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vander

Vandermonde matrix

Syntax

v = vander(x)
v = vander(x, n)

Arguments

x

real or complex vector

n

integer value, the number of columns of y. By default, n is equal to size(x, "*")

v

number of rows of x x n matrix

Description

v = vander(x [,n]) returns the Vandermonde matrix. The columns of y are powers of the x vector.

The Vandermonde matrix is a matrix defined by v(i,j) = x(i)^(j), i.e

v = \begin{bmatrix} x_1^0 \ \ x_1^1 \ \ x_0^2 \ \ ... \ \ x_0^n 
                \\ x_2^0 \ \ x_2^1 \ \ x_2^2 \ \ ... \ \ x_2^n 
                \\ ... \ \ ... \ \ ... \ \ ... \ \ ...
                \\ x_m^0 \ \ x_m^1 \ \ x_m^2 \ \ ... \ \ x_m^n  \end{bmatrix}.

If n is specified, the Vandermonde matrix will have n columns. By default, the Vandermonde matrix is a square matrix.

Examples

Vandermonde matrix with vector

x = 1:5
v = vander(x)

Vandermonde matrix with n columns

x = 2:2:10
n = 3;
v = vander(x, n)

See also

  • toeplitz — matrice de Toeplitz, à bandes diagonales constantes choisies

History

VersionDescription
2025.0.0 Introduction in Scilab.
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Last updated:
Thu Oct 24 11:15:58 CEST 2024