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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="hess">
    <refnamediv>
        <refname>hess</refname>
        <refpurpose>Hessenberg form</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>H = hess(A)
            [U,H] = hess(A)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>A</term>
                <listitem>
                    <para>real or complex square matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>H</term>
                <listitem>
                    <para>real or complex square matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>U</term>
                <listitem>
                    <para>orthogonal or unitary square matrix</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>[U,H] = hess(A)</literal> produces a unitary matrix
            <literal>U</literal> and a Hessenberg matrix <literal>H</literal> so that
            <literal>A = U*H*U'</literal> and <literal>U'*U</literal> =
            Identity.  By itself, <literal>hess(A)</literal> returns <literal>H</literal>.
        </para>
        <para>
            The Hessenberg form of a matrix is zero below the first
            subdiagonal. If the matrix is symmetric or Hermitian, the form is
            tridiagonal.
        </para>
    </refsection>
    <refsection>
        <title>References</title>
        <para>
            hess function is based on the Lapack routines
            DGEHRD, DORGHR for  real matrices and  ZGEHRD, ZORGHR for the complex case.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
A=rand(3,3);[U,H]=hess(A);
and( abs(U*H*U'-A)<1.d-10 )
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="qr">qr</link>
            </member>
            <member>
                <link linkend="contr">contr</link>
            </member>
            <member>
                <link linkend="schur">schur</link>
            </member>
        </simplelist>
    </refsection>
    <refsection>
        <title>Used Functions</title>
        <para>
            <literal>hess</literal> function is based on the Lapack routines
            DGEHRD, DORGHR for  real matrices and  ZGEHRD, ZORGHR for the
            complex  case.
        </para>
    </refsection>
</refentry>
