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      1 MatrixXf A(MatrixXf::Random(5,3)), thinQ(MatrixXf::Identity(5,3)), Q;
      2 A.setRandom();
      3 HouseholderQR<MatrixXf> qr(A);
      4 Q = qr.householderQ();
      5 thinQ = qr.householderQ() * thinQ;
      6 std::cout << "The complete unitary matrix Q is:\n" << Q << "\n\n";
      7 std::cout << "The thin matrix Q is:\n" << thinQ << "\n\n";
      8