function a = zero_matrix ( m, n )

%*****************************************************************************80
%
%% zero_matrix() returns the ZERO matrix.
%
%  Formula:
%
%    A(I,J) = 0
%
%  Example:
%
%    M = 4, N = 5
%
%    0 0 0 0 0
%    0 0 0 0 0
%    0 0 0 0 0
%    0 0 0 0 0
%
%  Properties:
%
%    A is integral.
%
%    A is Toeplitz: constant along diagonals.
%
%    A is a Hankel matrix: constant along anti-diagonals.
%
%    A is a circulant matrix: each row is shifted once to get the next row.
%
%    A is an anticirculant matrix.
%
%    A is singular.
%
%    A is symmetric: A' = A.
%
%    Because A is symmetric, it is normal.
%
%    Because A is normal, it is diagonalizable.
%
%    LAMBDA(1:N) = 0.
%
%    The matrix of eigenvectors of A is I.
%
%    det ( A ) = 0.
%
%    For any vector v, A*v = 0.
%
%    For any matrix B, A*B = B*A = 0.
%
%    A is persymmetric: A(I,J) = A(N+1-J,N+1-I).
%
%    The family of matrices is nested as a function of N.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    22 October 2007
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer M: the number of rows.
%
%    integer N: the number of columns.
%    N is optional input.  If omitted, N = M.
%
%  Output:
%
%    real A(M,N), the matrix.
%
  if ( nargin == 1 )
    n = m;
  end

  a = zeros ( m, n );

  return
end
