U =
      [[0.28, 0.96], [0.96, -0.28]]

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'
      [[0.7968, 0.1024, -0.768], [1.0176, 1.6368, 0.224]]

% Singular values: 3, 1
U*diag([3, 1])*V'
      [[0.9648, 0.3264, -0.768], [1.5936, 2.4048, 0.224]]

% Singular values: 3, 2
U*diag([3, 2])*V'
      [[1.4256, -0.0192, -1.536], [1.4592, 2.5056, 0.448]]

% Singular values: 4, 1
U*diag([4, 1])*V'
      [[1.1328, 0.5504, -0.768], [2.1696, 3.1728, 0.224]]

% Singular values: 4, 2
U*diag([4, 2])*V'
      [[1.5936, 0.2048, -1.536], [2.0352, 3.2736, 0.448]]

% Singular values: 4, 3
U*diag([4, 3])*V'
      [[2.0544, -0.1408, -2.304], [1.9008, 3.3744, 0.672]]

% Singular values: 5, 1
U*diag([5, 1])*V'
      [[1.3008, 0.7744, -0.768], [2.7456, 3.9408, 0.224]]

% Singular values: 5, 2
U*diag([5, 2])*V'
      [[1.7616, 0.4288, -1.536], [2.6112, 4.0416, 0.448]]

% Singular values: 5, 3
U*diag([5, 3])*V'
      [[2.2224, 0.0832, -2.304], [2.4768, 4.1424, 0.672]]

% Singular values: 5, 4
U*diag([5, 4])*V'
      [[2.6832, -0.2624, -3.072], [2.3424, 4.2432, 0.896]]