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

V =
      [[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]]

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

% Singular values: 3, 2, 1
U*diag([3, 2, 1])*V'
      [[1., 0.016, 1.36, 1.312], [0., 1.488, 0.48, 2.016], [-0.4, -0.16, -1.4, 0.88]]

% Singular values: 4, 2, 1
U*diag([4, 2, 1])*V'
      [[1.12, 0.256, 1.6, 1.792], [0.16, 1.808, 0.8, 2.656], [-0.4, -0.16, -1.4, 0.88]]

% Singular values: 4, 3, 1
U*diag([4, 3, 1])*V'
      [[1.312, 0.16, 1.984, 1.6], [0.016, 1.88, 0.512, 2.8], [-0.72, 0., -2.04, 1.2]]

% Singular values: 4, 3, 2
U*diag([4, 3, 2])*V'
      [[1.568, -0.352, 1.856, 1.856], [-0.176, 2.264, 0.608, 2.608], [-0.48, -0.48, -2.16, 1.44]]

% Singular values: 5, 2, 1
U*diag([5, 2, 1])*V'
      [[1.24, 0.496, 1.84, 2.272], [0.32, 2.128, 1.12, 3.296], [-0.4, -0.16, -1.4, 0.88]]

% Singular values: 5, 3, 1
U*diag([5, 3, 1])*V'
      [[1.432, 0.4, 2.224, 2.08], [0.176, 2.2, 0.832, 3.44], [-0.72, 0., -2.04, 1.2]]

% Singular values: 5, 3, 2
U*diag([5, 3, 2])*V'
      [[1.688, -0.112, 2.096, 2.336], [-0.016, 2.584, 0.928, 3.248], [-0.48, -0.48, -2.16, 1.44]]

% Singular values: 5, 4, 1
U*diag([5, 4, 1])*V'
      [[1.624, 0.304, 2.608, 1.888], [0.032, 2.272, 0.544, 3.584], [-1.04, 0.16, -2.68, 1.52]]

% Singular values: 5, 4, 2
U*diag([5, 4, 2])*V'
      [[1.88, -0.208, 2.48, 2.144], [-0.16, 2.656, 0.64, 3.392], [-0.8, -0.32, -2.8, 1.76]]

% Singular values: 5, 4, 3
U*diag([5, 4, 3])*V'
      [[2.136, -0.72, 2.352, 2.4], [-0.352, 3.04, 0.736, 3.2], [-0.56, -0.8, -2.92, 2]]