function lambda = kahan_eigenvalues ( alpha, n )

%*****************************************************************************80
%
%% kahan_eigenvalues() returns the eigenvalues of the KAHAN matrix.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    30 November 2019
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    real ALPHA, the scalar that defines A.  
%
%    integer N, the order of A.
%
%  Output:
%
%    real LAMBDA(N,1): the eigenvalues.
%
  lambda = zeros ( n, 1 );
  s = sin(alpha);
  lambda(1) = s;
  for i = 2 : n
    lambda(i) = lambda(i-1) * s;
  end

  return
end
