| vandermonde.matrix {matrixcalc} | R Documentation |
Vandermonde matrix
Description
This function returns an m by n matrix of the powers of the alpha vector
Usage
vandermonde.matrix(alpha, n)
Arguments
alpha |
A numerical vector of values |
n |
The column dimension of the Vandermonde matrix |
Details
In linear algebra, a Vandermonde matrix is an m \times n matrix with terms
of a geometric progression of an m \times 1 parameter vector {\bf{\alpha }} = {\left\lbrack {\begin{array}{cccc}
{{\alpha _1}}&{{\alpha _2}}& \cdots &{{\alpha _m}}
\end{array}} \right\rbrack^\prime }
such that V\left( {\bf{\alpha }} \right) = \left\lbrack {\begin{array}{ccccc}
1&{{\alpha _1}}&{\alpha _1^2}& \cdots &{\alpha _1^{n - 1}}\\
1&{{\alpha _2}}&{\alpha _2^2}& \cdots &{\alpha _2^{n - 1}}\\
1&{{\alpha _3}}&{\alpha _3^2}& \cdots &{\alpha _3^{n - 1}}\\
\cdots & \cdots & \cdots & \cdots & \cdots \\
1&{{\alpha _m}}&{\alpha _m^2}& \cdots &{\alpha _m^{n - 1}}
\end{array}} \right\rbrack.
Value
A matrix.
Author(s)
Frederick Novomestky fnovomes@poly.edu
References
Horn, R. A. and C. R. Johnson (1991). Topics in matrix analysis, Cambridge University Press.
Examples
alpha <- c( .1, .2, .3, .4 )
V <- vandermonde.matrix( alpha, 4 )
print( V )