# VANDER

## Purpose:

Generates a Vandermonde matrix.

## Syntax:

VANDER(c, n)

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

## Returns:

An array, a Vandermonde matrix.

## Example:

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.

## Example:

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.

## Remarks:

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.