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

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, 0
U*diag([3, 2, 1, 0])*V'
      [[0.9, -0.6, -0.1, 0.4], [0.54, 0.96, 1.22, 0.28], [1.72, -0.22, 0.96, 0.54], [0.4, 1.7, 0.6, 1.5]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.95, -0.55, -0.05, 0.45], [0.79, 1.21, 1.47, 0.53], [1.97, 0.03, 1.21, 0.79], [0.75, 2.05, 0.95, 1.85]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[1.3, -0.9, 0., 0.4], [0.72, 1.28, 1.46, 0.54], [2.46, -0.46, 1.28, 0.72], [0.4, 2.4, 0.9, 1.9]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[1.35, -0.95, -0.35, 0.75], [0.65, 1.35, 1.95, 0.05], [2.45, -0.45, 1.35, 0.65], [0.45, 2.35, 0.55, 2.25]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.7, -0.6, -0.7, 0.4], [0.9, 1.6, 1.7, -0.2], [2.2, -0.7, 1.6, 0.9], [0.4, 2.3, 0.6, 2.3]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[1., -0.5, 0., 0.5], [1.04, 1.46, 1.72, 0.78], [2.22, 0.28, 1.46, 1.04], [1.1, 2.4, 1.3, 2.2]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[1.35, -0.85, 0.05, 0.45], [0.97, 1.53, 1.71, 0.79], [2.71, -0.21, 1.53, 0.97], [0.75, 2.75, 1.25, 2.25]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[1.4, -0.9, -0.3, 0.8], [0.9, 1.6, 2.2, 0.3], [2.7, -0.2, 1.6, 0.9], [0.8, 2.7, 0.9, 2.6]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.75, -0.55, -0.65, 0.45], [1.15, 1.85, 1.95, 0.05], [2.45, -0.45, 1.85, 1.15], [0.75, 2.65, 0.95, 2.65]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[1.7, -1.2, 0.1, 0.4], [0.9, 1.6, 1.7, 0.8], [3.2, -0.7, 1.6, 0.9], [0.4, 3.1, 1.2, 2.3]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[1.75, -1.25, -0.25, 0.75], [0.83, 1.67, 2.19, 0.31], [3.19, -0.69, 1.67, 0.83], [0.45, 3.05, 0.85, 2.65]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[2.1, -0.9, -0.6, 0.4], [1.08, 1.92, 1.94, 0.06], [2.94, -0.94, 1.92, 1.08], [0.4, 3., 0.9, 2.7]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[1.8, -1.3, -0.6, 1.1], [0.76, 1.74, 2.68, -0.18], [3.18, -0.68, 1.74, 0.76], [0.5, 3., 0.5, 3]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[2.15, -0.95, -0.95, 0.75], [1.01, 1.99, 2.43, -0.43], [2.93, -0.93, 1.99, 1.01], [0.45, 2.95, 0.55, 3.05]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.5, -0.6, -1.3, 0.4], [1.26, 2.24, 2.18, -0.68], [2.68, -1.18, 2.24, 1.26], [0.4, 2.9, 0.6, 3.1]]