Get rid of useless spaces for refname and refpurpose
[scilab.git] / scilab / modules / linear_algebra / help / en_US / factorization / householder.xml
1 <?xml version="1.0" encoding="UTF-8"?>
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13 <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">
14     <refnamediv>
15         <refname>householder</refname>
16         <refpurpose>Householder orthogonal reflexion matrix</refpurpose>
17     </refnamediv>
18     <refsynopsisdiv>
19         <title>Calling Sequence</title>
20         <synopsis>u=householder(v [,w])</synopsis>
21     </refsynopsisdiv>
22     <refsection>
23         <title>Arguments</title>
24         <variablelist>
25             <varlistentry>
26                 <term>v</term>
27                 <listitem>
28                     <para>real or complex column vector</para>
29                 </listitem>
30             </varlistentry>
31             <varlistentry>
32                 <term>w</term>
33                 <listitem>
34                     <para>
35                         real or complex column vector with same size as <literal>v</literal>. Default value is <literal>eye(v)</literal>
36                     </para>
37                 </listitem>
38             </varlistentry>
39             <varlistentry>
40                 <term>u</term>
41                 <listitem>
42                     <para>real or complex column vector</para>
43                 </listitem>
44             </varlistentry>
45         </variablelist>
46     </refsection>
47     <refsection>
48         <title>Description</title>
49         <para>
50             given 2 column vectors <literal>v</literal>, <literal> w</literal> of same size, <literal>householder(v,w)</literal> returns a unitary 
51             column vector <literal>u</literal>, such that <literal> (eye()-2*u*u')*v</literal> is proportional to <literal>w</literal>.
52             <literal>(eye()-2*u*u')</literal> is the orthogonal Householder reflexion matrix .
53         </para>
54         <para>
55             <literal>w</literal> default value is <literal> eye(v)</literal>. In this case vector <literal> (eye()-2*u*u')*v</literal> is the 
56             vector  <literal> eye(v)*norm(v)</literal>.
57         </para>
58     </refsection>
59     <refsection role="see also">
60         <title>See Also</title>
61         <simplelist type="inline">
62             <member>
63                 <link linkend="qr">qr</link>
64             </member>
65             <member>
66                 <link linkend="givens">givens</link>
67             </member>
68         </simplelist>
69     </refsection>
70 </refentry>