Home > freetb4matlab > special-matrix > toeplitz.m

toeplitz

PURPOSE ^

% Return the Toeplitz matrix constructed given the first column @var{c},

SYNOPSIS ^

function retval = toeplitz (c, r)

DESCRIPTION ^

% -*- texinfo -*-
% @deftypefn {Function File} {} toeplitz (@var{c}, @var{r})
% Return the Toeplitz matrix constructed given the first column @var{c},
% and (optionally) the first row @var{r}.  If the first element of @var{c}
% is not the same as the first element of @var{r}, the first element of
% @var{c} is used.  If the second argument is omitted, the first row is
% taken to be the same as the first column.
%
% A square Toeplitz matrix has the form:
% @tex
% $$
% \left[\matrix{c_0    & r_1     & r_2      & \cdots & r_n\cr
%               c_1    & c_0     & r_1      & \cdots & r_{n-1}\cr
%               c_2    & c_1     & c_0      & \cdots & r_{n-2}\cr
%               \vdots & \vdots  & \vdots   & \ddots & \vdots\cr
%               c_n    & c_{n-1} & c_{n-2} & \ldots & c_0}\right]
% $$
% @end tex
% @ifnottex
%
% @example
% @group
% c(0)  r(1)   r(2)  @dots{}  r(n)
% c(1)  c(0)   r(1)  @dots{} r(n-1)
% c(2)  c(1)   c(0)  @dots{} r(n-2)
%  .     ,      ,   .      .
%  .     ,      ,     .    .
%  .     ,      ,       .  .
% c(n) c(n-1) c(n-2) @dots{}  c(0)
% @end group
% @end example
% @end ifnottex
% @seealso{hankel, vander, sylvester_matrix, hilb, invhilb}
% @end deftypefn

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:
Generated on Fri 22-May-2009 15:13:00 by m2html © 2003