U =
      [[1, 0, 0], [0, 0.6, 0.8], [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: 2, 2, 1
U*diag([2, 2, 1])*V'
      [[0.2, 0.2, 1.4, 1.4], [0.68, -0.68, 0.76, -0.76], [-0.26, 0.26, 1.18, -1.18]]

% Singular values: 3, 2, 1
U*diag([3, 2, 1])*V'
      [[0.3, 0.3, 2.1, 2.1], [0.68, -0.68, 0.76, -0.76], [-0.26, 0.26, 1.18, -1.18]]

% Singular values: 3, 3, 1
U*diag([3, 3, 1])*V'
      [[0.3, 0.3, 2.1, 2.1], [0.74, -0.74, 1.18, -1.18], [-0.18, 0.18, 1.74, -1.74]]

% Singular values: 3, 3, 2
U*diag([3, 3, 2])*V'
      [[0.3, 0.3, 2.1, 2.1], [1.3, -1.3, 1.1, -1.1], [-0.6, 0.6, 1.8, -1.8]]

% Singular values: 4, 2, 1
U*diag([4, 2, 1])*V'
      [[0.4, 0.4, 2.8, 2.8], [0.68, -0.68, 0.76, -0.76], [-0.26, 0.26, 1.18, -1.18]]

% Singular values: 4, 3, 1
U*diag([4, 3, 1])*V'
      [[0.4, 0.4, 2.8, 2.8], [0.74, -0.74, 1.18, -1.18], [-0.18, 0.18, 1.74, -1.74]]

% Singular values: 4, 3, 2
U*diag([4, 3, 2])*V'
      [[0.4, 0.4, 2.8, 2.8], [1.3, -1.3, 1.1, -1.1], [-0.6, 0.6, 1.8, -1.8]]

% Singular values: 4, 4, 1
U*diag([4, 4, 1])*V'
      [[0.4, 0.4, 2.8, 2.8], [0.8, -0.8, 1.6, -1.6], [-0.1, 0.1, 2.3, -2.3]]

% Singular values: 4, 4, 2
U*diag([4, 4, 2])*V'
      [[0.4, 0.4, 2.8, 2.8], [1.36, -1.36, 1.52, -1.52], [-0.52, 0.52, 2.36, -2.36]]

% Singular values: 4, 4, 3
U*diag([4, 4, 3])*V'
      [[0.4, 0.4, 2.8, 2.8], [1.92, -1.92, 1.44, -1.44], [-0.94, 0.94, 2.42, -2.42]]

% Singular values: 5, 2, 1
U*diag([5, 2, 1])*V'
      [[0.5, 0.5, 3.5, 3.5], [0.68, -0.68, 0.76, -0.76], [-0.26, 0.26, 1.18, -1.18]]

% Singular values: 5, 3, 1
U*diag([5, 3, 1])*V'
      [[0.5, 0.5, 3.5, 3.5], [0.74, -0.74, 1.18, -1.18], [-0.18, 0.18, 1.74, -1.74]]

% Singular values: 5, 3, 2
U*diag([5, 3, 2])*V'
      [[0.5, 0.5, 3.5, 3.5], [1.3, -1.3, 1.1, -1.1], [-0.6, 0.6, 1.8, -1.8]]

% Singular values: 5, 4, 1
U*diag([5, 4, 1])*V'
      [[0.5, 0.5, 3.5, 3.5], [0.8, -0.8, 1.6, -1.6], [-0.1, 0.1, 2.3, -2.3]]

% Singular values: 5, 4, 2
U*diag([5, 4, 2])*V'
      [[0.5, 0.5, 3.5, 3.5], [1.36, -1.36, 1.52, -1.52], [-0.52, 0.52, 2.36, -2.36]]

% Singular values: 5, 4, 3
U*diag([5, 4, 3])*V'
      [[0.5, 0.5, 3.5, 3.5], [1.92, -1.92, 1.44, -1.44], [-0.94, 0.94, 2.42, -2.42]]

% Singular values: 5, 5, 1
U*diag([5, 5, 1])*V'
      [[0.5, 0.5, 3.5, 3.5], [0.86, -0.86, 2.02, -2.02], [-0.02, 0.02, 2.86, -2.86]]

% Singular values: 5, 5, 2
U*diag([5, 5, 2])*V'
      [[0.5, 0.5, 3.5, 3.5], [1.42, -1.42, 1.94, -1.94], [-0.44, 0.44, 2.92, -2.92]]

% Singular values: 5, 5, 3
U*diag([5, 5, 3])*V'
      [[0.5, 0.5, 3.5, 3.5], [1.98, -1.98, 1.86, -1.86], [-0.86, 0.86, 2.98, -2.98]]

% Singular values: 5, 5, 4
U*diag([5, 5, 4])*V'
      [[0.5, 0.5, 3.5, 3.5], [2.54, -2.54, 1.78, -1.78], [-1.28, 1.28, 3.04, -3.04]]