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

<h2> Frobenius Matrix </h2>

<h3>Description</h3>

<p>This function returns an order n Frobenius matrix that is useful
in numerical mathematics.
</p>


<h3>Usage</h3>

<pre>
frobenius.matrix(n)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>n</code></td>
<td>
<p>  a positive integer value greater than 1</p>
</td></tr>
</table>


<h3>Details</h3>

<p>The Frobenius matrix is also called the companion matrix.  It arises
in the solution of systems of linear first order differential equations.
The formula for the order <i>n</i> Frobenius matrix is <i>{\bf{F}} = 
&le;ft[ {\begin{array}{*{20}{c}}0&amp;0&amp; \cdots &amp;0&amp;{{{&le;ft( { - 1} \right)}^{n - 1}}
&le;ft( {\begin{array}{*{20}{c}}n\\0\end{array}} \right)}\\1&amp;0&amp; \cdots &amp;0&amp;{{{&le;ft( { - 1} \right)}^{n - 2}}
&le;ft( {\begin{array}{*{20}{c}}n\\1\end{array}} \right)}\\0&amp;1&amp; \ddots &amp;0&amp;{{{&le;ft( { - 1} \right)}^{n - 3}}
&le;ft( {\begin{array}{*{20}{c}}n\\2\end{array}} \right)}\\ \vdots &amp; \vdots &amp; \ddots &amp; \vdots &amp; \vdots \\0&amp;0&amp; \cdots &amp;1&amp;{{{&le;ft( { - 1} \right)}^0}
&le;ft( {\begin{array}{*{20}{c}}n\\{n - 1}\end{array}} 
\right)}\end{array}} 
\right]</i>.
</p>


<h3>Value</h3>

<p>An order <i>n</i> matrix
</p>


<h3>Note</h3>

<p>If the argument n is not a positive integer that is greater than 1, 
the function presents an error message and stops.
</p>


<h3>Author(s)</h3>

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


<h3>References</h3>

<p>Aceto, L. and D. Trigiante (2001). Matrices of Pascal and Other Greats,
<em>American Mathematical Monthly</em>, March 2001, 108(3), 232-245.
</p>


<h3>Examples</h3>

<pre>
F &lt;- frobenius.matrix( 10 )
print( F )
</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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