U =
      [[0.1, 0.3, 0.3, 0.9],
       [0.3, -0.1, -0.9, 0.3],
       [0.3, 0.9, -0.1, -0.3],
       [0.9, -0.3, 0.3, -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'
      [[0.6, -0.3,  0,     0.3],
       [0.22, 0.68, 1.06, -0.16],
       [1.7, -0.8,  0.7,   0.2],
       [0.96, 1.74, 1.08,  1.62]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.65, -0.25, 0.05,  0.35],
       [0.37,  0.83, 1.21, -0.01],
       [1.85, -0.65, 0.85,  0.35],
       [1.41,  2.19, 1.53,  2.07]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[0.86, -0.46, 0.08, 0.32],
       [0.3, 0.9, 1.2, 0.],
       [2.48, -1.28, 0.94, 0.26],
       [1.2, 2.4, 1.5, 2.1]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[0.89, -0.49, -0.13,  0.53],
       [0.21,  0.99,  1.83, -0.63],
       [2.47, -1.27,  1.01,  0.19],
       [1.23,  2.37,  1.29,  2.31]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.34, -0.04, -0.58,  0.08],
       [0.36,  1.14,  1.68, -0.78],
       [2.32, -1.42,  1.16,  0.34],
       [1.18,  2.32,  1.34,  2.36]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[0.7, -0.2,  0.1,  0.4],
       [0.52, 0.98, 1.36, 0.14],
       [2,   -0.5,  1,    0.5],
       [1.86, 2.64, 1.98, 2.52]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[0.91, -0.41, 0.13, 0.37],
       [0.45,  1.05, 1.35, 0.15],
       [2.63, -1.13, 1.09, 0.41],
       [1.65,  2.85, 1.95, 2.55]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[0.94, -0.44, -0.08,  0.58],
       [0.36,  1.14,  1.98, -0.48],
       [2.62, -1.12,  1.16,  0.34],
       [1.68,  2.82,  1.74,  2.76]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.39, 0.01, -0.53, 0.13],
       [0.51, 1.29, 1.83, -0.63],
       [2.47, -1.27, 1.31, 0.49],
       [1.63, 2.77, 1.79, 2.81]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[1.12, -0.62, 0.16, 0.34],
       [0.38,  1.12, 1.34, 0.16],
       [3.26, -1.76, 1.18, 0.32],
       [1.44,  3.06, 1.92, 2.58]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[1.15, -0.65, -0.05,  0.55],
       [0.29,  1.21,  1.97, -0.47],
       [3.25, -1.75,  1.25,  0.25],
       [1.47,  3.03,  1.71,  2.79]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[1.6, -0.2, -0.5,   0.1],
       [0.44, 1.36, 1.82, -0.62],
       [3.1, -1.9,  1.4,   0.4],
       [1.42, 2.98, 1.76,  2.84]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[1.18, -0.68, -0.26, 0.76],
       [0.2,   1.3,   2.6, -1.1],
       [3.24, -1.74,  1.32, 0.18],
       [1.5,   3,     1.5,  3]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[1.63, -0.23, -0.71,  0.31],
       [0.35,  1.45,  2.45, -1.25],
       [3.09, -1.89,  1.47,  0.33],
       [1.45,  2.95,  1.55,  3.05]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.08,  0.22, -1.16, -0.14],
       [0.5,   1.6,   2.3,  -1.4],
       [2.94, -2.04,  1.62,  0.48],
       [1.4,   2.9,   1.6,   3.1]]