>
38                         real or complex column vector with same size as <literal>v</literal>. Default value is <literal>eye(v)</literal>
39                     </para>
40                 </listitem>
41             </varlistentry>
42             <varlistentry>
43                 <term>u</term>
44                 <listitem>
45                     <para>real or complex column vector</para>
46                 </listitem>
47             </varlistentry>
48         </variablelist>
49     </refsection>
50     <refsection>
51         <title>Description</title>
52         <para>
53             given 2 column vectors <literal>v</literal>, <literal> w</literal> of same size, <literal>householder(v,w)</literal> returns a unitary 
54             column vector <literal>u</literal>, such that <literal> (eye()-2*u*u')*v</literal> is proportional to <literal>w</literal>.
55             <literal>(eye()-2*u*u')</literal> is the orthogonal Householder reflexion matrix .
56         </para>
57         <para>
58             <literal>w</literal> default value is <literal> eye(v)</literal>. In this case vector <literal> (eye()-2*u*u')*v</literal> is the 
59             vector  <literal> eye(v)*norm(v)</literal>.
60         </para>
61     </refsection>
62     <refsection role="see also">
63         <title>See Also</title>
64         <simplelist type="inline">
65             <member>
66                 <link linkend="qr">qr</link>
67             </member>
68             <member>
69                 <link linkend="givens">givens</link>
70             </member>
71         </simplelist>
72     </refsection>
73 </refentry>