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.

See Also:

HANKEL

KRON

TOEPLITZ