U =
      [[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]]

V =
      [[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]]

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

% Singular values: 3, 2, 1, 0
U*diag([3, 2, 1, 0])*V'
      [[0.48, -0.36, 0.22, 0.46], [-0.42, 0.66, 0.08, -0.04], [0.86, 0.98, 2.04, 0.72], [-0.44, 1.12, 0.06, 2.22]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.49, -0.31, 0.27, 0.53], [-0.41, 0.71, 0.13, 0.03], [0.93, 1.33, 2.39, 1.21], [-0.37, 1.47, 0.41, 2.71]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[0.54, -0.32, 0.34, 0.48], [-0.46, 0.72, 0.06, 0.08], [1.28, 1.26, 2.88, 0.86], [-0.72, 1.54, -0.08, 3.06]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[0.89, -0.81, 0.27, 0.83], [-0.81, 1.21, 0.13, -0.27], [1.23, 1.33, 2.89, 0.81], [-0.67, 1.47, -0.09, 3.11]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.38, -0.46, -0.08, 0.76], [-0.32, 1.56, -0.22, -0.34], [1.16, 1.28, 2.94, 0.82], [-0.74, 1.42, -0.04, 3.12]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[0.5, -0.26, 0.32, 0.6], [-0.4, 0.76, 0.18, 0.1], [1., 1.68, 2.74, 1.7], [-0.3, 1.82, 0.76, 3.2]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[0.55, -0.27, 0.39, 0.55], [-0.45, 0.77, 0.11, 0.15], [1.35, 1.61, 3.23, 1.35], [-0.65, 1.89, 0.27, 3.55]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[0.9, -0.76, 0.32, 0.9], [-0.8, 1.26, 0.18, -0.2], [1.3, 1.68, 3.24, 1.3], [-0.6, 1.82, 0.26, 3.6]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.39, -0.41, -0.03, 0.83], [-0.31, 1.61, -0.17, -0.27], [1.23, 1.63, 3.29, 1.31], [-0.67, 1.77, 0.31, 3.61]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[0.6, -0.28, 0.46, 0.5], [-0.5, 0.78, 0.04, 0.2], [1.7, 1.54, 3.72, 1], [-1., 1.96, -0.22, 3.9]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[0.95, -0.77, 0.39, 0.85], [-0.85, 1.27, 0.11, -0.15], [1.65, 1.61, 3.73, 0.95], [-0.95, 1.89, -0.23, 3.95]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[1.44, -0.42, 0.04, 0.78], [-0.36, 1.62, -0.24, -0.22], [1.58, 1.56, 3.78, 0.96], [-1.02, 1.84, -0.18, 3.96]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[1.3, -1.26, 0.32, 1.2], [-1.2, 1.76, 0.18, -0.5], [1.6, 1.68, 3.74, 0.9], [-0.9, 1.82, -0.24, 4]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[1.79, -0.91, -0.03, 1.13], [-0.71, 2.11, -0.17, -0.57], [1.53, 1.63, 3.79, 0.91], [-0.97, 1.77, -0.19, 4.01]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.28, -0.56, -0.38, 1.06], [-0.22, 2.46, -0.52, -0.64], [1.46, 1.58, 3.84, 0.92], [-1.04, 1.72, -0.14, 4.02]]