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<h4 class="subsection" id="Empty-Matrices-1"><span>4.1.1 Empty Matrices<a class="copiable-link" href="#Empty-Matrices-1"> ¶</a></span></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 class="cite">An Empty Exercise</cite>, SIGNUM, Volume 25, pages 2–6, 1990 and
C. N. Nett and W. M. Haddad, in
<cite class="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 class="var">s</var>, an <var class="var">m</var> by
<var class="var">n</var> matrix <code class="code">M(mxn)</code>, and an <var class="var">m</var> by <var class="var">n</var> empty matrix
<code class="code">[](mxn)</code> (with either one or both dimensions equal to zero), the
following are true:
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">s * [](mxn) = [](mxn) * s = [](mxn)
[](mxn) + [](mxn) = [](mxn)
[](0xm) * M(mxn) = [](0xn)
M(mxn) * [](nx0) = [](mx0)
[](mx0) * [](0xn) = 0(mxn)
</pre></div></div>
<p>By default, dimensions of the empty matrix are printed along with the
empty matrix symbol, ‘<samp class="samp">[]</samp>’. The built-in variable
<code class="code">print_empty_dimensions</code> controls this behavior.
</p>
<a class="anchor" id="XREFprint_005fempty_005fdimensions"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-print_005fempty_005fdimensions"><span><code class="def-type"><var class="var">val</var> =</code> <strong class="def-name">print_empty_dimensions</strong> <code class="def-code-arguments">()</code><a class="copiable-link" href="#index-print_005fempty_005fdimensions"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-print_005fempty_005fdimensions-1"><span><code class="def-type"><var class="var">old_val</var> =</code> <strong class="def-name">print_empty_dimensions</strong> <code class="def-code-arguments">(<var class="var">new_val</var>)</code><a class="copiable-link" href="#index-print_005fempty_005fdimensions-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-print_005fempty_005fdimensions-2"><span><code class="def-type"><var class="var">old_val</var> =</code> <strong class="def-name">print_empty_dimensions</strong> <code class="def-code-arguments">(<var class="var">new_val</var>, "local")</code><a class="copiable-link" href="#index-print_005fempty_005fdimensions-2"> ¶</a></span></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 class="samp">[]</samp>’.
</p>
<p>For example, the expression
</p>
<div class="example">
<pre class="example-preformatted">zeros (3, 0)
</pre></div>
<p>will print
</p>
<div class="example">
<pre class="example-preformatted">ans = [](3x0)
</pre></div>
<p>When called from inside a function with the <code class="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 class="strong">See also:</strong> <a class="ref" 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 class="xref" href="Assignment-Ops.html">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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