TOEPLITZ

Purpose:

Generates a Toeplitz matrix.

Syntax:

TOEPLITZ(c, r)

c

-

A series, the first column of the output array.

r

-

Optional, a series, the first row of the output array. Defaults to c.

Returns:

An array, a symmetric or unsymmetric Toeplitz matrix.

Example:

c = {1, 2, 3};

t = toeplitz(c);

 

t == {{1, 2, 3},

      {2, 1, 2}, 

      {3, 3, 1}} 

 

The first row and column of t is identical to c.

Example:

c = {1, 2, 3};

r = {1, 8, 9};

t = toeplitz(c, r);

 

t == {{1, 8, 9},

      {2, 1, 8}, 

      {3, 2, 1}} 

 

The first row is identical to r and the first column is identical to c.

Remarks:

For column c and row r, a square Toeplitz matrix takes the form:

 

  c[1]   r[2]   r[3]  ...  r[n]

  c[2]   c[1]   r[2]  ...  r[n-1]

  c[3]   c[2]   c[1]  ...  r[n-2]

    .      .      .   .      .

    .      .      .     .    .

    .      .      .       .  .

  c[n]   c[n-1] c[n-2] ... c[1]

 

If r is not specified, a symmetric Toeplitz matrix is returned where c represents the first row and column.

 

If r is specified, an unsymmetric Toeplitz matrix is returned where the first column is c and the first row is r. In this case, if c[1] r[1], c[1] is used as the first element.

See Also:

HANKEL

KRON

VANDER