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

V =
      [[1, 0, 0], [0, 0.6, 0.8], [0, 0.8, -0.6]]

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

% Singular values: 2, 1
U*diag([2, 1])*V'
      [[1.2, 0.48, 0.64], [1.6, -0.36, -0.48]]

% Singular values: 3, 1
U*diag([3, 1])*V'
      [[1.8, 0.48, 0.64], [2.4, -0.36, -0.48]]

% Singular values: 3, 2
U*diag([3, 2])*V'
      [[1.8, 0.96, 1.28], [2.4, -0.72, -0.96]]

% Singular values: 4, 1
U*diag([4, 1])*V'
      [[2.4, 0.48, 0.64], [3.2, -0.36, -0.48]]

% Singular values: 4, 2
U*diag([4, 2])*V'
      [[2.4, 0.96, 1.28], [3.2, -0.72, -0.96]]

% Singular values: 4, 3
U*diag([4, 3])*V'
      [[2.4, 1.44, 1.92], [3.2, -1.08, -1.44]]

% Singular values: 5, 1
U*diag([5, 1])*V'
      [[3, 0.48, 0.64], [4, -0.36, -0.48]]

% Singular values: 5, 2
U*diag([5, 2])*V'
      [[3, 0.96, 1.28], [4, -0.72, -0.96]]

% Singular values: 5, 3
U*diag([5, 3])*V'
      [[3, 1.44, 1.92], [4, -1.08, -1.44]]

% Singular values: 5, 4
U*diag([5, 4])*V'
      [[3, 1.92, 2.56], [4, -1.44, -1.92]]