U =
      [[0.6, 0.8], [0.8, -0.6]]

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

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

% Singular values: 2, 1
U*diag([2, 1])*V'
      [[1.104, 0.672, -0.64], [0.672, 1.496, 0.48]]

% Singular values: 3, 1
U*diag([3, 1])*V'
      [[1.464, 1.152, -0.64], [1.152, 2.136, 0.48]]

% Singular values: 3, 2
U*diag([3, 2])*V'
      [[1.848, 0.864, -1.28], [0.864, 2.352, 0.96]]

% Singular values: 4, 1
U*diag([4, 1])*V'
      [[1.824, 1.632, -0.64], [1.632, 2.776, 0.48]]

% Singular values: 4, 2
U*diag([4, 2])*V'
      [[2.208, 1.344, -1.28], [1.344, 2.992, 0.96]]

% Singular values: 4, 3
U*diag([4, 3])*V'
      [[2.592, 1.056, -1.92], [1.056, 3.208, 1.44]]

% Singular values: 5, 1
U*diag([5, 1])*V'
      [[2.184, 2.112, -0.64], [2.112, 3.416, 0.48]]

% Singular values: 5, 2
U*diag([5, 2])*V'
      [[2.568, 1.824, -1.28], [1.824, 3.632, 0.96]]

% Singular values: 5, 3
U*diag([5, 3])*V'
      [[2.952, 1.536, -1.92], [1.536, 3.848, 1.44]]

% Singular values: 5, 4
U*diag([5, 4])*V'
      [[3.336, 1.248, -2.56], [1.248, 4.064, 1.92]]