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

<h2> List of H Matrices </h2>

<h3>Description</h3>

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


<h3>Usage</h3>

<pre>
H.matrices(r, c = r)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>r</code></td>
<td>
<p> a positive integer value for an order r identity matrix </p>
</td></tr>
<tr valign="top"><td><code>c</code></td>
<td>
<p> a positive integer value for an order c identify matrix </p>
</td></tr>
</table>


<h3>Details</h3>

<p>Let <i>{{\bf{I}}_r} = &le;ft[ {\begin{array}{*{20}{c}}
  {{{\bf{a}}_1}}&amp;{{{\bf{a}}_2}}&amp; \cdots &amp;{{{\bf{a}}_r}}
  \end{array}} \right]</i> be the order <i>r</i> identity matrix
with corresponding unit vectors <i>{{{\bf{a}}_i}}</i> with one in
its <i>i</i>th position and zeros elsewhere.  
Let <i>{{\bf{I}}_c} = &le;ft[ {\begin{array}{*{20}{c}}
  {{{\bf{b}}_1}}&amp;{{{\bf{b}}_2}}&amp; \cdots &amp;{{{\bf{b}}_c}}
  \end{array}} \right]</i> be the order <i>c</i> identity matrix
with corresponding unit vectors <i>{{{\bf{b}}_i}}</i> with one in
its <i>i</i>th position and zeros elsewhere.
The <i>r \times c</i> matrix <i>{\bf{H}}{}_{i,j} = {{\bf{a}}_i}\;{{\bf{b'}}_j}</i>
is used in the computation of the commutation matrix.
</p>


<h3>Value</h3>

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


<h3>Note</h3>

<p>The argument n must be an integer value greater than or equal to two.
</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 (1979). The commutation matrix: some properties and
applications, <em>The Annals of Statistics</em>, 7(2), 381-394.
</p>
<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>


<h3>Examples</h3>

<pre>
H.2.3 &lt;- H.matrices( 2, 3 )
H.3 &lt;- H.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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