U =
      [[0.1, 0.1, 0.7, 0.7], [0.1, -0.1, -0.7, 0.7], [0.7, 0.7, -0.1, -0.1], [0.7, -0.7, 0.1, -0.1]]

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'
      [[0.36, -0.06, -0.32, 0.62], [-0.06, 0.36, 0.62, -0.32], [2.02, 0.08, 1.26, 0.84], [0.08, 2.02, 0.84, 1.26]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.41, -0.01, -0.27, 0.67], [-0.01, 0.41, 0.67, -0.27], [2.37, 0.43, 1.61, 1.19], [0.43, 2.37, 1.19, 1.61]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[0.48, -0.08, -0.26, 0.66], [-0.08, 0.48, 0.66, -0.26], [2.86, -0.06, 1.68, 1.12], [-0.06, 2.86, 1.12, 1.68]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[0.55, -0.15, -0.75, 1.15], [-0.15, 0.55, 1.15, -0.75], [2.85, -0.05, 1.75, 1.05], [-0.05, 2.85, 1.05, 1.75]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[0.9, 0.2, -1.1, 0.8], [0.2, 0.9, 0.8, -1.1], [2.8, -0.1, 1.8, 1.1], [-0.1, 2.8, 1.1, 1.8]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[0.46, 0.04, -0.22, 0.72], [0.04, 0.46, 0.72, -0.22], [2.72, 0.78, 1.96, 1.54], [0.78, 2.72, 1.54, 1.96]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[0.53, -0.03, -0.21, 0.71], [-0.03, 0.53, 0.71, -0.21], [3.21, 0.29, 2.03, 1.47], [0.29, 3.21, 1.47, 2.03]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[0.6, -0.1, -0.7, 1.2], [-0.1, 0.6, 1.2, -0.7], [3.2, 0.3, 2.1, 1.4], [0.3, 3.2, 1.4, 2.1]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[0.95, 0.25, -1.05, 0.85], [0.25, 0.95, 0.85, -1.05], [3.15, 0.25, 2.15, 1.45], [0.25, 3.15, 1.45, 2.15]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[0.6, -0.1, -0.2, 0.7], [-0.1, 0.6, 0.7, -0.2], [3.7, -0.2, 2.1, 1.4], [-0.2, 3.7, 1.4, 2.1]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[0.67, -0.17, -0.69, 1.19], [-0.17, 0.67, 1.19, -0.69], [3.69, -0.19, 2.17, 1.33], [-0.19, 3.69, 1.33, 2.17]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[1.02, 0.18, -1.04, 0.84], [0.18, 1.02, 0.84, -1.04], [3.64, -0.24, 2.22, 1.38], [-0.24, 3.64, 1.38, 2.22]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[0.74, -0.24, -1.18, 1.68], [-0.24, 0.74, 1.68, -1.18], [3.68, -0.18, 2.24, 1.26], [-0.18, 3.68, 1.26, 2.24]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[1.09, 0.11, -1.53, 1.33], [0.11, 1.09, 1.33, -1.53], [3.63, -0.23, 2.29, 1.31], [-0.23, 3.63, 1.31, 2.29]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[1.44, 0.46, -1.88, 0.98], [0.46, 1.44, 0.98, -1.88], [3.58, -0.28, 2.34, 1.36], [-0.28, 3.58, 1.36, 2.34]]