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

<h2> Vandermonde matrix </h2>

<h3>Description</h3>

<p>This function returns an m by n matrix of the powers of the alpha vector
</p>


<h3>Usage</h3>

<pre>
vandermonde.matrix(alpha, n)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>alpha</code></td>
<td>
<p> A numerical vector of values </p>
</td></tr>
<tr valign="top"><td><code>n</code></td>
<td>
<p> The column dimension of the Vandermonde matrix </p>
</td></tr>
</table>


<h3>Details</h3>

<p>In linear algebra, a Vandermonde matrix is an <i>m \times n</i> matrix with terms
of a geometric progression of an <i>m \times 1</i> parameter vector <i>{\bf{&alpha; }} = {&le;ft[ {\begin{array}{*{20}{c}}
{{&alpha; _1}}&amp;{{&alpha; _2}}&amp; \cdots &amp;{{&alpha; _m}}
\end{array}} \right]^\prime }</i> 
such that <i>V&le;ft( {\bf{&alpha; }} \right) = &le;ft[ {\begin{array}{*{20}{c}}
1&amp;{{&alpha; _1}}&amp;{&alpha; _1^2}&amp; \cdots &amp;{&alpha; _1^{n - 1}}\\
1&amp;{{&alpha; _2}}&amp;{&alpha; _2^2}&amp; \cdots &amp;{&alpha; _2^{n - 1}}\\
1&amp;{{&alpha; _3}}&amp;{&alpha; _3^2}&amp; \cdots &amp;{&alpha; _3^{n - 1}}\\
 \cdots &amp; \cdots &amp; \cdots &amp; \cdots &amp; \cdots \\
1&amp;{{&alpha; _m}}&amp;{&alpha; _m^2}&amp; \cdots &amp;{&alpha; _m^{n - 1}}
\end{array}} \right]</i>.
</p>


<h3>Value</h3>

<p>A matrix.
</p>


<h3>Author(s)</h3>

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


<h3>References</h3>

<p>Horn, R. A. and C. R. Johnson (1991). <em>Topics in matrix analysis</em>, Cambridge
University Press.
</p>


<h3>Examples</h3>

<pre>
alpha &lt;- c( .1, .2, .3, .4 )
V &lt;- vandermonde.matrix( alpha, 4 )
print( V )
</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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