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<a name="Empty-Matrices-1"></a>
<h4 class="subsection">4.1.1 Empty Matrices</h4>
<p>A matrix may have one or both dimensions zero, and operations on empty
matrices are handled as described by Carl de Boor in
<cite>An Empty Exercise</cite>, SIGNUM, Volume 25, pages 2-6, 1990 and
C. N. Nett and W. M. Haddad, in
<cite>A System-Theoretic Appropriate Realization of the Empty Matrix Concept</cite>,
IEEE Transactions on Automatic Control, Volume 38, Number 5, May 1993.
Briefly, given a scalar <var>s</var>, an <var>m</var> by
<var>n</var> matrix <code>M(mxn)</code>, and an <var>m</var> by <var>n</var> empty matrix
<code>[](mxn)</code> (with either one or both dimensions equal to zero), the
following are true:
</p>
<div class="example">
<pre class="example">s * [](mxn) = [](mxn) * s = [](mxn)
[](mxn) + [](mxn) = [](mxn)
[](0xm) * M(mxn) = [](0xn)
M(mxn) * [](nx0) = [](mx0)
[](mx0) * [](0xn) = 0(mxn)
</pre></div>
<p>By default, dimensions of the empty matrix are printed along with the
empty matrix symbol, ‘<samp>[]</samp>’. The built-in variable
<code>print_empty_dimensions</code> controls this behavior.
</p>
<a name="XREFprint_005fempty_005fdimensions"></a><dl>
<dt><a name="index-print_005fempty_005fdimensions"></a><em><var>val</var> =</em> <strong>print_empty_dimensions</strong> <em>()</em></dt>
<dt><a name="index-print_005fempty_005fdimensions-1"></a><em><var>old_val</var> =</em> <strong>print_empty_dimensions</strong> <em>(<var>new_val</var>)</em></dt>
<dt><a name="index-print_005fempty_005fdimensions-2"></a><em></em> <strong>print_empty_dimensions</strong> <em>(<var>new_val</var>, "local")</em></dt>
<dd><p>Query or set the internal variable that controls whether the dimensions of
empty matrices are printed along with the empty matrix symbol, ‘<samp>[]</samp>’.
</p>
<p>For example, the expression
</p>
<div class="example">
<pre class="example">zeros (3, 0)
</pre></div>
<p>will print
</p>
<div class="example">
<pre class="example">ans = [](3x0)
</pre></div>
<p>When called from inside a function with the <code>"local"</code> option, the
variable is changed locally for the function and any subroutines it calls.
The original variable value is restored when exiting the function.
</p>
<p><strong>See also:</strong> <a href="Terminal-Output.html#XREFformat">format</a>.
</p></dd></dl>
<p>Empty matrices may also be used in assignment statements as a convenient
way to delete rows or columns of matrices.
See <a href="Assignment-Ops.html#Assignment-Ops">Assignment Expressions</a>.
</p>
<p>When Octave parses a matrix expression, it examines the elements of the
list to determine whether they are all constants. If they are, it
replaces the list with a single matrix constant.
</p>
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