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<table width="100%" summary="page for E.matrices {matrixcalc}"><tr><td>E.matrices {matrixcalc}</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2> List of E Matrices </h2>

<h3>Description</h3>

<p>This function constructs and returns a list of lists. The component of
each sublist is a square matrix derived from the column vectors of
an order n identity matrix.
</p>


<h3>Usage</h3>

<pre>
E.matrices(n)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>n</code></td>
<td>
<p> a positive integer for the order of the identity matrix
</p>
</td></tr>
</table>


<h3>Details</h3>

<p>Let <i>{{\bf{I}}_n} = &le;ft[ {\begin{array}{*{20}{c}}
  {{{\bf{e}}_1}}&amp;{{{\bf{e}}_2}}&amp; \cdots &amp;{{{\bf{e}}_n}}
  \end{array}} \right]</i> be the order <i>n</i> identity matrix
with corresponding unit vectors <i>{{{\bf{e}}_i}}</i> with one in
its <i>i</i>th position and zeros elsewhere.  
The <i>n \times n</i> matrix <i>{{\bf{E}}_{i,j}}</i> is computed
from the unit vectors <i>{{{\bf{e}}_i}}</i> and <i>{{{\bf{e}}_j}}</i>
as <i>{{\bf{E}}_{i,j}} = {{\bf{e}}_i}\;{{\bf{e'}}_j}</i>.  These matrices
are stored as components in a list of lists.
</p>


<h3>Value</h3>

<p>A list with <i>n</i> components
</p>
<table summary="R valueblock">
<tr valign="top"><td><code>1 </code></td>
<td>
<p>A sublist of <i>n</i> components</p>
</td></tr>
<tr valign="top"><td><code>2 </code></td>
<td>
<p>A sublist of <i>n</i> components</p>
</td></tr>
</table>
<p>...
</p>
<table summary="R valueblock">
<tr valign="top"><td><code>n </code></td>
<td>
<p>A sublist of <i>n</i> components</p>
</td></tr>
</table>
<p>Each component <i>j</i> of sublist <i>i</i> is a matrix <i>{\bf{E}}_{i,j}</i>
</p>


<h3>Note</h3>

<p>The argument n must be an integer value greater than or equal to 2.
</p>


<h3>Author(s)</h3>

<p> Frederick Novomestky <a href="mailto:fnovomes@poly.edu">fnovomes@poly.edu</a> </p>


<h3>References</h3>

<p>Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
<em>SIAM Journal on Algebraic Discrete Methods</em>, 1(4), December 1980, 422-449.
</p>
<p>Magnus, J. R. and H. Neudecker (1999). <em>Matrix Differential Calculus with Applications in Statistics and Econometrics</em>,
Second Edition, John Wiley.
</p>


<h3>Examples</h3>

<pre>
E &lt;- E.matrices( 3 )
</pre>

<hr /><div style="text-align: center;">[Package <em>matrixcalc</em> version 1.0-3 <a href="00Index.html">Index</a>]</div>
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