Vandermonde matrix
This function returns an m by n matrix of the powers of the alpha vector
vandermonde.matrix(alpha, n)
alpha |
A numerical vector of values |
n |
The column dimension of the Vandermonde matrix |
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{α }} = {≤ft[ {\begin{array}{*{20}{c}} {{α _1}}&{{α _2}}& \cdots &{{α _m}} \end{array}} \right]^\prime } such that V≤ft( {\bf{α }} \right) = ≤ft[ {\begin{array}{*{20}{c}} 1&{{α _1}}&{α _1^2}& \cdots &{α _1^{n - 1}}\\ 1&{{α _2}}&{α _2^2}& \cdots &{α _2^{n - 1}}\\ 1&{{α _3}}&{α _3^2}& \cdots &{α _3^{n - 1}}\\ \cdots & \cdots & \cdots & \cdots & \cdots \\ 1&{{α _m}}&{α _m^2}& \cdots &{α _m^{n - 1}} \end{array}} \right].
A matrix.
Frederick Novomestky fnovomes@poly.edu
Horn, R. A. and C. R. Johnson (1991). Topics in matrix analysis, Cambridge University Press.
alpha <- c( .1, .2, .3, .4 ) V <- vandermonde.matrix( alpha, 4 ) print( V )
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