Home > freetb4matlab > polynomial > compan.m

compan

PURPOSE ^

% Compute the companion matrix corresponding to polynomial coefficient

SYNOPSIS ^

function A = compan (c)

DESCRIPTION ^

% -*- texinfo -*-
% @deftypefn {Function File} {} compan (@var{c})
% Compute the companion matrix corresponding to polynomial coefficient
% vector @var{c}.
%
% The companion matrix is
% @iftex
% @tex
% $$
% A = \left[\matrix{
%  -c_2/c_1 & -c_3/c_1 & \cdots & -c_N/c_1 & -c_{N+1}/c_1\cr
%      1    &     0    & \cdots &     0    &         0   \cr
%      0    &     1    & \cdots &     0    &         0   \cr
%   \vdots  &   \vdots & \ddots &  \vdots  &      \vdots \cr
%      0    &     0    & \cdots &     1    &         0}\right].
% $$
% @end tex
% @end iftex
% @ifnottex
%
% @c Set example in small font to prevent overfull line
% @smallexample
%      _                                                        _
%     |  -c(2)/c(1)   -c(3)/c(1)  @dots{}  -c(N)/c(1)  -c(N+1)/c(1)  |
%     |       1            0      @dots{}       0             0      |
%     |       0            1      @dots{}       0             0      |
% A = |       .            .   .            .             .      |
%     |       .            .       .        .             .      |
%     |       .            .           .    .             .      |
%     |_      0            0      @dots{}       1             0     _|
% @end smallexample
% @end ifnottex
%
% The eigenvalues of the companion matrix are equal to the roots of the
% polynomial.
% @seealso{poly, roots, residue, conv, deconv, polyval, polyderiv,
% polyinteg}
% @end deftypefn

CROSS-REFERENCE INFORMATION ^

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