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<table width="100%" summary="page for Null {MASS}"><tr><td>Null {MASS}</td><td align="right">R Documentation</td></tr></table>
<h2>Null Spaces of Matrices</h2>


<h3>Description</h3>

<p>
Given a matrix, <code>M</code>, find a matrix <code>N</code> giving a basis for the
null space.  That is <code>t(N) %*% M</code>
is the zero and <code>N</code> has the maximum number of linearly
independent columns.
</p>


<h3>Usage</h3>

<pre>
Null(M)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>M</code></td>
<td>
Input matrix.  A vector is coerced to a 1-column matrix.
</td></tr>
</table>

<h3>Value</h3>

<p>
The matrix <code>N</code> with the basis for the null space, or an empty
vector if the matrix <code>M</code> is square and of maximal rank.</p>

<h3>References</h3>

<p>
Venables, W. N. and Ripley, B. D. (2002)
<EM>Modern Applied Statistics with S.</EM> Fourth edition.  Springer.
</p>


<h3>See Also</h3>

<p>
<code><a href="../../Matrix/html/qr-methods.html">qr</a></code>, <code><a href="../../base/html/qraux.html">qr.Q</a></code>
</p>


<h3>Examples</h3>

<pre>
# The function is currently defined as
function(M)
{
        tmp &lt;- qr(M)
        set &lt;- if(tmp$rank == 0) 1:ncol(M) else  - (1:tmp$rank)
        qr.Q(tmp, complete = TRUE)[, set, drop = FALSE]
}
</pre>



<hr><div align="center">[Package <em>MASS</em> version 7.2-44 <a href="00Index.html">Index]</a></div>

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