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

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
U*diag([3, 2, 1])*V'
      [[0.98, 0.356, 1.508, 1.1], [-0.36, 1.608, 0.744, 1.8], [-0.5, -0.26, -1.18, 1.1]]

% Singular values: 4, 2, 1
U*diag([4, 2, 1])*V'
      [[1.04, 0.656, 1.808, 1.52], [-0.28, 2.008, 1.144, 2.36], [-0.5, -0.26, -1.18, 1.1]]

% Singular values: 4, 3, 1
U*diag([4, 3, 1])*V'
      [[1.28, 0.608, 2.144, 1.28], [-0.46, 2.044, 0.892, 2.54], [-0.9, -0.18, -1.74, 1.5]]

% Singular values: 4, 3, 2
U*diag([4, 3, 2])*V'
      [[1.6, 0.16, 2.08, 1.6], [-0.7, 2.38, 0.94, 2.3], [-0.6, -0.6, -1.8, 1.8]]

% Singular values: 5, 2, 1
U*diag([5, 2, 1])*V'
      [[1.1, 0.956, 2.108, 1.94], [-0.2, 2.408, 1.544, 2.92], [-0.5, -0.26, -1.18, 1.1]]

% Singular values: 5, 3, 1
U*diag([5, 3, 1])*V'
      [[1.34, 0.908, 2.444, 1.7], [-0.38, 2.444, 1.292, 3.1], [-0.9, -0.18, -1.74, 1.5]]

% Singular values: 5, 3, 2
U*diag([5, 3, 2])*V'
      [[1.66, 0.46, 2.38, 2.02], [-0.62, 2.78, 1.34, 2.86], [-0.6, -0.6, -1.8, 1.8]]

% Singular values: 5, 4, 1
U*diag([5, 4, 1])*V'
      [[1.58, 0.86, 2.78, 1.46], [-0.56, 2.48, 1.04, 3.28], [-1.3, -0.1, -2.3, 1.9]]

% Singular values: 5, 4, 2
U*diag([5, 4, 2])*V'
      [[1.9, 0.412, 2.716, 1.78], [-0.8, 2.816, 1.088, 3.04], [-1., -0.52, -2.36, 2.2]]

% Singular values: 5, 4, 3
U*diag([5, 4, 3])*V'
      [[2.22, -0.036, 2.652, 2.1], [-1.04, 3.152, 1.136, 2.8], [-0.7, -0.94, -2.42, 2.5]]