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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) {date_debut_1}-{date_fin_1} - {organisme 1} {auteur 1}
* Copyright (C) {date_debut_2}-{date_fin_2} - {organisme 2} {auteur 2}
* ...
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
-->
<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" version="5.0-subset Scilab" xml:lang="en" xml:id="hat">
<info>
<pubdate>$LastChangedDate$</pubdate>
</info>
<refnamediv>
<refname>hat</refname>
<refpurpose> (^) exponentiation</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>A^b</synopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>
Exponentiation of matrices or vectors by a constant vector.</para>
<para>
If <literal>A</literal> is a vector or a rectangular matrix the exponentiation is done
element-wise, with the usual meaning.</para>
<para>
For square <literal>A</literal> matrices the exponentiation is done in the matrix sense.</para>
<para>
For boolean, polynomial and rational matrices, the exponent must be an
integer</para>
<refsection>
<title>Remarks </title>
<para><literal>123.^b</literal> is interpreted as <literal>(123).^b</literal>. In such
cases dot is part of the operator, not of the number.</para>
<para>
For two real or complex numbers <literal>x1</literal> et
<literal>x2</literal> the value of <literal>x1^x2</literal> is the "principal value"
determined by <literal>x1^x2 = exp(x2*log(x1))</literal>.
</para>
</refsection>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
2^4
(-0.5)^(1/3)
[1 2;2 4]^(1+%i)
s=poly(0,"s");
[1 2 s]^4
[s 1;1 s]^(-1)
]]></programlisting>
</refsection>
<refsection>
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="exp">exp</link>
</member>
<member>
<link linkend="inv">inv</link>
</member>
</simplelist>
</refsection>
</refentry>
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