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

V =
      [[0.5, 0.7, 0.1, 0.5], [0.5, -0.7, -0.1, 0.5], [0.5, 0.1, -0.7, -0.5], [0.5, -0.1, 0.7, -0.5]]

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

% Singular values: 3, 2, 1
U*diag([3, 2, 1])*V'
      [[1.636, 0.164, 0.548, 1.252], [0.648, 1.752, 1.464, 0.936], [-1.06, 1.06, -0.58, 0.58]]

% Singular values: 4, 2, 1
U*diag([4, 2, 1])*V'
      [[1.936, 0.464, 0.848, 1.552], [1.048, 2.152, 1.864, 1.336], [-1.06, 1.06, -0.58, 0.58]]

% Singular values: 4, 3, 1
U*diag([4, 3, 1])*V'
      [[2.272, 0.128, 0.896, 1.504], [0.796, 2.404, 1.828, 1.372], [-1.62, 1.62, -0.66, 0.66]]

% Singular values: 4, 3, 2
U*diag([4, 3, 2])*V'
      [[2.336, 0.064, 0.448, 1.952], [0.748, 2.452, 2.164, 1.036], [-1.56, 1.56, -1.08, 1.08]]

% Singular values: 5, 2, 1
U*diag([5, 2, 1])*V'
      [[2.236, 0.764, 1.148, 1.852], [1.448, 2.552, 2.264, 1.736], [-1.06, 1.06, -0.58, 0.58]]

% Singular values: 5, 3, 1
U*diag([5, 3, 1])*V'
      [[2.572, 0.428, 1.196, 1.804], [1.196, 2.804, 2.228, 1.772], [-1.62, 1.62, -0.66, 0.66]]

% Singular values: 5, 3, 2
U*diag([5, 3, 2])*V'
      [[2.636, 0.364, 0.748, 2.252], [1.148, 2.852, 2.564, 1.436], [-1.56, 1.56, -1.08, 1.08]]

% Singular values: 5, 4, 1
U*diag([5, 4, 1])*V'
      [[2.908, 0.092, 1.244, 1.756], [0.944, 3.056, 2.192, 1.808], [-2.18, 2.18, -0.74, 0.74]]

% Singular values: 5, 4, 2
U*diag([5, 4, 2])*V'
      [[2.972, 0.028, 0.796, 2.204], [0.896, 3.104, 2.528, 1.472], [-2.12, 2.12, -1.16, 1.16]]

% Singular values: 5, 4, 3
U*diag([5, 4, 3])*V'
      [[3.036, -0.036, 0.348, 2.652], [0.848, 3.152, 2.864, 1.136], [-2.06, 2.06, -1.58, 1.58]]