<?xml version="1.0" encoding="UTF-8"?>
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<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="expm">
    <refnamediv>
        <refname>expm</refname>
        <refpurpose>square matrix exponential</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>expm(X)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>X</term>
                <listitem>
                    <para>a square matrix with real or complex entries.</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            If <varname>X</varname> is a square matrix then <literal>expm(X)</literal> is the matrix
        </para>
        <para>
            <literal>expm(X) = I + X + X^2 /2 + ...</literal>
        </para>
        <para>
            The computation is performed by first
            block-diagonalizing <varname>X</varname> and then applying a Pade approximation
            on each block.
        </para>
        <para>
            Padé approximant is the "best" approximation of a function by a rational function
            of given order. The technique was developed by Henri Padé, a French mathematician.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
X=[1 2;3 4]
expm(X)
logm(expm(X))
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="logm">logm</link>
            </member>
            <member>
                <link linkend="bdiag">bdiag</link>
            </member>
            <member>
                <link linkend="coff">coff</link>
            </member>
            <member>
                <link linkend="log">log</link>
            </member>
            <member>
                <link linkend="exp">exp</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
