VANDER

Purpose:

Generates a Vandermonde matrix.

VANDER(c, n)

c	-	A series, the base of the Vandermonde matrix.
n	-	Optional. An integer, the degree. Defaults to length(c).

An array, a Vandermonde matrix.

c = {1, 2, 3, 4};

v = vander(c);

v == {{ 1, 1, 1, 1},

{ 8, 4, 2, 1},

{27, 9, 3, 1},

{64, 16, 4, 1}}

The second to last column of v is identical to c.

c = {1, 2, 3, 4};

v = vander(c, 3);

v == {{ 1, 1, 1},

{ 4, 2, 1},

{ 9, 3, 1},

{16, 4, 1}}

A third degree Vandermonde matrix is returned where the result is the same as the last 3 columns of the full Vandermonde matrix.

For column c, a square Vandermonde matrix takes the form:

c[1]^n-1 ... c[1]³ c[1]² c[1] 1

c[2]^n-2 ... c[2]² c[2]² c[2] 1

c[3]^n-3 ... c[3]³ c[3]² c[3] 1

. . . . . .

c[n]^n-1 ... c[n]³ c[n]² c[n] 1

If the degree n is not specified, a square Vandermonde matrix is returned where the degree is set to length(c) - 1.

If n is specified, a non-square Vandermonde matrix of size length(c) x n is returned.