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      1 Matrix4f A = MatrixXf::Random(4,4);
      2 cout << "Here is a random 4x4 matrix:" << endl << A << endl;
      3 HessenbergDecomposition<MatrixXf> hessOfA(A);
      4 MatrixXf H = hessOfA.matrixH();
      5 cout << "The Hessenberg matrix H is:" << endl << H << endl;
      6 MatrixXf Q = hessOfA.matrixQ();
      7 cout << "The orthogonal matrix Q is:" << endl << Q << endl;
      8 cout << "Q H Q^T is:" << endl << Q * H * Q.transpose() << endl;
      9