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

<h2> Fibonacci Matrix </h2>

<h3>Description</h3>

<p>This function constructs the order n + 1 square Fibonacci matrix
which is derived from a Fibonacci sequence.
</p>


<h3>Usage</h3>

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


<h3>Arguments</h3>

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


<h3>Details</h3>

<p>Let <i>&le;ft\{ {{f_0},\;{f_1},\; &hellip; ,\;{f_n}} \right\}</i> be the
set of <i> n + 1</i> Fibonacci numbers where <i>{f_0} = {f_1} = 1</i>
and <i>{f_j} = {f_{j - 1}} + {f_{j - 2}},\quad 2 &le; j &le; n</i>.  The
order <i>n + 1</i> Fibonacci matrix <i>{\bf{F}}</i> has as typical element
<i>{F_{i,j}} = &le;ft\{ {\begin{array}{*{20}{c}}
{{f_{i - j + 1}}}&amp;{i - j + 1 &ge; 0}\\
0&amp;{i - j + 1 &lt; 0}
\end{array}} \right.</i>.
</p>


<h3>Value</h3>

<p>An order <i>n + 1</i> matrix
</p>


<h3>Note</h3>

<p>If the argument n is not a positive integer, 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>Zhang, Z. and J. Wang (2006). Bernoulli matrix and its algebraic properties,
<em>Discrete Applied Nathematics</em>, 154, 1622-1632.
</p>


<h3>Examples</h3>

<pre>
F &lt;- fibonacci.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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