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 =
      [[0.1, 0.1, 0.7, 0.7], [0.1, -0.1, -0.7, 0.7], [0.7, 0.7, -0.1, -0.1], [0.7, -0.7, 0.1, -0.1]]

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

% Singular values: 3, 2, 1, 0
U*diag([3, 2, 1, 0])*V'
      [[0.6, -0.3, 1.7, 0.4], [-0.3, 0.6, 0.4, 1.7], [-0.1, 0.4, 1.8, 0.3], [0.4, -0.1, 0.3, 1.8]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.65, -0.25, 2.05, 0.75], [-0.25, 0.65, 0.75, 2.05], [-0.05, 0.45, 2.15, 0.65], [0.45, -0.05, 0.65, 2.15]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[0.7, -0.3, 2.4, 0.4], [-0.3, 0.7, 0.4, 2.4], [0., 0.4, 2.5, 0.3], [0.4, 0., 0.3, 2.5]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[1.05, -0.65, 2.35, 0.45], [-0.65, 1.05, 0.45, 2.35], [-0.35, 0.75, 2.55, 0.25], [0.75, -0.35, 0.25, 2.55]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.4, -0.3, 2.3, 0.4], [-0.3, 1.4, 0.4, 2.3], [-0.7, 0.4, 2.6, 0.3], [0.4, -0.7, 0.3, 2.6]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[0.7, -0.2, 2.4, 1.1], [-0.2, 0.7, 1.1, 2.4], [0., 0.5, 2.5, 1], [0.5, 0., 1., 2.5]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[0.75, -0.25, 2.75, 0.75], [-0.25, 0.75, 0.75, 2.75], [0.05, 0.45, 2.85, 0.65], [0.45, 0.05, 0.65, 2.85]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[1.1, -0.6, 2.7, 0.8], [-0.6, 1.1, 0.8, 2.7], [-0.3, 0.8, 2.9, 0.6], [0.8, -0.3, 0.6, 2.9]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.45, -0.25, 2.65, 0.75], [-0.25, 1.45, 0.75, 2.65], [-0.65, 0.45, 2.95, 0.65], [0.45, -0.65, 0.65, 2.95]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[0.8, -0.3, 3.1, 0.4], [-0.3, 0.8, 0.4, 3.1], [0.1, 0.4, 3.2, 0.3], [0.4, 0.1, 0.3, 3.2]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[1.15, -0.65, 3.05, 0.45], [-0.65, 1.15, 0.45, 3.05], [-0.25, 0.75, 3.25, 0.25], [0.75, -0.25, 0.25, 3.25]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[1.5, -0.3, 3., 0.4], [-0.3, 1.5, 0.4, 3], [-0.6, 0.4, 3.3, 0.3], [0.4, -0.6, 0.3, 3.3]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[1.5, -1., 3., 0.5], [-1., 1.5, 0.5, 3], [-0.6, 1.1, 3.3, 0.2], [1.1, -0.6, 0.2, 3.3]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[1.85, -0.65, 2.95, 0.45], [-0.65, 1.85, 0.45, 2.95], [-0.95, 0.75, 3.35, 0.25], [0.75, -0.95, 0.25, 3.35]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.2, -0.3, 2.9, 0.4], [-0.3, 2.2, 0.4, 2.9], [-1.3, 0.4, 3.4, 0.3], [0.4, -1.3, 0.3, 3.4]]