U =
      [[0.6, 0.8], [0.8, -0.6]]

V =
      [[0.28, 0.96], [0.96, -0.28]]

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

% Singular values: 1, 0
U*diag([1, 0])*V'
      [[0.168, 0.576], [0.224, 0.768]]

% Singular values: 2, 0
U*diag([2, 0])*V'
      [[0.336, 1.152], [0.448, 1.536]]

% Singular values: 2, 1
U*diag([2, 1])*V'
      [[1.104, 0.928], [-0.128, 1.704]]

% Singular values: 3, 0
U*diag([3, 0])*V'
      [[0.504, 1.728], [0.672, 2.304]]

% Singular values: 3, 1
U*diag([3, 1])*V'
      [[1.272, 1.504], [0.096, 2.472]]

% Singular values: 3, 2
U*diag([3, 2])*V'
      [[2.04, 1.28], [-0.48, 2.64]]

% Singular values: 4, 0
U*diag([4, 0])*V'
      [[0.672, 2.304], [0.896, 3.072]]

% Singular values: 4, 1
U*diag([4, 1])*V'
      [[1.44, 2.08], [0.32, 3.24]]

% Singular values: 4, 2
U*diag([4, 2])*V'
      [[2.208, 1.856], [-0.256, 3.408]]

% Singular values: 4, 3
U*diag([4, 3])*V'
      [[2.976, 1.632], [-0.832, 3.576]]

% Singular values: 5, 0
U*diag([5, 0])*V'
      [[0.84, 2.88], [1.12, 3.84]]

% Singular values: 5, 1
U*diag([5, 1])*V'
      [[1.608, 2.656], [0.544, 4.008]]

% Singular values: 5, 2
U*diag([5, 2])*V'
      [[2.376, 2.432], [-0.032, 4.176]]

% Singular values: 5, 3
U*diag([5, 3])*V'
      [[3.144, 2.208], [-0.608, 4.344]]

% Singular values: 5, 4
U*diag([5, 4])*V'
      [[3.912, 1.984], [-1.184, 4.512]]