U =
      [[0.6, 0.48, 0.64], [0.8, -0.36, -0.48], [0., -0.8, 0.6]]

V =
      [[0.5, 0.5, 0.5, 0.5], [0.5, -0.5, -0.5, 0.5], [0.5, 0.5, -0.5, -0.5], [0.5, -0.5, 0.5, -0.5]]

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

% Singular values: 3, 2, 1
U*diag([3, 2, 1])*V'
      [[1.7, 0.1, 1.06, 0.74], [0.6, 1.8, 1.08, 1.32], [-0.5, 0.5, -1.1, 1.1]]

% Singular values: 4, 2, 1
U*diag([4, 2, 1])*V'
      [[2., 0.4, 1.36, 1.04], [1., 2.2, 1.48, 1.72], [-0.5, 0.5, -1.1, 1.1]]

% Singular values: 4, 3, 1
U*diag([4, 3, 1])*V'
      [[2.24, 0.16, 1.6, 0.8], [0.82, 2.38, 1.3, 1.9], [-0.9, 0.9, -1.5, 1.5]]

% Singular values: 4, 3, 2
U*diag([4, 3, 2])*V'
      [[2.56, -0.16, 1.28, 1.12], [0.58, 2.62, 1.54, 1.66], [-0.6, 0.6, -1.8, 1.8]]

% Singular values: 5, 2, 1
U*diag([5, 2, 1])*V'
      [[2.3, 0.7, 1.66, 1.34], [1.4, 2.6, 1.88, 2.12], [-0.5, 0.5, -1.1, 1.1]]

% Singular values: 5, 3, 1
U*diag([5, 3, 1])*V'
      [[2.54, 0.46, 1.9, 1.1], [1.22, 2.78, 1.7, 2.3], [-0.9, 0.9, -1.5, 1.5]]

% Singular values: 5, 3, 2
U*diag([5, 3, 2])*V'
      [[2.86, 0.14, 1.58, 1.42], [0.98, 3.02, 1.94, 2.06], [-0.6, 0.6, -1.8, 1.8]]

% Singular values: 5, 4, 1
U*diag([5, 4, 1])*V'
      [[2.78, 0.22, 2.14, 0.86], [1.04, 2.96, 1.52, 2.48], [-1.3, 1.3, -1.9, 1.9]]

% Singular values: 5, 4, 2
U*diag([5, 4, 2])*V'
      [[3.1, -0.1, 1.82, 1.18], [0.8, 3.2, 1.76, 2.24], [-1., 1., -2.2, 2.2]]

% Singular values: 5, 4, 3
U*diag([5, 4, 3])*V'
      [[3.42, -0.42, 1.5, 1.5], [0.56, 3.44, 2., 2], [-0.7, 0.7, -2.5, 2.5]]