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

V =
      [[0.1, 0.1, 0.7, 0.7], [0.1, -0.1, -0.7, 0.7], [0.7, 0.7, -0.1, -0.1], [0.7, -0.7, 0.1, -0.1]]

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

% Singular values: 3, 2, 1
U*diag([3, 2, 1])*V'
      [[0.724, -0.364, 1.868, 0.652], [-0.168, 0.648, 1.224, 2.136], [0.26, -0.26, -1.18, 1.18]]

% Singular values: 4, 2, 1
U*diag([4, 2, 1])*V'
      [[0.784, -0.304, 2.288, 1.072], [-0.088, 0.728, 1.784, 2.696], [0.26, -0.26, -1.18, 1.18]]

% Singular values: 4, 3, 1
U*diag([4, 3, 1])*V'
      [[0.832, -0.352, 2.624, 0.736], [-0.124, 0.764, 1.532, 2.948], [0.18, -0.18, -1.74, 1.74]]

% Singular values: 4, 3, 2
U*diag([4, 3, 2])*V'
      [[1.28, -0.8, 2.56, 0.8], [-0.46, 1.1, 1.58, 2.9], [0.6, -0.6, -1.8, 1.8]]

% Singular values: 5, 2, 1
U*diag([5, 2, 1])*V'
      [[0.844, -0.244, 2.708, 1.492], [-0.008, 0.808, 2.344, 3.256], [0.26, -0.26, -1.18, 1.18]]

% Singular values: 5, 3, 1
U*diag([5, 3, 1])*V'
      [[0.892, -0.292, 3.044, 1.156], [-0.044, 0.844, 2.092, 3.508], [0.18, -0.18, -1.74, 1.74]]

% Singular values: 5, 3, 2
U*diag([5, 3, 2])*V'
      [[1.34, -0.74, 2.98, 1.22], [-0.38, 1.18, 2.14, 3.46], [0.6, -0.6, -1.8, 1.8]]

% Singular values: 5, 4, 1
U*diag([5, 4, 1])*V'
      [[0.94, -0.34, 3.38, 0.82], [-0.08, 0.88, 1.84, 3.76], [0.1, -0.1, -2.3, 2.3]]

% Singular values: 5, 4, 2
U*diag([5, 4, 2])*V'
      [[1.388, -0.788, 3.316, 0.884], [-0.416, 1.216, 1.888, 3.712], [0.52, -0.52, -2.36, 2.36]]

% Singular values: 5, 4, 3
U*diag([5, 4, 3])*V'
      [[1.836, -1.236, 3.252, 0.948], [-0.752, 1.552, 1.936, 3.664], [0.94, -0.94, -2.42, 2.42]]