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, 0.3, 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]]

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

% Singular values: 3, 2, 1, 0
U*diag([3, 2, 1, 0])*V'
      [[0.42, -0.26, 0.86, 0.42], [-0.24, 1.12, 0.08, 0.96], [0.54, 0.38, 1.82, 0.54], [0.12, 0.44, -0.04, 2.52]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.44, -0.2, 0.92, 0.6], [-0.2, 1.24, 0.2, 1.32], [0.58, 0.5, 1.94, 0.9], [0.2, 0.68, 0.2, 3.24]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[0.56, -0.24, 1.28, 0.48], [-0.26, 1.26, 0.02, 1.38], [0.82, 0.42, 2.66, 0.66], [0.08, 0.72, -0.16, 3.36]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[0.68, -0.6, 1.24, 0.6], [-0.5, 1.98, 0.1, 1.14], [0.76, 0.6, 2.68, 0.6], [0.2, 0.36, -0.2, 3.48]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.4, -0.36, 1., 0.52], [-0.14, 2.1, -0.02, 1.1], [0.4, 0.48, 2.8, 0.64], [0.02, 0.3, -0.14, 3.5]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[0.46, -0.14, 0.98, 0.78], [-0.16, 1.36, 0.32, 1.68], [0.62, 0.62, 2.06, 1.26], [0.28, 0.92, 0.44, 3.96]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[0.58, -0.18, 1.34, 0.66], [-0.22, 1.38, 0.14, 1.74], [0.86, 0.54, 2.78, 1.02], [0.16, 0.96, 0.08, 4.08]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[0.7, -0.54, 1.3, 0.78], [-0.46, 2.1, 0.22, 1.5], [0.8, 0.72, 2.8, 0.96], [0.28, 0.6, 0.04, 4.2]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.42, -0.3, 1.06, 0.7], [-0.1, 2.22, 0.1, 1.46], [0.44, 0.6, 2.92, 1], [0.1, 0.54, 0.1, 4.22]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[0.7, -0.22, 1.7, 0.54], [-0.28, 1.4, -0.04, 1.8], [1.1, 0.46, 3.5, 0.78], [0.04, 1., -0.28, 4.2]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[0.82, -0.58, 1.66, 0.66], [-0.52, 2.12, 0.04, 1.56], [1.04, 0.64, 3.52, 0.72], [0.16, 0.64, -0.32, 4.32]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[1.54, -0.34, 1.42, 0.58], [-0.16, 2.24, -0.08, 1.52], [0.68, 0.52, 3.64, 0.76], [-0.02, 0.58, -0.26, 4.34]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[0.94, -0.94, 1.62, 0.78], [-0.76, 2.84, 0.12, 1.32], [0.98, 0.82, 3.54, 0.66], [0.28, 0.28, -0.36, 4.44]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[1.66, -0.7, 1.38, 0.7], [-0.4, 2.96, -0., 1.28], [0.62, 0.7, 3.66, 0.7], [0.1, 0.22, -0.3, 4.46]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.38, -0.46, 1.14, 0.62], [-0.04, 3.08, -0.12, 1.24], [0.26, 0.58, 3.78, 0.74], [-0.08, 0.16, -0.24, 4.48]]