U =
      [[0.2, 0.4, 0.4, 0.8], [0.4, -0.2, -0.8, 0.4], [0.4, 0.8, -0.2, -0.4], [0.8, -0.4, 0.4, -0.2]]

V =
      [[0.5, 0.7, 0.1, 0.5], [0.5, -0.7, -0.1, 0.5], [0.5, 0.1, -0.7, -0.5], [0.5, -0.1, 0.7, -0.5]]

%%%%%%%%%%%%%%%%%%%%%%%%%
% Matrices with integer %
%    singular values    %
%%%%%%%%%%%%%%%%%%%%%%%%%

% Singular values: 3, 2, 1, 0
U*diag([3, 2, 1, 0])*V'
      [[0.9, -0.3, 0.1, 0.5], [0.24, 0.96, 1.12, 0.08], [1.7, -0.5, 0.9, 0.3], [0.68, 1.72, 0.84, 1.56]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[1., -0.2, 0.2, 0.6], [0.44, 1.16, 1.32, 0.28], [1.9, -0.3, 1.1, 0.5], [1.08, 2.12, 1.24, 1.96]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[1.28, -0.48, 0.24, 0.56], [0.3, 1.3, 1.3, 0.3], [2.46, -0.86, 1.18, 0.42], [0.8, 2.4, 1.2, 2]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[1.32, -0.52, -0.04, 0.84], [0.22, 1.38, 1.86, -0.26], [2.44, -0.84, 1.32, 0.28], [0.84, 2.36, 0.92, 2.28]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.72, -0.12, -0.44, 0.44], [0.42, 1.58, 1.66, -0.46], [2.24, -1.04, 1.52, 0.48], [0.74, 2.26, 1.02, 2.38]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[1.1, -0.1, 0.3, 0.7], [0.64, 1.36, 1.52, 0.48], [2.1, -0.1, 1.3, 0.7], [1.48, 2.52, 1.64, 2.36]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[1.38, -0.38, 0.34, 0.66], [0.5, 1.5, 1.5, 0.5], [2.66, -0.66, 1.38, 0.62], [1.2, 2.8, 1.6, 2.4]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[1.42, -0.42, 0.06, 0.94], [0.42, 1.58, 2.06, -0.06], [2.64, -0.64, 1.52, 0.48], [1.24, 2.76, 1.32, 2.68]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.82, -0.02, -0.34, 0.54], [0.62, 1.78, 1.86, -0.26], [2.44, -0.84, 1.72, 0.68], [1.14, 2.66, 1.42, 2.78]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[1.66, -0.66, 0.38, 0.62], [0.36, 1.64, 1.48, 0.52], [3.22, -1.22, 1.46, 0.54], [0.92, 3.08, 1.56, 2.44]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[1.7, -0.7, 0.1, 0.9], [0.28, 1.72, 2.04, -0.04], [3.2, -1.2, 1.6, 0.4], [0.96, 3.04, 1.28, 2.72]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[2.1, -0.3, -0.3, 0.5], [0.48, 1.92, 1.84, -0.24], [3., -1.4, 1.8, 0.6], [0.86, 2.94, 1.38, 2.82]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[1.74, -0.74, -0.18, 1.18], [0.2, 1.8, 2.6, -0.6], [3.18, -1.18, 1.74, 0.26], [1., 3., 1., 3]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[2.14, -0.34, -0.58, 0.78], [0.4, 2., 2.4, -0.8], [2.98, -1.38, 1.94, 0.46], [0.9, 2.9, 1.1, 3.1]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.54, 0.06, -0.98, 0.38], [0.6, 2.2, 2.2, -1], [2.78, -1.58, 2.14, 0.66], [0.8, 2.8, 1.2, 3.2]]