<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: List of T Matrices</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<link rel="stylesheet" type="text/css" href="R.css" />
</head><body>

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

<h2> List of T Matrices </h2>

<h3>Description</h3>

<p>This function constructs a list of lists.  The number of components in
the high level list is n.  Each of the n components is also a list.
Each sub-list has n components each of which is an order n square matrix.
</p>


<h3>Usage</h3>

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


<h3>Arguments</h3>

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


<h3>Details</h3>

<p>Let <i>{{\bf{E}}_{i,j}}\;i = 1, &hellip; ,n\;;\;j = 1, &hellip; ,n</i> 
be a representative order <i>n</i> matrix created with function <code>E.matrices</code>.
The order <i>n</i> matrix <i>{{\bf{T}}_{i,j}}</i> is defined as follows
<i>{{\bf{T}}_{i,j}} = &le;ft\{ {\begin{array}{*{20}{c}}
{{{\bf{E}}_{i,j}}}&amp;{i = j}\\
{{{\bf{E}}_{i,j}} + {{\bf{E}}_{j,i}}}&amp;{i \ne j}
\end{array}} \right.</i>
</p>


<h3>Value</h3>

<p>A list of <i>n</i> components.
</p>
<table summary="R valueblock">
<tr valign="top"><td><code>1 </code></td>
<td>
<p>A list of <i>n</i> components</p>
</td></tr>
<tr valign="top"><td><code>2 </code></td>
<td>
<p>A list 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 list 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{T}}_{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>See Also</h3>

<p><code><a href="E.matrices.html">E.matrices</a></code>
</p>


<h3>Examples</h3>

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

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