<?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="unobs">
    <refnamediv>
        <refname>unobs</refname>
        <refpurpose>unobservable subspace</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>
            [n, U] = unobs(A, C)
            [n, U] = unobs(A, C, tol)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>A, C</term>
                <listitem>
                    <para>real matrices</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol</term>
                <listitem>
                    <para>tolerance used when evaluating ranks (QR factorizations).</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>n</term>
                <listitem>
                    <para>dimension of unobservable subspace.</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>U</term>
                <listitem>
                    <para>
                        orthogonal change of basis which puts <literal>(A,B)</literal> in canonical form.
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>[n,[U]]=unobs(A,C,[tol])</literal> gives the unobservable form of an <literal>(A,C)</literal>
            pair.
            The <literal>n</literal> first columns of <literal>U</literal> make a basis for the unobservable
            subspace.
        </para>
        <para>
            The <literal>(2,1)</literal> block (made of last <literal>nx-n</literal> rows and <literal>n</literal> first
            columns) of <literal>U'*A*U</literal> is zero and the <literal>n</literal> first columns
            of <literal>C*U</literal> are zero.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
A=diag([1,2,3]);C=[1,0,0];
unobs(A,C)
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="contr">contr</link>
            </member>
            <member>
                <link linkend="contrss">contrss</link>
            </member>
            <member>
                <link linkend="canon">canon</link>
            </member>
            <member>
                <link linkend="cont_mat">cont_mat</link>
            </member>
            <member>
                <link linkend="spantwo">spantwo</link>
            </member>
            <member>
                <link linkend="dt_ility">dt_ility</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
