U =
      [[0.5, 0.5, 0.5, 0.5], [0.5, -0.5, -0.5, 0.5], [0.5, 0.5, -0.5, -0.5], [0.5, -0.5, 0.5, -0.5]]

V =
      [[0.2, 0.4, 0.4, 0.8], [0.4, -0.2, -0.8, 0.4], [0.4, 0.8, -0.2, -0.4], [0.8, -0.4, 0.4, -0.2]]

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

% Singular values: 3, 2, 1, 0
U*diag([3, 2, 1, 0])*V'
      [[0.9, 0., 1.3, 1], [-0.3, 1.2, -0.1, 1.4], [0.5, 0.8, 1.5, 0.6], [0.1, 0.4, -0.3, 1.8]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[1., 0.2, 1.5, 1.4], [-0.2, 1.4, 0.1, 1.8], [0.6, 1., 1.7, 1], [0.2, 0.6, -0.1, 2.2]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[1.2, 0.1, 1.9, 1.2], [-0.4, 1.5, -0.3, 2], [0.8, 0.9, 2.1, 0.8], [-0., 0.7, -0.5, 2.4]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[1.4, -0.3, 1.8, 1.4], [-0.6, 1.9, -0.2, 1.8], [0.6, 1.3, 2.2, 0.6], [0.2, 0.3, -0.6, 2.6]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.8, -0.1, 1.6, 1.3], [-0.2, 2.1, -0.4, 1.7], [0.2, 1.1, 2.4, 0.7], [-0.2, 0.1, -0.4, 2.7]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[1.1, 0.4, 1.7, 1.8], [-0.1, 1.6, 0.3, 2.2], [0.7, 1.2, 1.9, 1.4], [0.3, 0.8, 0.1, 2.6]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[1.3, 0.3, 2.1, 1.6], [-0.3, 1.7, -0.1, 2.4], [0.9, 1.1, 2.3, 1.2], [0.1, 0.9, -0.3, 2.8]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[1.5, -0.1, 2., 1.8], [-0.5, 2.1, -0., 2.2], [0.7, 1.5, 2.4, 1], [0.3, 0.5, -0.4, 3]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.9, 0.1, 1.8, 1.7], [-0.1, 2.3, -0.2, 2.1], [0.3, 1.3, 2.6, 1.1], [-0.1, 0.3, -0.2, 3.1]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[1.5, 0.2, 2.5, 1.4], [-0.5, 1.8, -0.5, 2.6], [1.1, 1., 2.7, 1], [-0.1, 1., -0.7, 3]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[1.7, -0.2, 2.4, 1.6], [-0.7, 2.2, -0.4, 2.4], [0.9, 1.4, 2.8, 0.8], [0.1, 0.6, -0.8, 3.2]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[2.1, -0., 2.2, 1.5], [-0.3, 2.4, -0.6, 2.3], [0.5, 1.2, 3., 0.9], [-0.3, 0.4, -0.6, 3.3]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[1.9, -0.6, 2.3, 1.8], [-0.9, 2.6, -0.3, 2.2], [0.7, 1.8, 2.9, 0.6], [0.3, 0.2, -0.9, 3.4]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[2.3, -0.4, 2.1, 1.7], [-0.5, 2.8, -0.5, 2.1], [0.3, 1.6, 3.1, 0.7], [-0.1, -0., -0.7, 3.5]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.7, -0.2, 1.9, 1.6], [-0.1, 3., -0.7, 2], [-0.1, 1.4, 3.3, 0.8], [-0.5, -0.2, -0.5, 3.6]]