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

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
U*diag([3, 2, 1])*V'
      [[0.66, -0.132, 1.34, 1.524], [-0.12, 1.224, 0.12, 2.232], [-0.3, -0.38, -1.5, 0.66]]

% Singular values: 4, 2, 1
U*diag([4, 2, 1])*V'
      [[0.72, 0.048, 1.52, 2.064], [-0.04, 1.464, 0.36, 2.952], [-0.3, -0.38, -1.5, 0.66]]

% Singular values: 4, 3, 1
U*diag([4, 3, 1])*V'
      [[0.864, -0., 1.952, 1.92], [-0.148, 1.5, 0.036, 3.06], [-0.54, -0.3, -2.22, 0.9]]

% Singular values: 4, 3, 2
U*diag([4, 3, 2])*V'
      [[1.056, -0.576, 1.888, 2.112], [-0.292, 1.932, 0.084, 2.916], [-0.36, -0.84, -2.28, 1.08]]

% Singular values: 5, 2, 1
U*diag([5, 2, 1])*V'
      [[0.78, 0.228, 1.7, 2.604], [0.04, 1.704, 0.6, 3.672], [-0.3, -0.38, -1.5, 0.66]]

% Singular values: 5, 3, 1
U*diag([5, 3, 1])*V'
      [[0.924, 0.18, 2.132, 2.46], [-0.068, 1.74, 0.276, 3.78], [-0.54, -0.3, -2.22, 0.9]]

% Singular values: 5, 3, 2
U*diag([5, 3, 2])*V'
      [[1.116, -0.396, 2.068, 2.652], [-0.212, 2.172, 0.324, 3.636], [-0.36, -0.84, -2.28, 1.08]]

% Singular values: 5, 4, 1
U*diag([5, 4, 1])*V'
      [[1.068, 0.132, 2.564, 2.316], [-0.176, 1.776, -0.048, 3.888], [-0.78, -0.22, -2.94, 1.14]]

% Singular values: 5, 4, 2
U*diag([5, 4, 2])*V'
      [[1.26, -0.444, 2.5, 2.508], [-0.32, 2.208, -0., 3.744], [-0.6, -0.76, -3., 1.32]]

% Singular values: 5, 4, 3
U*diag([5, 4, 3])*V'
      [[1.452, -1.02, 2.436, 2.7], [-0.464, 2.64, 0.048, 3.6], [-0.42, -1.3, -3.06, 1.5]]