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

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

% Singular values: 3, 2, 1, 0
U*diag([3, 2, 1, 0])*V'
      [[0.66, -0.06, 0.82, 0.22], [-0.48, 1.2, 0.4, 0.64], [0.82, 0.58, 1.74, -0.06], [0.04, 1, 0.6, 2.28]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.68, 0.04, 0.92, 0.36], [-0.44, 1.4, 0.6, 0.92], [0.86, 0.78, 1.94, 0.22], [0.12, 1.4, 1, 2.84]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[0.88, 0, 1.2, 0.16], [-0.54, 1.42, 0.46, 1.02], [1.26, 0.7, 2.5, -0.18], [-0.08, 1.44, 0.72, 3.04]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[1.08, -0.28, 1.16, 0.36], [-0.94, 1.98, 0.54, 0.62], [1.16, 0.84, 2.52, -0.28], [0.12, 1.16, 0.68, 3.24]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.64, 0.12, 0.76, 0.28], [-0.66, 2.18, 0.34, 0.58], [0.88, 0.64, 2.72, -0.24], [-0.02, 1.06, 0.78, 3.26]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[0.7, 0.14, 1.02, 0.5], [-0.4, 1.6, 0.8, 1.2], [0.9, 0.98, 2.14, 0.5], [0.2, 1.8, 1.4, 3.4]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[0.9, 0.1, 1.3, 0.3], [-0.5, 1.62, 0.66, 1.3], [1.3, 0.9, 2.7, 0.1], [0, 1.84, 1.12, 3.6]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[1.1, -0.18, 1.26, 0.5], [-0.9, 2.18, 0.74, 0.9], [1.2, 1.04, 2.72, 0], [0.2, 1.56, 1.08, 3.8]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.66, 0.22, 0.86, 0.42], [-0.62, 2.38, 0.54, 0.86], [0.92, 0.84, 2.92, 0.04], [0.06, 1.46, 1.18, 3.82]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[1.1, 0.06, 1.58, 0.1], [-0.6, 1.64, 0.52, 1.4], [1.7, 0.82, 3.26, -0.3], [-0.2, 1.88, 0.84, 3.8]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[1.3, -0.22, 1.54, 0.3], [-1, 2.2, 0.6, 1], [1.6, 0.96, 3.28, -0.4], [0, 1.6, 0.8, 4]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[1.86, 0.18, 1.14, 0.22], [-0.72, 2.4, 0.4, 0.96], [1.32, 0.76, 3.48, -0.36], [-0.14, 1.5, 0.9, 4.02]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[1.5, -0.5, 1.5, 0.5], [-1.4, 2.76, 0.68, 0.6], [1.5, 1.1, 3.3, -0.5], [0.2, 1.32, 0.76, 4.2]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[2.06, -0.1, 1.1, 0.42], [-1.12, 2.96, 0.48, 0.56], [1.22, 0.9, 3.5, -0.46], [0.06, 1.22, 0.86, 4.22]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.62, 0.3, 0.7, 0.34], [-0.84, 3.16, 0.28, 0.52], [0.94, 0.7, 3.7, -0.42], [-0.08, 1.12, 0.96, 4.24]]